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The Islamic University of Gaza
Engineering Faculty
Civil Engineering Department
Hydraulics Lab ECIV 3122 This course involves conducting a number of lab experiments to support and verify the principles taught in fluid mechanics and hydraulics courses.
2012-2013
Hydraulics Lab - ECIV 3122 Table of contents
I
Contents
Experiment (1): Hydrostatic Force on a Plane Surface 1
Experiment (2): Buoyancy & Flotation – Metacentric Height 8
Experiment (3): Impact Jets 24
Experiment (4): Flow Measurement 32
Experiment (5): Flow through orifice 43
Experiment (6): Flow Over Weirs 48
Experiment (7): Investigation of Bernoulli Theorem 56
Experiment (8): Minor Losses 61
Experiment (10): Centrifugal Pump 73
Exercise B 74
Exercise C 79
Exercise D 85
Exercise E 86
Experiment (11): Series and Parallel Pumps 88
Exercise F 90
Exercise G 93
Experiment (12): Open Channel Flow 95
REFERENCES 96
APPENDIX A: Report Cover Page 97
APPANDIX B: FINAL EXAM 2nd Semester 2010-2011 98
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
1
Exp. (1): Hydrostatic Force on a Plane Surface
Purpose: To verify the theoretical prediction of the resultant hydrostatic force and its
point of action on both (a) partially submerged and (b) fully submerged plane surface
in a liquid.
Apparatus: Armfield Hydrostatic Force Demonstration Unit (Fig1).
Theory:
Review the derivation of the resultant magnitude and point of action of hydrostatic
force on a submerged plane surface. List these expressions for a vertical surface that
is (a) partially submerged, and (b) fully submerged.
(a) When the surface is fully submerged (Fig2):
) 2
d -(y d b g F (Theoretical)
H 12
d
2
d a
L g M F
2 (Practical)
)2
d -(y
H 12
d H
2
P (Centre of pressure)
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
2
Figure 2 - Surface is fully submerged
(b) When the surface is partially submerged (Fig3):
y b g 0.5 F 2 (Theoretical)
3
y d a
L g M F (Practical)
y 3
2 H P (Centre of pressure)
Figure 3 - surface is partially submerged
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
3
Procedure:
1. Measure the dimensions a, b and d of the quadrant, and the distance between the
pivot and the weight hanger L.
2. Insert the quadrant into the tank locating the balance arm on the knife edges.
Adjust the counter-balance weight until the balance arm is horizontal, as indicated
on the datum level indicator.
3. Add all the weights supplied to the weight. Fill the tank with water until the
balance beam tips lifting the weights then drain out a small quantity of water to
bring the balance arm horizontal, don't level the balance arm by adjustment of the
counter balance weight or the datum setting of the balance arm will be lost.
Record the water level shown on the scale. Fine adjustment of the water level may
be achieved by over-filling and slowly draining, using the drain cock.
4. Remove one or more weights from the weight carrier and level the balance arm by
draining out more of the water. When the arm is level record the depth of
immersion shown on the scale on the quadrant.
5. Repeat reading for reducing masses on the weight carrier.
Data & Results:
L= ……… mm , a=……… mm , d= ……… mm , b= ……… mm
1) Complete Immersion
Trials 1 2 3
Total weight on arm (M grams)
Depth of Water (y mm)
F=
H12
2d( 2)d(aMgL (N)
Force on End Surface
(Theoretical) F = ρgbd(y - 2d ) (N)
Depth of Centre of Pressure Hp
(mm)
2) Partial Immersion
Trials 1 2 3
Total weight on arm (M grams)
Depth of Water (y mm)
F= 3ydaMgL (N)
Force on End Surface
(Theoretical) F = 0.5ρgby2 (N)
Depth of Centre of Pressure Hp
(mm)
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
4
Exp 1: Hydrostatic Force
SI US
mass kg Slug
Force N (kg.m/s2) lb (Slug.ft/s2)
1 lb = 4.4482 N
1 slug = 14.5938 kg
1 ft = 0.3048 m
g = 9.81 m/s2 = 32.2 ft/s2
( Times New Roman 21الخط )التقرير باللغة اإلنجليزية باستخدام الكمبيوتر
مع وضع عناوين للجداول و التقارير. وضع صور للتجربة في التقرير
.التعليق على النتائج و سبب الخطأ باالضافة الى مقارنات
الهدف من التجربة:
Center of pressureعمليا و مقارنتها مع القيمة النظرية + حساب بعد Fحساب قيمة
(.pivot)ربع الدائرة( ال تحدث عزم حول نقطة الدوران ) quadrantمالحظة: قوة دفع الماء على
θ
H Hp
Pivot CounterWeight
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
5
مع العمقالضغط يزداد
ف : تحديد القوة المؤثرة من المائع على السطحلهدا
المائع الساكن القوة عموديةفي
( القوة نفس االتجاه الجمع صحيحPlaneإذا كان السطح مستوي )
القوة نفس االتجاه لكن القيم مختلفة
δ
إلى سطح المائع centroid المسافة الرأسية من
مكونات الجهاز:
Quadrant ربع دائرة لهplane surface.
Scale لقياس قيمةy من أسفلquadrant .إلى مكان وصول الماء
( عمودpole( عليه نقطة )pivot عندها ).نجعل العزم متساوي
Counterweight على الpole يعادل وزن الquadrant.
جرام. 05حامل أوزان وزنه
أرجل و عدسة لضبط أفقية الجهاز. 3اإلناء شفاف له
θ D
0
R
P C
G
S A
A
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
6
Complete Immersion:
Area, A = bd
,
( ) (
)
(
)
(
)
(Theoritical)
( )
(Practical)
Partial Immersion:
Area, A = by
,
( )
(
)
(
)
(Theoritical)
( )
(Practical)
خطوات التجربة:
a, b, d and Lنقيس األبعاد (2
(a=10 cm, b=7.5 cm, d=10 cm, L=27.5 cm)
نضبط أفقية الجهاز (1
.counterweightنتأكد من أن وزن الجهاز ملغي باستخدام (3
(counterweightمالحظة: بعد معادلة وزن الجهاز ال نغير موضع (
.quadrant)جم )يمكن وضعه بالبداية وإلغاء وزنه مع وزن ال 05نضع األوزان: وزن الحامل (4
+ أوزان إضافية
.Complete Immersionنمأل الجهاز بالماء (0
.y>100mmبحيث تكون أفقي poleنبدأ بتصريف المياه حتى يصبح ال نضيف كتلة مناسبة و (6
بمحاذاة الخط األوسط( pole)السطح السفلي لل
m(kg)، و الكتلة y(mm)نقرأ التدريج (7
. Fالماء دفع نعوض في القوانين لحساب قوة (8
.complete Immersionمرتين أخريين حالة 8و 7و 6الخطوات نكرر (9
.Partial Immersion (0<y<100mm) نبدأ بتصريف المياه حتى تصبح (25
أفقي. poleنضع كتلة مناسبة ونبدأ بتصريف المياه حتى يصبح ال (22
m(kg)، و الكتلة y(mm)نقرأ التدريج (21
. Fنعوض في القوانين لحساب قوة دفع الماء (23
.Partial Immersionمرتين أخريين حالة 23و 21و 22نكرر الخطوات (24
Pole
Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force
7
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
8
Exp. (2): BUOYANCY & FLOTATION – METACENTRIC HEIGHT
Purpose: To determine the metacentric height of a flat bottomed vessel.
Introduction:
A floating body is stable if it tends to return to its original equilibrium position
after it had been tilted through a small angle.
For a floating body to be stable it is essential that the metacenter (M) is above the
center of gravity; metacentric height (MG) should be positive.
Fig. (1) Stable & unstable equilibrium
The greater the metacentric height, the greater is the stability, however, very large
metacentric heights causes undesirable oscillations in the ships and are avoided.
Theory:
If a body is tilted through an angle θ, B1 will be the position of the center of buoyancy
after tilting. A vertical line through B1 will intersect the center line of the body at (M)
(Metacenter of the body), MG is the metacentric height. The force due to buoyancy
acts vertically up through B1 and is equal to W, the weight of the body acts
downwards through G. The resulting couple is of magnitude Px
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
9
Px = W. GG1
= W. GM. sinθ
→W
PxGM …………(1)
θ in radian
Fig.(2) Metacentric height
* The metacentric height can be calculated as followed:
MG = BM + OB – OG………………..........(2)
Where:
- V
IBM - BM is the metacentric radius ,
- 3
12
1LDI - I : Moment of inertia of pontoon
- V: Total volume of displaced liquid.
- OB = 0.5 ( LxD
V )
Experimental Set-up:
The set up consists of a small water tank having transparent side walls in which a
small ship model is floated, the weight of the model can be changed by adding or
removing weights. Adjustable mass is used for tilting the ship, plump line is attached
to the mast to measure the tilting angle.
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
10
Fig.(3) Experimental set-up Fig.(4) Cross section
Pontoon measurement:
- Pontoon dimension : Depth (H) = 170 mm
Length (L) = 380 mm, Width (D) = 250 mm.
- The height of the center of gravity of the pontoon is OGvm = 125 mm from outer
surface of vessel base.
- The balance weight is placed at x = 123 mm from pontoon center line.
- The weight of the pontoon and the mast Wvm = 3000 gm.
PART (1) : Determination of floatation characteristic for unloaded and for
loaded pontoon
Procedure:
1. Assemble the pontoon by positioning the bridge piece and mast.
2. Weigh the pontoon and determine the height of its center of gravity up the line of
the mast.
3. Fill the hydraulic bench measuring tank with water and float the pontoon in it, then
ensure that the plumb line on the zero mark.
4. Apply a weight of 50 g on the bridge piece loading pin then measure and record
the angle of tilting and the value of applied weight.
5. Repeat step 4 for different weights; 100, 150, & 200 g, and take the corresponding
angle of tilting.
6. Repeat the above procedure with increasing the bottom loading by 2000 gm and
4000 gm.
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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7. Record the results in the table ( Table " 1" ),
8. Calculate GM practically where sin
)123(
W
PGM , W has three cases.
9. Draw a relationship between θ (x-axis) and GM (y-axis), then obtain GM when θ
equals zero.
10. Calculate GM theoretically according to equation (2),
where WbWvm
xWbOGWvm
WbWvm
OGWbOGWvmOG vmbvm
)1()()()(
OGvm = 125 mm, OGb= x1: from table "1".
PART (2) : Determination of floatation characteristic when changing the center
of gravity of the pontoon.
1.Replace the bilge weights by 4x 50 gm weights.
2. Apply a weight of 300gm on a height of 190 mm from the pontoon surface.
3. Apply weights of 40, 80 &120 gms on the bridge piece loading pin, then record the
corresponding tilting angle.
4. Move 50 gm bilge weight to the mast ahead, then repeat step 3.
5. Repeat step 3 moving 100, 150 & 200 gm bilge weight to the mast.
6. Calculate GM practically where sin3500
)123(PGM .
7. Determine the height of the center of gravity for each loading condition.
8. Calculate GM theoretically according to equation (2),
where W
LWmWbWbWvm
OG
)2
790()190(1)35()125(
Where : In case of 50 gm, L = 10 mm.
In case of 100 gm, L = 20 mm.
In case of 150 gm, L = 30 mm.
In case of 200 gm, L = 40 mm.
Fig.(5) Weights & Dimensions
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
12
Tables of results:
Table "1": Part(1)
Bilge Weight Off balance wt. Mean
Def.
Exp.
GM
GM at
θ =0 BM OB
Theo.
GM
Wb (gm) P (gm) θ
(degree) (mm)
from
graph (mm) (mm) (mm)
0.00 50 2.13
100 4.45
150 6.90
200 9.23
2000.00 50 1.95
x1 = 30 100 3.98
150 6.10
200 8.25
4000.00 100 3.35
x1 = 37.5 150 5.10
200 6.90
250 8.75
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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Table "2": Part(2)
Off balance wt.
Mean
Def. Exp. GM BM OG
Theo.
GM M above
P (gm)
θ
(degree) (mm) (mm) (mm) (mm)
water
level
Mast Weight = 0.0
40 2.40
80 4.88
120 7.50
Mast Weight = 50.0
40 3.45
80 7.23
120 10.50
Mast weight = 100.0
20 3.28
40 6.35
80 12.00
Mast Weight = 150.0
10 3.70
20 10.23
40 14.78
Mast weight = 200.0
Unstable
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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Experiment 2: Buoyancy
When a body is submerged or floating in a static fluid, the resultant force exerted on it
.Buoyancy Forceby the fluid is called the
كثافة السائل *عجلة الجاذبية األرضية قوة الدفع إلى أعلى = وزن السائل المزاح = حجم الجسم المغمور *
Upthrust force on the body = weight of the fluid displaced by the body
.vertically upward للشكل، و اتجاهها center of volume مكان تأثير هذه القوة في
Center of Buoyancy: centroid of the volume of fluid displaced.
Archimedes Principle:
نتعامل مع الجزئية المغمورة فقط، ألن كثافة الهواء صغيرة. مالحظة: عندما يكون الجسم طاف
The equilibrium of a body may be:
Stable: if when displaced returns to equilibrium position.
عندما نطبق إزاحة صغيرة يرجع إلى وضعه األصلي
Unstable: إذا أخذ وضع اتزان جديد
Neutral: إذا بقي كما هو
Stability of submerged Bodies: ( األجسام المغمورة)
Center of gravity ال يتغير, Center of Buoyancy يتغيرال .
.Center of Buoyancy(B)، و Center of gravity (G)يتم التحديد باالعتماد على
I) Stable:
Center of gravity below Center of Buoyancy (B( أسفل )Gعندما يكون )
restoring moment ينشأ عزم إرجاع
II) Unstable:
G is above , B is below
III) Neutral: على بعض B,G إذا انطبق
B G
B
G
R
W W
R
B G G
R
W
R
W
B
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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Stability of Floating Bodies: ( لطافيةاألجسام ا)
Center of gravity ال يتغير, Center of Buoyancy يتغير.
. Metacenter (M)، و Center of gravity (G)يتم التحديد باالعتماد على
I) Stable:
Center of gravity below Metacenter
Mأسفل G عندما تكون
:Mالجديد مع الخط الرأسي Bنقطة تقاطع الخط الرأسي القديم من
Metacentric Height ( ): M الى G المسافة من
II) Unstable:
G is above , M is below
III) Neutral: M على G إذا انطبق
If M coincides with G, the body is in neutral equiblrium
أي انطباق neutralتعني just stableمالحظة:
Floating Bodies Submerged Bodies
Gو Bالمقارنة بين Gو Mالمقارنة بين
Center of gravity (G):
يبقى مكانه، ألن توزيع األوزان ال تتغير
Center of Buoyancy (B):
يتغير مكانه، ألن
The shape of submerged part is
altered when the body is tilted
Center of gravity (G):
يبقى مكانه، ألن األوزان ال تتغير
Center of Buoyancy (B):
يبقى مكانه، ألن
The shape of displaced fluid is not
altered when the body is tilted
B G
B G
M
G W=mg
W=mg R=W R=W
θ
G
x
G
B
G
B G
W=mg
W=mg R=W
R=W x
G
M
G
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
16
If M lies above G arighting moment is produced, equilibrium is stable and GM is
regarded as +ve.
( is small)
( )
Determination of the Metacentric Height ( ):
,
القوة الخارجية المسببة للدوران
P ذراع القوة
W: weight of the vessel including P الماء المزاحوزن
[ ]
Determination of the position of the Metacenter relative to the center of Buoyancy:
BM: metacentric radius
V: حجم السائل المزاح
I: moment of inertia
معرفة المساحة و حول أي محور يلزم
ألن إمكانية االنقالب حوله أكبر longitudinalالمحور بالشكل المجاور
Water line plane حول محورaa
center of volumeتقع في Bمالحظة:
G
W=mg R=W
B1 B
O
M
Water line plane
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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(flat bottomed vesselدراسة الطفو لقارب مستوي القاع ) عنوان التجربة:
تنقسم التجربة إلى جزئين:
دراسة الطفو في حاالت تحميل مختلفة (2
Center of gravityدراسة الطفو في حالة الوزن ثابت و تغيير (1
Part 1: Determination of floatation characteristics for unloaded and for loaded
pontoon:
Wvm (i.e. vessel + mast) = 3000 gmوزن القارب مع السارية
أبعاد القارب:
Depth H = 170 mm
Length L = 380 mm
Width D = 250 mm
مرات 4حاالت و في كل حالة نقيس الزاوية part1 3في
[ Wb (i.e. bilge weight) = 0.0 ]ال نضع أوزان داخل القارب الحالة األولى:
و نقيس 200gmثم 150gmثم 100gmثم ,50gm (P)نضع القارب في الماء و نضع أوزان على الطرف
الزاوية في كل حالة تحميل.)نمأل القيم في الجدول(
OG = OGvm = 125mm
جرام في كل جهة 2555الوزن اإلضافي داخل القارب Wb (bilge) = 2000g الحالة الثانية:
جرام و نوجد الزوايا.)نمأل الجدول( 155، و 205، 255، 05باستخدام أوزان طرفية 2نكرر خطوات الحالة
OGbو OGvmتتغير لوجود OGهنا
( ) ( )
Wb = 4000)جرام في كل جهة فيصبح 2555أخر في جوف القارب جرام 1555: نضيف الحالة الثالثة
gm)
مم من المركز( 213كما بالسابق )على طرف الجسر على بعد و نضع أوزان على الطرف
جرام و نقيس الزاوية في كل مرة 105، 155، 205، 255
OG تتغير هنا أيضا
( ) ( )
نمأل القيم بالجدول و نبدأ بالحسابات
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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و (P)األوزان على الطرف بالجرام الثاني( و Wbاألوزان في جوف القارب بالجرام )األولالعمود
)الزاوية بالدرجات( يتم الحصول عليهم في المختبر.الثالث
ل center of gravity)أي بعد OGbتتغير حسب قيمة الوزن في جوف القارب و هي عبارة عن x1قيمة
bilge weight عن النقطةO )الموجودة أسفل القارب
:الرابعالعمود
x = 123 mm
P: off balance weight )من العمود الثاني(
W: W total = Wb + Wvm جم( 7555، الثالثة 0555جرام، الثانية 3555)الحالة األولى
من الجدول و لكن نحولها الى راديان :
:الخامسالعمود
Draw a relationship between θ (x-axis) & Exp. GM (y-axis)
لكل حالة. ( yعلى محور Exp GM ( و ) x على محور باستخدام برنامج اكسل نرسم عالقة بين )
الحاالت الثالثة على رسمة واحدة و لكن كل حالة لها منحنى يتكون من أربع نقاط
( لكل منحنى.y-intercept) θ=0عند Exp. GMنصل أفضل خط مستقيم يمر بالنقاط ثم نحدد قيمة
:سادسالالعمود
, L = 380 mm, D = 250 mm, V = ?
( )
OB or EB:السابعالعمود
(
الطول العرض )
(الحجم المغمور
المساحة )
OC: ارتفاع الماء
العمود الثامن:
[ ] السابع العمود السادس
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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( ) ( )
في الحالة األولى ( )
في الحالة الثانية ( ) ( )
في الحالة الثالثة ( ) ( )
النظرية مع العملية GMالهدف مقارنة
.θ=0عند تحسب GM theoretical، ألن θ=0عند GM practicalيتم حساب
Part 2: Determination of effect on floatation characteristics of altering the center of
gravity of the pontoon, with given total loading:
Gالوزن ثابت و يتغير
التجربة:خطوات
نضع القارب في الماء -2
(.bilgeجرام في جوف المركب ) 4x05نضع أوزان -1
Wb = 200 gm وOGb = 35 mm
على كل جهة على الجسر حول السارية 150gm(:300gmنضع أوزان اتزان ) -3
Wb1 = 300 gm وOGb1 = 190 mm
وزن القارب مع السارية
Wvm = 3000 gm وOGvm = 125 mm
ثابت في كل الجزء الثاني Wtotal = 3500 gmيصبح الوزن الكلي
مرات لألوزان الطرفية 3حاالت كل حالة P (off balance weight ) :4نطبق أوزان -4
Wm = 0و Wb = 200 gm :األولىالحالة
في كل مرة. θجم و نقرأ قيمة 215جم ثم 85جرام ثم P 45:نضع وزن
.Wtotو عدم إدخالها في حساب Pمالحظة: يمكن إهمال قيمة
Wm = 50 gmو Wb = 150 gm :الثانيةالحالة
( و نكرر خطوات mastجرام من قاع القارب و نضعها أعلى السارية ) 155جرام من ال 05نرفع
الحالة األولى
( )
L is given in by the following table:
Wb (
gm
)
200
Wm
(gm
)
0
L (
mm
)
-
150 50 10
100 100 20
50 150 30
0 200 40
790 mm .هي المسافة من أسفل القارب إلى مركز تثبيت الوزن على الصاري
150 gm 150 gm
35
mm
OG
m =
79
0 +
L/2
mm
Wm
Wb
OG
vm =
12
5 m
m
OG
b1
= 1
90
mm
Wb1
OG
tota
l = ?
?
Wvm
P
X = 123 mm
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
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في كل حالة center of gravityمالحظة: يلزم حساب
( ) ( ) ( ) (
)
ثابتة في كل حاالت الجزء الثاني
الثانيثابتة في كل حاالت الجزء
ثابتة في كل حاالت الجزء الثاني
Wm = 100 gmو Wb = 100 gm: الثالثةالحالة
جرام أخرى من القاع و نضعها أعلى السارية 05نرفع
. في كل مرة، و نحسب θجم و نقرأ قيمة 85جم ثم 45جرام ثم P 15:نضع وزن
Wm = 150 gmو Wb = 50 gm: الرابعةالحالة
جرام أخرى من القاع و نضعها أعلى السارية 05نرفع
. في كل مرة، و نحسب θجم و نقرأ قيمة 45جم ثم 15جرام ثم P 25:نضع وزن
Wm = 200 gmو Wb = 0 gmالحالة الخامسة:
Unstableهذه الحالة
الحسابات:
عليهم في المختبر. : يتم الحصولالثالث و الثاني و األولالعمود
:الرابعالعمود
P: من العمود الثاني,
x = 123 mm ثابت
W = 3500 gm ثابت
θ: tanθ sinθ من العمود الثالث و لكن بالراديان أو
:خامسالالعمود
.yعلى محور GMو xعلى محور θكما في الجزء األول
:سادسالالعمود
→
ثابت
ثابت ثابت ⇒
ثابتة في كل الجزء الثاني ⇒
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
21
:سابعالالعمود
(ثابتة) ⇒
:ثامنالالعمود
( )
(من العمود السادس) (من العمود السابع) (متغيرة)
( ) ( ) ( ) (
)
:تاسعالالعمود
(من عمود ) (من المعادلة السابقة)
Homework:
Write the momentum equation on a paper with explanation of the symbols.
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
22
Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy
23
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
24
Exp. (3): Impact Jets
Purpose: To investigate the reaction force produced by the impact of a jet of water
on various target vanes.
Apparatus: Impact Jet Apparatus (Fig. 1), Targets (Fig. 2).
Figure 1: Impact jet apparatus
Figure 2: Interchangeable Target Vanes
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
25
Theory:
Figure 3 : Impact of a Jet
θ - ρ Q V
R
i
cos1
A
QVn
g hVV ni 2 - 22
Where:
R : Impulse force.
iV : incident velocity.
Q : Volumetric flow rate.
nV : jet velocity.
h : height of target above nozzle.
Procedure:
1. Position the weight carrier on the weight platform and add weights until the top of
the target is clear of the stop and the weight platform is floating in mid position.
Move the pointer so that it is aligned with the weight platform.
2. Start the pump and establish the water flow by steadily opening the bench
regulating valve until it is fully open.
3. The vane will now be deflected by the impact of the jet. Place additional weights
onto the weight carrier until the weight platform is again floating in mid position.
Measure the flow rate (volume collected in certain time) and record the result on
the test sheet, together with the corresponding value of additional weight on the
tray. Observe the form of the deflected jet and note its shape.
4. Reduce the weight on the weight carrier in steps and maintain balance of the
weight platform by regulating the flow rate in about eight or ten even steps (In the
lab we made 3 steps only), each time recording the value of the flow rate and
weights on the weight carrier.
5. Close the control valve and switch off the pump. Allow the apparatus to drain.
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
26
6. Replace the 5mm nozzle with the 8mm diameter nozzle and repeat the tests.
7. Replace the normal vane with the 45 conical vane and repeat the test with both
the 5mm and 8mm nozzles.
8. Replace the 45 conical vane with the hemispherical vane and repeat the test with
both the 5mm and 8mm nozzles.
Data & Results:
1. Record the results on a copy of the result sheet provided.
2. Calculate for each result the flow rate and the nozzle exit velocity. Correct the
nozzle velocity for the height of the target above the nozzle to obtain the
impact velocity.
3. Calculate the impact momentum, and plot graphs of the impact force R against
impact momentum and determine the slope of the graphs for each target.
Compare with the theoretical values.
Target Vanes
(degrees)
Nozzle
Dia -- d --
(mm)
Additional
Weights -- m --
(gm)
Volume of water
Collected - V - (Liter)
Time to
collect -- t --
(sec)
°
5
90
θ=
Flat
8
320 20 48
250 20 58
160 20 71
°
5
45
θ=
Co
nic
al
8
110 20 48
80 20 52
60 20 82
°
5
135
θ=
Sem
i-
sph
eric
al
8
450 20 55
300 20 66
150 20 88
Comment:
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
27
Experiment 3: Impact of jet
Rate of flow
Mass rate of flow ( ) Volume rate of flow (Q)
(الحجم)
(السرعة)
Momentum Equation: m
Σفي األجسام الصلبة قانون نيوتن للحركة:
في الموائع:
⇒
⇒ ( ) [vector equation]
x-direction y-direction
resultant force acting on the fluid
نحن نريد تأثير الماء على األشياء قانون نيوتن الثالث ⇐
1- F1 = FR: by any solid body touching the control volume
2- F2 = FB: body force such as gravity
3- F3 = FP: fluid Pressure
R = - FR
FR + FP + FB = ( ) …. Vector equation
Application of the momentum equation:
Impact of a jet on a plane surface
Force due to flow round a curved vane
Force due to the flow of fluid round a pipe bend
Reaction of a jet
Pelton Wheelأحد تطبيقاته :
momentum equationيعتمد الجهاز على
( )
( )
( )
( )
(هذه القيمة نظريا معروفة) , R: Impact Force, : Incident Momentum
V1
V1 A1
V2
V2
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
28
3 Target Vanes:
Flat Conical Hemispherical
1-cos
=1 = 0.293 = 1.707
Nozzle diameter:
5 mm or 8 mm
خطوات التجربة:
(nozzle 5 mmو نركب ) ( ) Flat Vaneأوال: نركب
ال بحيث تنزل )ال يدخل في الحسابات( نضع وزن ابتدائي platform .للنصف تقريبا
( نحرك المؤشرpointerحتى يكون بمحاذاة ال )platform .
نشغل المضخة ثم نزيد الflow إلى أعلى قيمة تدريجيا. 5من
نالحظ ارتفاع الplatform نتيجةimpact of the jet.
ترجع إلى محاذاة المؤشر. نضع أوزان إضافية )تدخل في الحسابات( حتى
نقيس الvolume .المتجمع خالل فترة زمنية، و نسجل كتلة األوزان اإلضافية
نالحظ شكل الjet .و انحرافه
نقلل األوزان و نحقق االتزان للplatform عن طريق تقليل الflow .
.نحسب حجم الماء المتجمع خالل فترة زمنية، و الكتلة
تين مرة ثالثة.نكرر الخطوتين السابق
نغلق الflow و نطفئ المضخة و نبدل الnozzle (0 ( ب )و نكرر 8مم ،)الخطوات و نأخذ قراءات مم
حاالت. 3
.8mmو 5mmأخذ قراءات ل ننكرر الخطوات و ، و ب ال targetنبدل الثانيا:
.hemispherical نكرر نفس الخطوات و لكن ثالثا:
Pointer Weights
Weight Carrier
Weight Platform
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
29
الحسابات:
Volume) الرابع( و Additional Weights) الثالث( و .Nozzle Dia) الثاني( و Target) األولالعمود
Collected الخامس( و العمود (Time to collect.يتم الحصول عليهم في المختبر :)
Volumetric Flow Rate (Q): السادسالعمود
( )
t = 1 : 41.25 = 1*60+41.25لتحويل الزمن
) Nozzle Velocity:بعالساالعمود
)
( )
( ) Height above Nozzle :ثامنالالعمود
Height of the target above the nozzle (h) 2 mm
) Impact Velocity:تاسعالالعمود )
,
( )
( ) Impact Force:عاشرالالعمود
( ) (من العمود الثالث) ( )
):حادي عشرالالعمود ) Incident Momentum
(
(تحويل الوحدات إلى
( ),
( )
:ثاني عشرالالعمود
:عشر لثثاالالعمود
، و yعلى محور R(N)نرسم عالقة بين xعلى محور ( )
(5،5من خيارات خط االتجاه نختار أفضل خط مستقيم يمر بنقطة األصل )
.aفيكون الميل = y=axنظهر المعادلة
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
30
Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet
31
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
32
Exp. (4) : FLOW MEASUREMENT
Purpose: To study some of the famous instruments used in flow measurements.
Theory:
There are many instruments used in flow measurements such as Venturi meter, orifice
plate and the Rotameter.
Fig.(1) Flow measurement instruments
Fig.(2) Flow measurement instruments
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
33
1. Sudden Enlargement
The head loss through the sudden enlargement he
g
Vkehe
2
2
1 ……………………. (1)
Where 22
2
2
1 11
A
Ake
2
1
D
D ,
2
12
A
A →
Fig.(3) Sudden enlargement
2. Venturi Meter
The flow through venturi meter can calculated from the following equation
42
1
2
gHACQ dact …………… (2)
Where Cd is the coefficient of discharge.
Fig.(4) Venturi Meter
3. Orifices plate
The flow through venturi meter can calculated from the following equation
42
1
2
gHACQ dact ………………. (3)
Where Cd is the coefficient of discharge.
Fig.(5) Orifices plate
4. Elbows
The head loss through the elbow hb
g
Vkh bb
2
2
1 ………………………… (4)
Where kb is the coefficient of the elbow
5. Rotameter
The Rotameter reads the flow directly.
21
2
12
2
1
)12(2
A
A
A
A
hhgV
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
34
Procedure:
1. Prepare the instruments such that the water passes Sudden Enlargement, then
Venturi meter, Orifice plate , Elbow , and finally Rotameter .
2. Switch the pump on , allow the water to enter the flow measurement instruments ,
which are connected to Manometers tubes.
3. Control the flow valve to obtain different readings of the heads in manometers and
the corresponding flow from the volume tank .
4. Record the results.
5. Calculate the head losses from the manometer readings and the flow and Cd
for Venturi and orifice plate .
Data & Results
Volume flow (Liters)
Time (min)
Head at tapping 1 (cm)
Head at tapping 2 (cm)
Head at tapping 3 (cm)
Head at tapping 4(cm)
Head at tapping 5 (cm)
Head at tapping 6 (cm)
Head at tapping 7 (cm)
Head at tapping 8 (cm)
Rotameter flow rate
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
35
Experiment 4: Flow Measurement
From Bernoulli:
⇒
(
) … (1)
from Continuity equation * في األنابيب الساكنة *
⇒
⇒ … (2)
From (1) and (2) we get
(
)
From Mechanics of fluids by B.S. Massey, Sixth Edition
The net force acting towards right
( )
the mean pressure of eddying fluid over the annular face GD
Assume
Net force:
⇒( )
From steady-flow momentum equation this force equals the rate of increase of
momentum in the same direction:
( ) ( )
( ) ( )
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
36
From energy equation for a constant :-
represents the loss of total head between 1 & 2
( )
( )
(
)
( )
From J.C. Borda and L.M. M Carnot
H.G.L is below E.G.L by
Step up occur in pressure
line at Enlargement.
{
( )
} ( )
Since negative, exceeds
Exit Loss
(E.G.L)
Pressure Line
(H.G.L)
( )
( )
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
37
For sudden enlargement ( اشتقاق المعادلة توضيح ) :
Continuity equation:
⇒
⇒
2أعلى من ارتفاعه في 1نالحظ أن ارتفاع الماء في البيزوميتر
Using Bernoulli equation - Head Loss equations:
( )
, or
(
) (
)
( )
(
)
Substitute continuity equation, we get:
( )
(
)
(
)
(
)
[ (
)
(
)
]
[ (
)
(
(
)
)]
[ (
)
(
)
]
[
(
)
]
√
( )
(
)
1 2
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
38
Purpose: To study some of the famous instruments used in flow measurement.
باستخدام أجهزة مختلفة Qقياس
There are many instruments used in flow measurements such as Venturimeter,
orifice plate and rotameter (Variable area meter).
Description of apparatus:
Water Flow Measuring Apparatus is designed as a free-standing apparatus for
use on the Hydraulics Bench, although it could be used in conjunction with a low
pressure water supply controlled by a valve and a discharge to drain. Water enters the
apparatus through the lower left-hand end and flows horizontally through a sudden
enlargement into a transparent venturi meter, and into an orifice plate, a 90º elbow
changes the flow direction to vertical and connects to a variable area flow meter, a
second bend passes the flow into a discharge pipe which incorporates an atmospheric
break.
The static head at various points in the flow path may be measured on a
manometer panel. The water flow through the apparatus is controlled by the delivery
valve of the Hydraulics Bench and the flow rate may be confirmed by using the
volumetric measuring tank of the Hydraulics Bench.
Calculations:
I. Sudden Enlargement:
√
( )
(
)
√
( )
. yعلى محور مع xعلى محور عن طريق رسم عالقة بين Cdنحصل على
حيث يساوي الميل Cdنرسم أفضل خط مستقيم يمر بنقطة األصل فنحصل على
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
39
II. Venturi:
اشتقاق المعادلة: -
[
]
√
( )
(
) √
:الحسابات -
√
√
.yعلى محور مع xعلى محور √نرسم عالقة بين
و نوجد الميل عن طريق إظهار المعادلة (0,0)خط مستقيم يمر بنقطة األصل نرسم أفضل
(Excel)
√
…. Calculate Cd & check in the range (0.975 – 0.995)
III. Orifice:
h6, h7نستخدم h3, h4و نفس الحسابات، و لكن الفرق بدل ventureنفس اشتقاق
IV. Rotameter:
. L/minمباشرة بوحدة flowيقيس ال
K=Slope، حيث Kفنحصل على yعلى محور مع xعلى محور نرسم عالقة بين
أثناء الحسابات و الرسم. (Units)للوحداتانتبه -مالحظة مهمة:
عند أخذ قراءات المانوميتر يجب التأكد من عدم وجود أي فقاعات هواء داخل األنابيب. -
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
40
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
41
Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement
42
Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice
43
Experiment 5: Flow through orifice
Purpose:
- Studying the flow through small orifice discharging to atmosphere.
- Calculating the coefficient of discharge (Cd).
- Calculating the coefficient of velocity (Cv).
- Calculating the coefficient of contraction (Cc).
حساب زمن تفريغ خزان -
استخدام عدة أشكال و مقارنتها -
Theory:
Orifice: H قطرها صغير مقارنة مع ارتفاع عبارة عن فتحة صغيرة في خزان )في الجانب أو في األسفل(
الماء
مم. 8مم، أو 0مم، 3متوفرة مع الجهاز : أقطار 3
H is constant ⇒
⇒ √
√
√
سببين الختالف التدفق: السرعة و المساحة
Cd in the range [0.6-0.65]
√ , where is the coefficient of velocity
, where is the coefficient of contraction
√
نأخذها بعيدة شوي عشان الضغط يكون صفر
Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice
44
√
:trajectoryو الحصول على yو xيتم قياس مسافات
In x-direction:
⇒
In y-direction:
, assuing positive is downward +
(
)
√
⇒ √
√
√
√
Calculations:
o Part 1 (Cd):
Head 50cm and 25 cm
√
√
لها قيمتين. Hألن نحصل على قيمتين ل
Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice
45
yعلى محور مع xعلى محور √نرسم عالقة بين
مع إظهار المعادلة (0,0)أفضل خط مستقيم يمر بنقطة األصل نرسم
√
⇒
√ (
→ )
o Part 2 (Cv):
في حالة عدم وجود تدفق نتأكد من أفقية الجهاز عن طريق التأكد من أن ارتفاع الماء في األنابيب متساو
مم 8( dسم و قطر) 05(H) نستخدم ارتفاع ماء
√
√
√
√
√ √
⇒ √ √ √
.yعلى محور ، مع xعلى محور √نرسم عالقة بين
مع إظهار المعادلة (0,0)نرسم أفضل خط مستقيم يمر بنقطة األصل
√
باستخدام الجدول التالي: trajectoryنرسم شكل ال
x
y
y (-ve)
or
بالسالب yنرسم قيم أو يتم عكس اتجاه المحور باستخدام اكسل
Homework:
لكل من: flow in open channel (Notches and Weirs)اشتقاق قانون + معادلة
{Rectangular, Triangular (Vee) and Trapezoidal}
√
√
( )
Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice
46
مالحظات:
بالصورة التالية: كما point gaugeيمكن استخدام yلقياس المسافة -
.للوحداتأثناء الحسابات و اختيار بيانات المحاور بالرسم يجب االنتباه -
Extension Pipe للمحافظة على
head ثابت، يمكن إزالته للحصول
سم. 25سم بدل 52على ارتفاع
أنبوب للتخلص من التدفق الزائد
)أعلى من االرتفاع المطلوب(.
.السفلييصل إلى الخزان
pointحجرين لرفع ال
gauge حتى نحصل
على قراءة الصفر.
Pipe به ثقوب جانبية عديدة، حتى
يرتفع الماء بشكل منتظم.
Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice
47
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
48
Exp. (6): Flow Over Weirs
Purpose:
o To demonstrate the characteristics of flow over weirs.
o To determine the 'Coefficient of Discharge' for each type of weir.
Introduction:
In open channel hydraulics, weirs are commonly used to either regulate or to
measure the volumetric flow rate. They are of particular use in large scale situations
such as irrigation schemes, canals and rivers. For small scale applications, weirs are
often referred to as notches and invariably are sharp edged and manufactured from
thin plate material.
Apparatus:
Hydraulics Bench incorporates a weir channel. The rectangular notch weir or
(V) vee notch weir to be tested is clamped to the weir carrier in the channel by thumb
nuts.
Figure 1: Flow over Weirs - Figure 2: Flow over Weirs -
vee notch weir rectangular notch weir
Hydraulics Bench Basket of glass spheres
Weir channel Volumetric measuring tank
(V) Vee notch weir Rectangular weir
Hook & point gauge Hook Gauge and Scale
There are different shapes of weirs that can be used to measure the volumetric
flow rate. These shapes with their dimension are shown in fig 3 below.
4
3
5 8
7
1
2
5
6
7
1
3
2
6
8 4
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
49
Figure 3: Details of weirs
Theory:
Rectangular Weir:
A rectangular notch is a thin square edged weir plate installed in a weir channel as
shown in figure 4.
Figure 4: Rectangular Notch
Consider the flow in an element of height at a depth h below the surface.
Assuming that the flow is everywhere normal to the plane of the weir and that the
free surface remains horizontal up to the plane of the weir, then
velocity through element √
Theoretical discharge through element √
Integrating between h = 0 and h = H
Total theoretical discharge ∫ √
√ ∫
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
50
So,
√
In practice the flow through the notch will not be parallel and therefore will not be
normal to the plane of the weir. The free surface is not horizontal and viscosity
and surface tension will have an effect. There will be a considerable change in the
shape of the nappe as it passes through the notch with curvature of the stream
lines in both vertical and horizontal planes as indicated in Figure 5, in particular
the width of the nappe is reduced by the contractions at each end.
Figure 5: Shape of a Nappe
The discharge from a rectangular notch will be considerably less.
time
VolumeHgBCQCQ dthdact 2
3
23
2
√
In British Code:
2
3
)001.0](2716.05461.0[ HHQact Important Note: This Equation is special for Cussons Hydraulic Bench
(Rectangular Notch B = 10 cm ), For other notches (like Armfield Hydraulic
Bench) refer to original equation in British code.
Vee (Triangular) Notch:
A sharp edged triangular notch with an included angle of is shown in Figure 6
√ (
)
√ (
)
√
Figure 6: Triangular or V Notch
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
51
Operation:
1. FLOW
MEASUREMENT
The discharge from the weir may be measured using either the
Rotameter (if fitted) or by using the volumetric measuring tank
and taking the time required to collect a quantity of water. The
time to collect the water is at least 120 seconds to obtain a
sufficiently accurate result.
2. Measuring the
Weir Datum
head-gauge datum or gauge zero, which is defined as the gauge reading corresponding to the level of the weir crest (rectangular weirs) or
the level of the vertex of the notch (triangular-notch weirs) …..BS ISO
1438:2008
3. Measuring the
Head
The surface of the water as it approaches the weir will fall, this is
particularly noticeable at high rates of discharge caused by high
heads. To obtain an accurate measure of the undisturbed water
level above the crest of the weir it is necessary to place the hook
gauge at a distance at least three times the head.
Experimental Procedure:
1. Place the flow stilling basket of glass spheres into the left end of the weir channel
and attach the hose from the bench regulating valve to the inlet connection into the
stilling basket.
2. Place the specific weir plate which is to be tested first and hold it using the five
thumb nuts. Ensure that the square edge of the weir faces upstream.
3. Start the pump and slowly open the bench regulating valve until the water level
reaches the crest of the weir and measure the water level to determine the datum
level Hzero.
4. Adjust the bench regulating valve to give the first required head level of
approximately 10mm. Measure the flow rate using the volumetric tank or the
rotameter. Observe the shape of the nappe.
5. Increase the flow by opening the bench regulating valve to set up heads above the
datum level in steps of approximately 10mm until the regulating valve is fully
open. At each condition measure the flow rate and observe the shape of the nappe.
6. Close the regulating valve, stop the pump and then replace the weir with the next
weir to be tested. Repeat the test procedure.
Results and Analysis:
1. Record the results on a copy of the results sheet. Record any observations of the
shape and type of nappe paying particular attention to whether the nappe was
clinging or sprung clear, and of the end contraction and general change in shape.
2. Plot a graph of loge (Q) against loge (H) for each weir. Measure the slopes and the
intercepts.
From the intercept calculate the coefficients of discharge and from the slopes of
the graphs confirm that the index is approximately 1.5 for the rectangular weir
and 2.5 for the triangular weirs.
3. Compare the results with those predicted using the empirical formula for
rectangular weir in British Standard BS3680.
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
52
Experiment 6: Flow Over Weirs
Purpose:
To investigate the discharge-head characteristics of weirs
Determination of the coefficient of discharge for different shapes of weirs
Introduction:
In open channel weirs are used to either regulate or to measure the volumetric
flow rate.
Qو حساب flowتستخدم لتنظيم ال
.notchأكبر من weir: أن ال notchو ال weirالفرق بين ال
Vee Notchتكون أوضح في H، حيث rectangular: أدق في القياس من Veeميزة
Types:
o Rectangular:
o Triangular or Vee Notch:
Angle 60o or 90
o.
o Trapezoidal or Cippoletti:
o Linear:
Produce linear head flow characteristics
(general equation)
∫ √
√ ∫
Rectangular
√ ∫
[ √
]
√
Triangular (Vee)
b= …
√ (
)
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
53
For Rectangular Notch:
√
,
√
سم weir =25عرض cussonsخاصة بجهاز التالية معادلة ال
( ) [ ] ( )
For Vee Notch:
√ (
)
:Cdاشتقاق
(
√ (
)
)
(
√ (
))
(
√ (
))
y-axis y-intercept x-axis
(
√ (
))
√ (
)
√
( )
:الخطوات
o تركيبRectangular weir .
o تنظيم التدفق باستخدام(Basket of glass spheres) غلول(، أما جهاز(Armfield .فله قطعة أخرى
o .نمأل القناة حتى يصل الماء لحافة الحاجز
o .نقيس مستوى الصفر
o نزيد التدفق و نأخذ قراءةH .و نحسب حجم الماء المتجمع مع الزمن
o Measuring head: place the hook guage at a distance at least three times the head
o عدة مرات.نكرر الخطوة السابقة
o نرسم عالقة بينlnH على محورx ، وlnQ على محورy و نوجد التقاطع مع محور ،y و نحسب ،Cd.
√
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
54
o تركيبVee Notch.
o .نكرر الخطوات السابقة و نأخذ عدة قراءات
o نرسم عالقة بينlnH على محورx و ،lnQ على محورy و نوجد التقاطع مع محور ،y و نحسب ،Cd.
√
( )
:الحسابات
كل منيتم حساب
Qact = V/t
ln Qact
ln H
Qth
Intercept and Cd
مع ضرورة االنتباه للوحدات
:مالحظات
the shape of the Nappeمن أسباب االختالف في التدفق:
منسوب الماء ينخفض مع االقتراب من الحاجز العرض يتناقص
قبل الحاجز بمسافة Hلذلك يتم قراءة
Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs
55
Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem
56
Exp. (7): Investigation of Bernoulli Theorem
Purpose: To investigate Bernoulli Theorem Experimentally.
Apparatus: Bernoulli’s Apparatus (Fig. 1, Fig. 2)
Figure 2:
Bernoulli’s Apparatus
Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem
57
Table (1): Area of each section:
Tapping
Number 1 2 3 4 5 6 7 8 9 10 11
Flow
Area
(mm2)
102.56 90.11 77.66 65.22 52.77 40.32 52.77 65.22 77.66 90.11 102.56
Theory:
Bernoulli’s Theorem
tconszg
v
g
ptan
2
2
Where:
g
p
: pressure head
g
v
2
2
: kinetic head
z : potential head
Losses
fHzg
v
g
pz
g
v
g
p 2
2
221
2
11
22
Where:
fHHH 111
pressure Recovery
Recovery pressure = 611 hh
Loss pressure = 61 hh
61
611
hh
hhR degree of pressure recovery
Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem
58
Procedure:
1. Open the pump and let the water go through the apparatus until all the air bubbles leave.
2. Set the difference between the tanks to 10 cm by using the arm beside the shorter tank.
3. When the height of water in the piezometers not change put a white paper (
A3 ) behind the piezometers and mark on it the height of water.
4. Close the valve of the basin and begin the stop watch to calculate Q.
5. Repeat the previous steps with different differences between the two tanks (
15 then 20 cm )
6. Take the paper and connect every set of points with lines.
Data & Results:
1. Record the results on a copy of the result sheet provided. 2. Calculate the flow rate for each set of results. 3. For each set of results calculate at the cross-section adjacent to each
manometer tube, the flow velocity. 4. Plot a graph of head (H) against distance (S) and also (H+V2/2g) against
distance (S).
Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem
59
Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem
60
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
61
Experiment 8: Minor Losses
Purpose:
To determine the loss factors for flow through a range of pipe fittings
including bends, a contraction, an enlargement and a gate-valve.
Introduction:
Energy losses in pipe flows are the result of friction between the fluid and the
pipe walls and internal friction between fluid particles. Minor (secondary) head
losses occur at any location in a pipe system where streamlines are not straight, such
as at pipe junctions, bends, valves, contractions, expansions, and reservoir inlets and
outlets. In this experiment, minor head losses through a pipe section that has several
bends, transitions, and fittings will be measured.
Apparatus:
Energy Losses in Bends and Fittings Apparatus.
It consists of:
- Sudden Enlargement
- Sudden Contraction
- Long Bend
- Short Bend
- Elbow Bend
- Mitre Bend figure 1:minor losses apparatus
Figure 2: Schematic drawing of the energy-loss apparatus
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
62
Figure 3: Minor Losses Apparatus with hydraulic bench
- Flow rate through the circuit is controlled by a flow control valve.
- Pressure tappings in the circuit are connected to a twelve bank manometer, which
incorporates an air inlet/outlet valve in the top manifold. An air bleed screw
facilitates connection to a hand pump. This enables the levels in the manometer
bank to be adjusted to a convenient level to suit the system static pressure.
- A clamp which closes off the tappings to the mitre bend is introduced when
experiments on the valve fitting are required. A differential pressure gauge gives a
direct reading of losses through the gate valve.
Theory:
The energy balance between two points in a pipe can be described by the
Bernoulli equation, given by
where pi is static pressure (in Pa) at point i, g is specific weight of the fluid (in
N/m3), zi is the elevation (in meters) of point i, Vi is the fluid velocity (in m/s) at
point i, g is the gravitational constant (in m/s2), and hL is head loss (in meters).
The term pi/ is referred to as the static head; zi is the elevation head; and Vi2/2g is the
dynamic (or velocity) head. The summation of the static head and the elevation head, pi/ +
zi, is referred to as the piezometric head. The piezometric head is what is measured with the
piezometer (manometer) board on the apparatus for this experiment.
Head loss, hL, includes the sum of pipe friction losses, hf, and all minor losses,
where hi is the minor head loss (in meters) for the ith component and n is the number
of components (fittings, bends, etc.).
Lhg
Vz
p
g
Vz
p
22
2
22
2
2
11
1
ni
ifL hhh1
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
63
Pipe friction losses are expressed as the Darcy-Weisbach equation given by
where f is a friction factor, L is the pipe length, and D is the pipe diameter. Pipe
friction losses are assumed to be negligible in this experiment
The energy loss which occurs in a pipe fitting (so-called secondary loss) is
commonly expressed in terms of a head loss (h, meters) in the form:
Where K = the loss coefficient and
v = mean velocity of flow into the fitting, For the expansion and contraction,
the V used is the velocity of the fluid in the smaller-diameter pipe.
Because of the complexity of flow in many fittings, K is usually determined
by experiment. For the pipe fitting experiment, the head loss is calculated from two
manometer readings, taken before and after each fitting, and K is then determined as
Due to the change in pipe cross-sectional area through the enlargement and
contraction, the system experiences an additional change in static pressure. This
change can be calculated as
To eliminate the effect of this area change on the measured head losses, this
value should be added to the head loss readings for the enlargement and the
contraction. Note that (h1 - h2) will be negative for the enlargement and
will be negative for the contraction.
For the gate valve experiment, pressure difference before and after gate is measured
directly using a pressure gauge. This can then be converted to an equivalent head loss
using the equation
1 bar = 10.2 m water
Procedure:
It is not possible to make measurements on all fittings simultaneously and,
therefore, it is necessary to run two separate tests.
o Part A:
1) Set up the losses apparatus on the hydraulic bench so that its base is horizontal
by adjusting the feet on the base plate if necessary. (this is necessary for accurate
height measurements from the manometers). Connect the test rig inlet to the bench
g
V
D
Lfh f
2
2
g
VKh
2
2
g
VhK
2/
2
gvgv 2/2/2
2
2
1
gvgv 2/2/2
2
2
1
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
64
flow supply and run the outlet extension tube to the volumetric tank and secure it
in place.
2) Fully open the gate valve and the outlet flow control valve at the right hand end of the
apparatus.
3) Close the bench flow control valve then start the service pump.
4) Gradually open the bench flow control valve and allow the pipework to fill with
water until all air has been expelled from the pipework.
5) In order to bleed air from pressure tapping points and the manometers close
both the bench valve and the test rig flow control valve and open the air bleed
screw and remove the cap from the adjacent air valve. Connect a length of small
bore tubing from the air valve to the volumetric tank. Now, open the bench valve
and allow flow through the manometers to purge all air from them; then, tighten
the air bleed screw and partly open both the bench valve and the test rig flow
control valve.
Next, open the air bleed screw slightly to allow air to enter the top of the
manometers, re-tighten the screw when the manometer levels reach a convenient
height.
6) Check that all manometer levels are on scale at the maximum volume flow rate
required (approximately 17 liters/ minute). These levels can be adjusted further by
using the air bleed screw and the hand pump supplies. The air bleed screw
controls the air flow through the air valve, so when using the hand pump, the
bleed screw must be open. To retain the hand pump pressure in the system, the
screw must be closed after pumping.
7) If the levels in the manometer are too high then the hand pump can be used to
pressurise the top manifold. All levels will decrease simultaneously but retain the
appropriate differentials.
If the levels are too low then the hand pump should be disconnected and the
air bleed screw opened briefly to reduce the pressure in the top manifold.
Alternatively the outlet flow control valve can be closed to raise the static pressure
in the system which will raise all levels simultaneously.
If the level in any manometer tube is allowed to drop too low then air will
enter the bottom manifold. If the level in any manometer tube is too high then
water will enter the top manifold and flow into adjacent tubes.
8) Adjust the flow from the bench control valve and, at a given flow rate, take
height readings from all of the manometers after the levels have steadied. In order
to determine the volume flow rate, you should carry out a timed volume collection
using the volumetric tank. This is achieved by closing the ball valve and
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
65
measuring (with a stopwatch) time taken to accumulate a known volume of fluid
in the tank, which is read from the sight glass. You should collect fluid for at least
one minute to minimize timing errors. ( note: valve should be kept fully open.)
9) Repeat this procedure to give a total of at least five sets of measurements over a
flow range from approximately 8 - 17 liters per minute.
o Part B:
10) Clamp off the connecting tubes to the mitre bend pressure tappings (to prevent
air being drawn into the system).
11) Start with the gate valve closed and open fully both the bench valve and the
lest rig flow control valve.
12) open the gate valve by approximately 50% of one turn (after taking up any
backlash).
13) For each of at least 5 flow rates, measure pressure drop across the valve from
the pressure gauge; adjust the flow rate by use of the test rig flow control valve.
Once measurements have started, do not adjust the gale valve. Determine the
volume flow rate by timed collection.
14) Repeat this procedure for the gate valve opened by approximately 70% of one
turn and then approximately 80% of one turn.
Data & Results:
The following dimensions from the equipment are used in the appropriate
calculations.
Internal diameter of pipework d = 0.0183 m
Internal diameter of pipework at enlargement outlet and contraction inlet
d = 0.0240 m
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
66
Table 1. Raw Data for All Fittings Except Gate Valve
Case No. I II III IV V
Volume (L)
Time (sec)
Pie
zom
ete
r R
ead
ings
(m
m)
Enlargement 1
2
Contraction 3
4
Long Bend 5
6
Short Bend 7
8
Elbow 9
10
Mitre Bend 11
12
Table 2. Raw Data for Gate Valve
Case No. I II III IV V
50%
Op
ened
Volume (L)
Time (sec)
Gauge Reading
(bar)
Red (upstream)
Black (downstream)
70%
Op
ened
Volume (L)
Time (sec)
Gauge Reading
(bar)
Red (upstream)
Black (downstream)
80%
Op
ened
Volume (L)
Time (sec)
Gauge Reading
(bar)
Red (upstream)
Black (downstream)
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
67
Table 3. Minor Head Losses of All Fittings Except Gate Valve
Case No. I II III IV V
Q (m3/sec)
V (m/s)
V2/2g (m)
Min
or
He
ad L
osse
s
(m)
Enlargement Δh
Δh +V12/2g- V2
2/2g
Contraction Δh Δh +V1
2/2g- V22/2g
Long Bend
Short Bend
Elbow
Mitre Bend
Table 4. Loss Coefficients for All Fittings Except Gate Valve
Case No. I II III IV V
Q (m3/sec)
V (m/s)
V2/2g (m)
Loss
C
oef
fici
ents
Enlargement
Contraction
Long Bend
Short Bend
Elbow
Mitre Bend
Table 5. Equivalent Minor Head Loss and Loss Coefficient for Gate Valve
Case No. I II III IV V
50%
Op
ened
Q (m3/sec)
V (m/sec)
V2/2g (m)
Minor Head Loss (m)
Loss Coefficient
70%
Op
ened
Q (m3/sec)
V (m/sec)
V2/2g (m)
Minor Head Loss (m)
Loss Coefficient
80%
Op
ened
Q (m3/sec)
V (m/sec)
V2/2g (m)
Minor Head Loss (m)
Loss Coefficient
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
68
Calculations and Results
Fill in Tables 3 – 5 with calculated results. Assume that the pipe friction
losses between the upstream and downstream manometer ports are negligible, so the
total head loss is due to minor head losses. Remember the piezometric head is what is
measured with the piezometer (manometer) board on the experimental apparatus.
Questions
1. For Exercise A, prepare plots that show the effect of dynamic head on minor head
loss (i.e. plot graphs of head loss (∆h) against dynamic head (
)), and the effect of flow
rate on loss coefficients (i.e. K against volume flow rate Q).
2. For Exercise B, prepare plots that show the effect of dynamic head on equivalent
head loss (i.e. (∆h) against (
)), and the effect of flow rate on loss coefficients (i.e. K
against volume flow rate Q).
3. Comment on and explain the relationships evident in the plots of Questions 1 and
2. Include a comparison of the loss coefficients and geometry for the four types of
bends.
a. Is it justifiable to treat the loss coefficient as constant for a given
fitting? Explain.
b. How does the loss coefficient for the gate valve vary with the extent of
the opening of the valve? Explain.
4. Compare the experimental loss-coefficient values for different fittings to those
found in a fluid mechanics text book (or another source). Be sure to site the
source of the published values.
5. Does the static pressure increase or decrease for the enlargement and contraction?
Explain the increase or decrease in static pressure.
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
69
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
70
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
71
Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses
72
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
73
Experiment 10: Centrifugal Pump
Introduction:
Pumps fall into two main categories: positive displacement pumps and
rotodynamic pumps.
In a positive displacement pump, a fixed volume of fluid is forced from one
chamber into another. One of the oldest and most familiar designs is the reciprocating
engine, utilising a piston moving inside a cylinder. Steam pumps, the 'nodding
donkey', stirrup pumps and hydraulic rams are all of this type. Animal hearts are also
positive displacement pumps, which use volume reduction of one chamber to force
flow into another chamber.
The FM50 pump is, by contrast, a rotodynamic machine. Rotodynamic (or simply
dynamic) pumps impart momentum to a fluid, which then causes the fluid to move
into the delivery chamber or outlet. Turbines and centrifugal pumps all fall into this
category.
Pumps
Turbo-hydraulic (Kinetic) pumps Positive Displacement Pumps
Centrifugal Propeller Jet Screw Reciprocating
Pump (Radial) (Axial) (Mixed)
Description:
The apparatus consists of a tank and pipework which delivers water to and from a
small centrifugal pump. The unit is fitted with electronic sensors which measure the
process variables. Signals from these sensors are sent to a computer via an interface
device, and the unit is supplied with data
logging software as standard.
Pump speed and outlet pressure may
be varied to allow the collection of
performance data over a range of
parameters. The inlet (suction) head
pressure may be adjusted to investigate
the onset of cavitation. An alternative
impeller is also supplied so that the effect
of impeller design may be studied.
For more Details refer to Instruction
Manual FM50.
Figure 1: Centrifugal Pump Demonstration Unit
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
74
Exercise B
Objective
To create head, power and efficiency characteristic curves for a centrifugal
pump.
Theory
One way of illustrating pump characteristics is to construct contour lines of
constant power or efficiency on a graph of pump head plotted against pump
discharge. These allow engineers to see the maximum efficiency of a pump
over a range of operating parameters, which can assist in the selection of an
appropriate pump to suit particular conditions. An example is given in Figure
2.
Figure 2
Equipment Set Up
If the equipment is not yet ready for use, proceed as follows:
Ensure the drain valve is fully closed.
If necessary, fill the reservoir to within 20cm of the top rim.
Ensure the inlet valve and gate valve are both fully open.
Ensure the equipment is connected to the IFD7 and the IFD7 is connected to a
suitable PC. The red and green indicator lights on the IFD7 should both be
illuminated.
Ensure the IFD7 is connected to an appropriate mains supply, and switch on
the supply.
Run the FM50-304 software. Check that 'IFD: OK' is displayed in the bottom
right corner of the screen and that there are values displayed in all the sensor
display boxes on the mimic diagram.
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
75
Procedure
Switch on the IFD7.
Switch on the FM50 pump within the software using the Pump On button.
In the software, rename the current (blank) results table to '50%' (this will be
the only table if results from Exercise A are not available).
On the mimic diagram of the software, set the pump speed to 50%.
The interface will increase the pump speed until it reaches the required setting.
Allow water to circulate until all air has been f1ushed from the system.
Partially closing and opening the inlet and gate valves a few times will help in
priming the system and eliminating any bubbles caught within the valve
mechanism. Leave the inlet valve fully open.
Close the gate valve to give a flow rate Q of 0. (Note that the pump may not
run well with the gate valve closed or nearly closed, as the back pressure
produced is outside normal operating parameters. The pump should begin to
run more smoothly as the experiment progresses).
Select the icon to record the sensor readings and pump settings on the
results table of the software.
Open the gate valve to allow a low flow rate. Allow sufficient time for the
sensor readings to stabilise then select the icon to record the next set of
data.
Open the gate valve in small increments, allowing the sensor readings to
stabilise then recording the sensor and pump data each time.
Create a new results sheet by selecting the icon (you may also wish to
save the results at this time to avoid losing the data in the event of problems).
Close the gate valve.
Set the pump to 60%.
Select the icon to record the sensor readings and pump settings on the new
results table.
Repeat as before, opening the gate valve in small increments and allowing the
sensor readings to stabilise then recording the sensor and pump data each time.
Close the gate valve.
Repeat the procedure at 70%, 80%, 90% and 100%. Create a new results sheet
for each setting (and save the results if desired- the same file may be
overwritten each time as more data is added). For convenience, rename each
sheet of results in the software with the pump setting.
Ensure the results are saved after taking the final set of results.
Switch the pump off. If not proceeding directly to another exercise then switch off the IFD7 and close the FM50 software.
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
76
Results
On the same graph plot Total Head Ht against Flow Rate Q for each setting. Graphs may be produced using the software graph facility, in which case the resulting graph with multiple plots must be printed. Alternatively the results may be imported into a more sophisticated spreadsheet program that allows the following procedure to be performed.
Select a value for efficiency, for example 40%. On each line plotted, mark the points at which an efficiency of 40% is achieved (the data is unlikely to include recorded points at which the efficiency is exactly 40%, so estimate the points based on the values obtained). Where the pump performance at a particular setting does not ever correspond to the efficiency chosen, note whether the efficiency would lie above the line or to the right of the pump performance curve. Join the marked points to form a smooth curve.
Repeat for other efficiency values. for example 35%.45% and 5090. to give a
family of efficiency curves.
Create and/or print a second head-flow rate graph for all pump frequencies.
Using the same procedure as for drawing contour lines of constant efficiency,
produce curves for constant mechanical power.
Conclusion
Examine and describe the shapes of the efficiency and power curves obtained.
Are the shapes consistent? How do they relate to the head-flow rate
characteristic? How do the efficiency and power curves relate to each other?
Compare the results to the example pump curves presented in the theory
section. How does the pump in the example compare to the pump on the FM50
in terms of capacity, power, and efficiency?
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
77
Calculations
Table 1: Example of data taken from the Software (Setting 50%)
Sample Number
Notes
Pump Setting
S [%]
Pump Speed
n [rpm]
Water Temperature
T [°C]
Inlet Pressure
Pin [kPa]
Outlet Pressure
Pout [kPa]
Motor Torque
t [Nm]
Flow Rate
Q [l/s]
Density of
water
[kg/m³]
1
50 750 26.7 2.6 18.5 0.62 0.04 997
2
50 750 27.2 2.7 18.3 0.64 0.12 996
3
50 750 26.7 2.3 17.7 0.64 0.21 997
4
50 750 26.9 2.2 17.0 0.66 0.29 997
5
50 750 27.1 1.6 15.4 0.65 0.40 997
6
50 750 27.4 1.3 14.0 0.67 0.49 996
7
50 750 26.7 0.9 13.1 0.66 0.54 997
8
50 750 27.0 0.3 11.0 0.67 0.60 997
9
50 750 26.6 0.2 10.1 0.69 0.64 997
10
50 750 26.7 -0.4 9.5 0.68 0.66 997
11
50 750 26.8 -0.6 8.6 0.68 0.69 997
12
50 750 27.1 -0.9 8.1 0.68 0.72 996
13
50 750 26.7 -1.1 7.1 0.67 0.74 997
14
50 750 27.1 -1.0 7.2 0.70 0.76 996
15
50 750 26.7 -1.1 6.5 0.68 0.76 997
16
50 750 27.5 -1.0 6.2 0.69 0.76 996
17
50 750 27.1 -1.2 6.2 0.72 0.77 996
18
50 750 26.7 -1.2 6.2 0.70 0.77 997
19
50 750 27.4 -1.2 6.4 0.68 0.76 996
Table 1 (Cont.): Example 50% setting (n = 750 rpm)
Inlet Velocity
Vin [m/s]
Outlet Velocity
Vout [m/s]
Static Head
Hs [m]
Velocity Head
Hv [m]
Elevation Head
He [m]
Total Head
Ht [m]
Hydraulic Power
Ph [W]
Mechanical Power
Pm [W]
Pump Efficiency
E [%]
Predicted Flow Rate [l/s]
0.090 0.162 1.627 0.001 0.075 1.70 0.7 48.4 1.3 0.03
0.275 0.495 1.596 0.009 0.075 1.68 2.0 50.5 3.9 0.08
0.491 0.885 1.570 0.028 0.075 1.67 3.5 50.3 6.9 0.14
0.675 1.218 1.516 0.052 0.075 1.64 4.7 52.1 9.0 0.20
0.919 1.657 1.413 0.097 0.075 1.58 6.2 50.8 12.2 0.27
1.135 2.046 1.302 0.148 0.075 1.52 7.3 52.7 13.9 0.33
1.256 2.266 1.250 0.181 0.075 1.51 8.0 51.8 15.5 0.36
1.378 2.485 1.097 0.218 0.075 1.39 8.1 52.6 15.5 0.40
1.468 2.647 1.020 0.247 0.075 1.34 8.4 54.4 15.4 0.42
1.531 2.761 1.012 0.269 0.075 1.36 8.8 53.2 16.6 0.44
1.594 2.875 0.935 0.292 0.075 1.30 8.8 53.3 16.5 0.46
1.653 2.980 0.919 0.313 0.075 1.31 9.2 53.4 17.2 0.48
1.716 3.094 0.837 0.338 0.075 1.25 9.1 52.8 17.2 0.50
1.747 3.151 0.839 0.350 0.075 1.26 9.4 54.9 17.1 0.51
1.747 3.151 0.777 0.350 0.075 1.20 8.9 53.1 16.8 0.51
1.747 3.151 0.733 0.350 0.075 1.16 8.6 54.2 15.9 0.51
1.774 3.199 0.757 0.361 0.075 1.19 9.0 56.2 16.0 0.51
1.774 3.199 0.754 0.361 0.075 1.19 9.0 55.1 16.2 0.51
1.747 3.151 0.775 0.350 0.075 1.20 8.9 53.8 16.5 0.51
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
78
Table 1 (Cont.): 50% setting (n = 750 rpm)
Predicted Total Head [m]
Vapour Pressure
Pv [kPa]
Net +ve Suction Head
Available [m]
Pipe Length
L [m]
Pipe Diameter
d [m]
Coefficient k
[-]
Coefficient C
[-]
System Head Loss [m]
Walkthrough Questions
Score [%]
0.757 36.64 6.73 0.916 0.032 4.9 140 0.06 0.746 37.33 6.68 0.916
4.9
0.21
0.743 36.64 6.72 0.916
4.9
0.40 0.730 36.89 6.71 0.916
4.9
0.58
0.704 37.14 6.67 0.916
4.9
0.86 0.678 37.58 6.64 0.916
4.9
1.13
0.669 36.70 6.72 0.916
4.9
1.29 0.618 37.08 6.66 0.916
4.9
1.46
0.597 36.57 6.73 0.916
4.9
1.60 0.603 36.64 6.69 0.916
4.9
1.69
0.578 36.82 6.68 0.916
4.9
1.79 0.581 37.20 6.63 0.916
4.9
1.88
0.555 36.64 6.69 0.916
4.9
1.98 0.562 37.20 6.65 0.916
4.9
2.04
0.534 36.70 6.69 0.916
4.9
2.04 0.515 37.65 6.60 0.916
4.9
2.04
0.530 37.20 6.64 0.916
4.9
2.08 0.529 36.64 6.70 0.916
4.9
2.08
0.533 37.58 6.59 0.916
4.9
2.04
Figure 3: Pump Curves for different velocities
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60
Tota
l He
ad H
t [m
]
Flow Rate Q [l/s]
Pump Curves for different velocities (rpm)
725
955
1525
1555
1325
1255
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
79
Exercise C
Objective
To investigate the use of the affinity laws in predicting the head-flow
characteristic for a pump.
Theory
When selecting a pump for a system, it is seldom practical to test the
performance of every size of pump in a manufacturer's range at all speeds at
which it may be designed to run. It is therefore useful to have a mathematical
solution that allows assumptions can be made about operating characteristics
of a pump running at one speed, impeller size, etc. from experimental results
taken at another.
The multiple curves obtained from plotting measured pump characteristics on
dimensional axes can be reduced to a single curve if appropriate dimensionless
groups are used. Provided the effects of t1uid viscosity on pump performance
are small, and that cavitation is not occurring, the characteristic of a given type
and shape of pump may be represented by:
∫
[ ]
where n is the pump speed (rpm or Hz), and D is the impeller diameter (m)
For a single curve of the type suggested by this equation to represent more
than one operating condition of the particular type of pump, the criterion of
dynamic similarity must be fulfilled. That is, all fluid velocities at
corresponding points within the machine are in the same direction and
proportional to impeller speed. When this is the case, as for a particular pump
operated at different speeds, a simple graph of data is formed, as depicted in
Figure 4:
Figure 4: Dimensionless head-discharge characteristic of a particular centrifugal pump
operated at different speeds
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
80
The dimensionless equation given previously is the basis from which the
affinity laws are derived. The affinity laws allow the performance of
geometrically similar pumps of different sizes or speeds to be predicted
accurately enough for practical purposes.
The methods used for deriving the affinity laws will not be presented here, but
the laws are as follows:
Power Coefficient
Flow Coefficient
Head Coefficient
These Laws are most often used to calculate changes in now rate, head and
power of a pump when the size, rotational speed or fluid density is changed.
The following formulae are derived from the above considerations, and allow
calculation of total head H, and power Pm at one speed n. to be deduced from
those measured at another speed n2:
More generally, the relationship between two geometrically similar machines
with characteristic diameters D1 and D2 operating at rotational speeds n1 and
n2 is shown in Figure 5. For any two points at which values of (gH / n2D
2) and
(Q / nD3) are the same, it follows that:
(
)
(
)
and
(
)
These are termed corresponding points.
The power coefficient
and the resulting efficiency E can be compared in
a similar manner.
Figure 5: Relationship of performance characteristics for geometrically similar machines
operating at different speeds
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
81
Equipment Set Up
If the results from Exercise B are available then no further data is required.
Ensure you understand the Theory section then proceed directly to the results.
This experiment may be undertaken directly following another experiment, in
which case the equipment will already be prepared and need only be switched
back out of standby mode again.
If the equipment is not yet ready for use, proceed as follows:
Ensure the drain valve is fully closed.
If necessary, fill the reservoir to within 20cm of the top rim. Ensure the inlet
valve and the gate valve are both fully open.
Ensure the equipment is connected to the IFD7 and the IFD7 is connected to a
suitable PC. The red and green indicator lights on the IFD7 should both be
illuminated.
Ensure the IFD7 is connected to an appropriate mains supply, and switch on
the supply.
Run the FM50-304 software. Check that 'IFD: OK' is displayed in the bottom
right corner of the screen and that there are values displayed in all the sensor
display boxes on the mimic diagram
Procedure
The results from Exercise B may be used to perform the calculations and to
create the graphs for this exercise. Where these results are available, no further
data is required. Proceed directly to the Results section. If results are not
available, proceed as follows:
Switch on the IFD7.
Switch on the FM50 pump within the software.
In the software, set the pump to 50%.
Allow water to circulate until all air has been flushed from the system. Close
the gate valve to give a flow rate Q of 0.
Select the icon to record the sensor readings and pump settings on the
results table of the software.
Open the gate valve to give a very low flow rate. Allow sufficient time for the
sensor readings to stabilise then select the icon to record the next set of
data.
Open the gate valve in small increments, allowing the sensor readings to
stabilise then recording the sensor and pump data each time.
Create a new results sheet by selecting the icon (you may also wish to
save the results at this time to avoid losing the data in the event of problems).
Set the pump to 70%.
Close the gate valve.
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
82
Select the icon to record the sensor readings and pump settings on the new
results table.
Open the gate valve to give a very low flow rate. Allow sufficient time for the
sensor readings to stubilise, then select the icon to record the next set of
data.
Repeat, opening the gate valve in small increments and allowing the sensor
readings to stabilise, then recording the sensor and pump data each time.
Ensure the results are saved using 'Save' or 'Save As .. .' from the software File
menu after taking the final set of results.
Switch off the FM50 within the software using the Power On/Standby button.
Switch off the IFD7.
Results The results taken at 70% will be used with the affinity laws to give predicted
results at 50%. This will then be compared to the actual results at 50%.
The software uses the affinity laws
and
to calculate the predicted values of Ht2 at predicted flow rates Q2 and 50%
setting from the measured values of Htl and Q1 and the values n1 = 70 and n2 =
50.
Plot a graph of Predicted Head against Predicted Flow Rate.
Plot the measured Total Head at 50% against measured Flow Rate at 50% (if
the data is exported into a dedicated spread sheet package or similar then it
may be possible to plot both graphs on the same axes).
Conclusion
Compare the predicted results at 50% with the measured results. How accurate
were the values obtained using the affinity laws? Discuss the advantages and
disadvantages of this technique for pump system design
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
83
Calculations
Table 2: Data for 50% Setting and 70% setting from software
Practical
70% = 1050 rpm 50% = 750 rpm
Sample Number
Flow Rate
Q [l/s]
Total Head
Ht [m]
Flow Rate
Q [l/s]
Total Head
Ht [m]
1 0.08 3.41 0.04 1.70
2 0.15 3.38 0.12 1.68
3 0.27 3.26 0.21 1.67
4 0.43 3.26 0.29 1.64
5 0.56 3.11 0.40 1.58
6 0.66 2.99 0.49 1.52
7 0.76 2.88 0.54 1.51
8 0.82 2.79 0.60 1.39
9 0.89 2.68 0.64 1.34
10 0.93 2.63 0.66 1.36
11 1.00 2.58 0.69 1.30
12 1.01 2.52 0.72 1.31
13 1.04 2.42 0.74 1.25
14 1.04 2.33 0.76 1.26
15 1.06 2.44 0.76 1.20
16 1.05 2.34 0.76 1.16
17 1.06 2.34 0.77 1.19
18 1.08 2.38 0.77 1.19
19 1.08 2.35 0.76 1.20
20 1.06 2.34
Figure 6
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.00 0.50 1.00 1.50
Tota
l He
ad H
t [m
]
Flow Rate Q [l/s]
Practical
70% = 1050 rpm
50% = 750 rpm
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
84
Using Similarity Laws to calculate Q and Ht for 50%
and
Table 3: Data for 70% setting from software and 50% Setting from Similarity Laws
Similarity Laws
70% = 1050 rpm Calculated 50% = 750 rpm
Sample Number
Flow Rate
Q [l/s]
Total Head
Ht [m]
Flow Rate
Q [l/s]
Total Head
Ht [m]
1 0.08 3.41 0.06 1.74
2 0.15 3.38 0.10 1.72
3 0.27 3.26 0.19 1.66
4 0.43 3.26 0.30 1.66
5 0.56 3.11 0.40 1.59
6 0.66 2.99 0.47 1.53
7 0.76 2.88 0.54 1.47
8 0.82 2.79 0.59 1.42
9 0.89 2.68 0.64 1.37
10 0.93 2.63 0.66 1.34
11 1.00 2.58 0.71 1.32
12 1.01 2.52 0.72 1.29
13 1.04 2.42 0.74 1.23
14 1.04 2.33 0.74 1.19
15 1.06 2.44 0.76 1.24
16 1.05 2.34 0.75 1.19
17 1.06 2.34 0.76 1.19
18 1.08 2.38 0.77 1.22
19 1.08 2.35 0.77 1.20
20 1.06 2.34 0.76 1.19
Figure 7
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.00 0.50 1.00 1.50
Tota
l He
ad H
t [m
]
Flow Rate Q [l/s]
Affinity Laws
70% = 1050rpm
Calculated50% = 750rpm
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
85
Exercise D
Objective
To investigate the effect of changing inlet head on pump performance.
Method
By varying the pressure at the inlet to the pump using a manual valve to
control the available flow.
Theory
In both the design and operation of a rotodynamic machine, careful attention
has to be paid to the fluid conditions on the suction side. In particular, it is
important to check the minimum pressure that can arise at any point to ensure
that cavitation does not take place.
Cavitation
If the pressure at any point is less than the vapour pressure of the liquid at the
temperature at that point, vaporisation will occur. This is most likely to arise in
the suction side where the lowest pressures are experienced. The vaporised
liquid appears as bubbles within the liquid, and these subsequently collapse
with such force that mechanical damage may be sustained. This condition,
known as cavitation, is accompanied by a marked increase in noise and
vibration in addition to the loss of head.
بالتدريج. suction pipeرؤية تكون الفقاعات عن طريق إغالق الصمام الموجود في يمكن
FM 51مالحظة: الفقاعات تكون اوضح في الجهاز االخر
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
86
Exercise E
Objective
To obtain a Head - Flow curve for the piping system through which the fluid is
to be pumped. To determine the operating point of the pump.
Theory
System analysis for a pumping installation is used to select the most suitable
pumping units and to define their operating points. System analysis involves
calculating a head - flow curve for the pumping system (valves, pipes, fittings
etc.) and using this curve in conjunction with the performance curves of the
available pumps to select the most appropriate pump(s) for use within the
system.
The system curve is a graphic representation of the flow rate in the system with
respect to system head. It represents the relationship between flow rate and
hydraulic losses in a system. Such losses are due to the system design (e.g.
bends and fittings, surface roughness) and operating conditions (e.g.
temperature).
Assuming that
Flow velocity is proportional to volume now rate
Losses in the system are proportional to the square of the now velocity
it follows that system head loss must be proportional to the square of the
volume flow rate, and the system head - now graph will therefore be parabolic
in shape.
باقي الشرح موجود في الكتالوج الخاص بالجهاز
Calculations
Table 4
System Curve
Sample Number
Pump Setting
S [%]
Pump Speed
n [rpm]
Flow Rate
Q [l/s]
Total Head
Ht [m]
1 100 1500 1.49 4.28
2 90 1350 1.36 3.78
3 80 1200 1.22 3.03
4 70 1050 1.08 2.33
5 60 900 0.92 1.71
6 50 750 0.77 1.16
7 40 600 0.61 0.74
8 30 450 0.46 0.38
9 20 300 0.30 0.15
10 10 150 0.13 -0.01
11 0 0 0.00 -0.05
Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump
87
Table 5
Pump Curve
Sample Number
Pump Setting
S [%]
Pump Speed
n [rpm]
Flow Rate
Q [l/s]
Total Head
Ht [m]
1 70 1050 1.08 2.28
2 70 1050 1.02 2.38
3 70 1050 1.00 2.55
4 70 1050 0.97 2.60
5 70 1050 0.92 2.69
6 70 1050 0.85 2.74
7 70 1050 0.80 2.86
8 70 1050 0.69 2.89
9 70 1050 0.61 3.10
10 70 1050 0.49 3.16
11 70 1050 0.35 3.28
12 70 1050 0.24 3.34
13 70 1050 0.13 3.39
14 70 1050 0.09 3.41
Figure 8
تم اخذها system curve، ألن قراءات pump curveمالحظة: نقطة التشغيل في الرسمة كانت اخر نقطة في
flow (outlet valve fully opened.)عند أعلى
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0.00 0.50 1.00 1.50 2.00Tota
l He
ad H
t [m
]
Flow Rate Q [l/s]
Operating Point
Pump Curve
System Curve
Operating Point
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
88
Experiment 11: Series and Parallel Pumps
Introduction to the Equipment
The apparatus consists of a tank and pipework which delivers water to and
from two identical centrifugal pumps. The unit is fitted with electronic sensors
which measure the process variables. Signals from these sensors are sent to a
computer via an interface device, and the unit is supplied with data logging
software as standard.
The speed of one of the pumps may be varied to allow the collection of
performance data over a range of parameters. Outlet pressures may be varied
to control the flow rate. Flow through the system may be set to allow single
pump operation, series pump operation or parallel pump operation.
Figure 1: Series and Parallel Pumps Demonstration Unit
Pumps
The two pumps are motor-driven centrifugal pumps. On pump 1 the speed of the motor is adjustable to give a range of 0 to 100%, allowing operation as a single pump for pump performance analysis. Pump 2 is an identical model but is run at its design speed, which is equivalent to a setting of 80% on the variable-speed pump for a 50Hz electrical supply, or 100% for a 60 Hz supply. The pump bodies and cover plates are made from clear acrylic, allowing the
impellers to be observed.
Inlet valve
A manual ball valve controls the inlet (suction) head supplied to the pumps. This valve should be fully open except when investigating the effect of inlet pressure on pump performance and cavitation formation.
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
89
Setting the flow path
The system may be configured to drive flow
using single, series or parallel pumps. The
system valves are as shown:
Valves should be set to configure the system as follows. The software should also be
set to the corresponding flow path to ensure that the correct calculations are
performed.
Single Pump:
Series Pumps:
Parallel Pumps:
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
90
Exercise F
Objective
To investigate the result on discharge and total head of operating pumps in
series.
Theory
A single pump may be insufficient to produce the performance required.
Combining two pumps increases the pumping capacity of the system. Two
pumps may be connected in series, so that water passes first through one pump
and then through the second. When two pumps operate in series, the flow rate
is the same as for a single pump but the total head is increased. The combined
pump head-capacity curve is found by adding the heads of the single pump
curves at the same capacity.
Figure 2
Equipment Set Up
Ensure the drain valve is fully closed.
If necessary, fill the reservoir to within 10 cm of the top rim.
Check that both pumps are fitted with similar impellers (the impellers may be
viewed through the clear cover plate of each pump).
Ensure the inlet valve and gate valve are both fully open.
Set the 3-way valve for flow in series (the earlier experiments have all used
this valve set for flow in parallel).
Ensure the equipment is connected to the IFD7 and the IFD7 is connected to a
suitable PC. The red and green indicator lights on the IFD7 should both be
illuminated.
Ensure the IFD7 is connected to an appropriate mains supply, and switch on
the supply. Switch on the IFD7.
Run the FM51-304 software. Check that 'IFD: OK' is displayed in the bottom
right corner of the screen and that there are values displayed in all the sensor
display boxes on the mimic diagram.
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
91
Procedure
Both pumps must be used at the same setting in this experiment, to ensure
identical performance. As the speed of Pump 2 is fixed at its design
operational point, Pump 1 should be set to match - select 80% for a 50Hz
electrical supply, or 100% for 60 Hz.
Allow water to circulate until all air has been flushed from the system.
If results are already available for a single pump across its full flow range,
load those results into the software now and jump to the section of this
exercise using two pumps. If results are not available then proceed as follows:
Single pump performance:
Close Pump 2 outlet valve and open Pump 1 outlet valve.
In the software, on the mimic diagram, set the 'Mode' to 'Single' by selecting
the appropriate radio button.
Rename the results sheet to 'Single'.
Select the icon to record the sensor readings and pump settings on the
results table of the software.
Close the gate valve to reduce the flow by a small amount. Select the icon
again.
Continue to close the gate valve to give incremental changes in flow rate,
recording the sensor data each time.
After taking the final set of data, fully open the gate valve.
Series pump performance:
Create a new results sheet using the icon. Rename this new results sheet to
'Series'. In the software, on the mimic diagram, set the 'Mode' to 'Series' by
selecting the appropriate radio button.
Open Pump 2 outlet valve, close Pump 1 outlet valve and wait for any air to
circulate out of the system.
Select the icon to record the sensor readings and pump settings on the
results table of the software.
Close the gate valve to reduce the flow by a small increment. Select the
icon again.
Continue to close the gate valve to give incremental changes in flow rate,
recording the sensor data each time.
After taking the final set of data, fully open the gate valve again.
Exercise G may be performed immediately after this experiment without
closing the software; otherwise, save the results and ensure they are available
for Exercise G when required. (It may also be advisable to save the results
from this exercise before starting exercise G even if continuing straight on, to
ensure that the data is not lost in the event of a computer failure. The results
sheet may be overwritten with the combined results once Exercise G has been
completed).
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
92
Results
On a base of flow rate, plot a graph of total head gain for the single pump and
for two pumps connected in series. Calculate the difference between the total
head gain for single and series pumps.
Conclusion
Does the total head gain for the two pumps in series match the theoretical
prediction of twice the head gain for a single pump (assuming the two pumps
used gave identical performance)?
Give examples of applications where pumps might be connected in series
Figure 3 Figure 4
عند توصيل المضخات على التوالي فإن
.تزداد Hقيمة
يجب أن تكون قيمة و لرؤية ذلك عمليا،
التدفق التي نقارن عندها منخفضة )أي أن
outlet valve مفتوح قليال( حتى يكون
لمضخة واحدة و headالفرق بين
لمضختين على التوالي واضح، كما بالشكل
المجاور.
Figure 5
Low Flow High Flow
حض
واق
رلفا
قرالف
رغي
حض
وا
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
93
Exercise G
Objective
To investigate the result on discharge and total head of operating pumps in
parallel.
Theory
A single pump may be insufficient to produce the performance required.
Combining two pumps increases the pumping capacity of the system. Two
pumps may be connected in parallel, so that half the flow passes through one
of the pumps and the other half through the second pump. When two pumps
operate in parallel the total head increase remains unchanged but the flow rate
is increased. The head-capacity curve is found by adding the capacities of the
single pump curves at the same head.
Figure 6
Equipment Set Up
Ensure the drain valve is fully closed.
If necessary, fill the reservoir to within 10 cm of the top rim.
Check that both pumps are fitted with similar impellers (the impellers may be
viewed through the clear cover plate of each pump).
Ensure the inlet valve and gate valve are both full y open.
Set the 3-way valve for flow in parallel
Fully open the Pump 1 outlet valve and Pump 2 outlet valve. Opening both
valves fully ensures that the outlet pressure on both pumps is equal.
Ensure the equipment is connected to the IFD7 and the IFD7 is connected to a
suitable PC. The red and green indicator lights on the IFD7 should both be
illuminated.
Ensure the IFD7 is connected to an appropriate mains supply, and switch on
the supply. Switch on the IFD7.
Run the FM51-304 software. Check that 'IFD: OK' is displayed in the bottom
right corner of the screen and that there are values displayed in all the sensor
display boxes on the mimic diagram.
In the software, on the mimic diagram, set the 'Mode' to 'Parallel' by selecting
the appropriate radio button
Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps
94
Procedure
Both pumps must be used at the same setting in this experiment, to ensure
identical performance. As the speed of Pump 2 is fixed at its design
operational point, Pump 1 should be set to match - select 80% for a 50Hz
electrical supply, or 100% for 60 Hz.
Allow water to circulate until all air has been flushed from the system.
Exercise F should be performed before this experiment, and the results loaded
into the software if the software is not still open from that exercise. If the
software is still open from Exercise F then create a new results sheet by
selecting the icon.
Rename the current (blank) results sheet to 'Parallel'.
Select the icon to record the sensor readings and pump settings on the
results table of the software.
Close the gate valve to reduce the flow by a small increment. Select the
icon again.
Continue to close the gate valve to give incremental changes in flow rate,
recording the sensor data each time
After taking the final set of data, fully open the gate valve. Set Pump 1 to 0%
and switch off both pumps
Results
On a base of flow rate, plot a graph of total head gain for the single pump and
for two pumps connected in parallel. Calculate the difference between the
capacity for single and parallel pumps.
Conclusion
Does the total head gain for the two pumps in parallel match the theoretical
prediction of twice the capacity of a single pump (assuming the two pumps
used gave identical performance)?
Compare the graphs for pumps in series and pumps in parallel, and describe
the similarities and differences.
Give examples of applications where pumps might be connected in parallel.
Drawing on the conclusions of earlier exercises, contrast these with
applications where it would be more appropriate to connect pumps in series,
and also with situations where it would be more appropriate to select a single
pump of higher performance.
Hydraulics Lab - ECIV 3122 References
95
مالحظات:
Qعند توصيل المضخات على التوازي فإن قيمة -
.تزداد
و لرؤية ذلك عمليا، يجب أن تكون قيمة التدفق -
outlet valveعالية )أي أن التي نقارن عندها
fully opened حتى يكون الفرق بين )flow
ي واضح، ازلمضخة واحدة و لمضختين على التو
كما بالشكل المجاور.
Figure 7
Low Flow High Flow
أوضح منه 25تدريجيا في تجربة inlet valveعند إغالق cavitationتكون فقاعات الهواء التي تسبب -
.9في تجربة
Experiment 12: Open Channel Flow
http://www.cussons.co.uk/SOFTWARE/Part15/Part15.htm
18-7-2011
الفرق واضح
قليل الفرق
Hydraulics Lab - ECIV 3122 Appendix A
96
REFERENCES
م. أحمد عبد القادر: مختبر الهيدروليكاملخص مختبر ميكانيكا موائع و
الكتب التالية:
o Fluid Mechanics, by Douglas, J.F., Gasiorek, J.M., Swaffield, J.A., Fourth Edition,2001
o Lecture notes for Hydraulics, Eng. Khalil Alastal
موقع شركة Cussons:
http://www.cussons.co.uk/SOFTWARE/Content.htm
18-7-2011
http://www.cussons.co.uk/SOFTWARE/ المعادالتإلظهار
18-7-2011
http://www.cussons.co.uk/en/ukindex.htm pdf ملفات
18-7-2011
موقع شركة Armfield:
http://www.discoverarmfield.co.uk/?js=enabled
18-7-2011
http://www.discoverarmfield.co.uk/data/fm51/ Series and Parallel Pumps
18-7-2011
http://www.discoverarmfield.co.uk/data/fm50/ Centrifugal Pump
18-7-2011
جامعة أجنبية موقع:
http://itll.colorado.edu/modular_experiments/experiment_directory/modules.php?f
ocus_area_id=6
18-7-2011 تحتوي ملفات لعدة تجارب
Instruction Manual .الخاص بجهاز التجربة الثامنة و التاسعة و العاشرة
(1522-7-28) :فيديوروابط للتجارب ملفات
- http://www.youtube.com/watch?v=Gi4qBOjVAXk&feature=related Exp.1
- http://www.youtube.com/watch?v=tXLI-IeAynI&feature=related Exp.3
- http://www.youtube.com/watch?v=_Y_vInO8gqw Exp.6, P1
- http://www.youtube.com/watch?v=l8kDN0E4x-k&feature=related Exp.6, P2
- http://www.youtube.com/watch?v=JXgkAyimSTM Exp.6, P3
- http://www.youtube.com/watch?v=h3ikeDyAoOE&feature=related Exp.11
Hydraulics Lab - ECIV 3122 Appendix A
97
- http://www.youtube.com/watch?v=5etwhZ0d2GU Exp.11
- http://www.youtube.com/watch?v=h3ikeDyAoOE Exp.11
APPENDICES
APPENDIX A: Report Cover Page
THE ISLAMIC UNIVERSITY OF GAZA
FACULTY OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
HYDRAULICS LABORATORY
ECIV 3122
EXPERIMENT No.: …….
EXPERIMENT TITLE:
………………………………………………………………………
SUBMITTED BY:
1. …………………………………………….. 120………….
2. …………………………………………….. 120………….
CLASS NO.: …….
TEST DATE: ……..day …. / …. / ……..
REPORT SUBMITTAL DATE: ……..day …. / …. / ……..
Hydraulics Lab - ECIV 3122 Appendix A
98
SUPERVISOR:
ENG. ……………………………..
Hydraulics Lab - ECIV 3122 Appendix B
99
APPANDIX B: FINAL EXAM 2nd
Semester 2010-2011
Question 1 ( 36 points)
State whether the following statements are true or false (T/F) :
1
Major head losses occur at any location in pipe system where stream lines are not
straight
2
Minor head losses due to enlargement equals to the difference between piezometer
readings.
3 At Bernoulli theorem, the term (
) called the dynamic head.
4 Increasing in dynamic head leads to increasing in minor losses.
5 Actual flow through notches is less than theoretical flow.
6 Zero degree of pressure recovery occur when there is no losses in a pipe.
7
At Bernoulli theorem, increasing in pipe velocity leads to increasing in pressure
head.
8 Pipe diameter is directly proportional with pressure head in the pipe.
9 Rotameter is used to measure stream velocity directly.
10 In Hydrostatic force experiment we can level the balance arm for each reading by
adding or draining some water.
11 In Hydrostatic force experiment the hydrostatic force acting on the two curved
faces of the quadrant make a moment about the knife edge axis.
12 In Buoyancy experiment MG is the metacentric radius.
13 In Buoyancy experiment, as the off balance weight increases the deflection angle
increases.
14
In impact of jet experiment, the impact force in case of conical target is larger than
hemispherical target for the same flow rate.
15
In flow measurement experiment, the static head at various points in the flow path
can be measured by manometers.
Hydraulics Lab - ECIV 3122 Appendix B
100
16
When an orifice is fitted in the horizontal discharge position, a Hook gauge can be
used to determine the jet profile.
17 The purpose of extension pipe is to get constant head by increasing the flow
through the orifice.
18
The height of water in manometers can be taken and used in calculations, although
air bubbles still in manometers.
19
Bernoulli’s theorem states that an increase in the speed of the fluid occurs
simultaneously (في نفس الوقت) with a decrease in pressure.
20
In Bernoulli experiment, the height of water in manometer # 11 returns to its
original height in manometer # 1.
21 The loss coefficient for the gate valve can be determined experimentally.
22
The minor head loss for enlargement and contraction equals to the difference in
manometers readings.
23
In minor losses experiment the gate valve should be kept fully closed during taking
the readings for all fittings except the gate valve.
24
In minor losses experiment, readings for all fittings including gate valve can be
taken simultaneously.
1
0 Pelton Wheel is an example of impact of jet applications.
1
6 The difference between weir and notch is that the weir is larger than the notch.
Question 2 ( 36 points)
Choose the most suitable answer from a, b or c :
1) In Hydrostatic force experiment, the counter-balance weight is adjusted:
a. before filling water b. before each reading c. Non of above
after filling water
2) In Hydrostatic force experiment, the total weight needed to level the balance arm in
complete immersion is …………… partial immersion.
Hydraulics Lab - ECIV 3122 Appendix B
101
a. less than b. more than c. equal to
3) In Hydrostatic force experiment, if the mass used to level the balance arm is (100
gm) and the depth of water was (66 mm), then the practical force acting on the plane
surface is
a. 1.335 N b. 1.602 N c. 1.516 N
4) A floating body is stable if :
a. M is above G b. M coincides with G c. B is above G
5) If a floating pontoon on water weigh (3 kg), then the volume of submerged body
equal to:
a. 0.003 m3 b. 0.0003 m
3 c. can’t be calculated
6) If GM is negative, then the floating body is ……………
a. stable b. Unstable c. Neutral
7) If the coefficient of velocity = (0.9) and the coefficient of contraction is (0.6), then
the coefficient of discharge will be …………… .
a. 1.5 b. 0.54 c. 0.667
8) When the constant head is 50 cm, then the theoretical velocity of the flow
discharged through an orifice will be …………… .
a. 3.13 mm/s b. 3.13 cm/s c. 3.13 m/s
9) For rectangular notch with width = 3 cm, when drawing a relationship between
ln(Q) in (m3/s ) and ln (H) in m, if the intercept was (-2.73), then Cd will be
…………… .
a. 0.0736 b. 0.64 c. 0.736
10) The purpose of collecting a volume of water for at least two minutes is to:
a. increase the flow b. obtain sufficiently c. waste time
accurate results
11) The basket of glass spheres is used to:
a. smooth the flow b. increase velocity c. make the flow turbulent
12) Measuring the weir datum (zero level) by mounting the point gauge on:
a. half weir height b. channel bed c. weir plate crest level
13) If the height of water level in manometer #1 is (44.6 cm), in manometer #6 is
(16.9 cm), and in manometer #11 is (33.8 cm), then the degree of pressure recovery
equal:
a. 0.169 b. 0.61 c. 0.277
14) In the previous question the head loss equal to:
a. 0.61 m b. 0.277 m c. 0.108 m
Hydraulics Lab - ECIV 3122 Appendix B
102
15) In Bernoulli experiment, when the difference between Inlet Tank and Outlet Tank
increases, the velocity …………… .
a. increases b. decreases c. remains constant
16) If the pressure gauge reading is 2 bar, this equivalent to …………… .
a. 1.02 m water b. 20.4 m water c. 2.04 m water
17) In Minor Losses experiment, clamping off the connecting tubes to the mitre bend
pressure tappings to …………… .
a. prevent increasing the b. prevent air being c. It should not be
flow after the gate valve drawn into the system clamped off
18) The loss coefficient for the gate valve 50% closed is …………… the loss
coefficient of the same gate valve 70% closed.
a. more than b. less than c. equal to
19) The term (
) is called …………… .
a. pressure head b. piezometric head c. elevation head
20) In Bernoulli experiment, the height of water in manometer # 11 ……………
height in manometer # 1.
a. is more than the b. is less than the c. returns to its original
Hydraulics Lab - ECIV 3122 Appendix B
103
0.000
0.500
1.000
1.500
2.000
2.500
0.000 0.500 1.000 1.500 2.000 2.500
Slope for θ = .....°
diameter 5 mm
Question 3 ( 28 points )
1) Describe the form of the deflected jet and draw its shape for the three types of
targets (90°,45° and 135°)
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………..
2) In Impact of Jet Experiment the following data where obtained
Calculate the following and complete the table:
a. Impact Force.
b. Incident momentum.
c. Slope where y-intercept = 0 (draw graph).
d. Calculate θ for the type of target vane, and decide if it is flat, conical, or
semispherical.
e. Comment on the results.
Note: Neglect the influence of the distance between the nozzle and the target (i.e.
assume velocity at nozzle = impact velocity).
…………………………………………………………………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
5 mm dia
Hydraulics Lab - ECIV 3122 Appendix B
104
Question 4 ( 28 points )
1) What are the following terms in Bernoulli equation called:
a)
(………………………)
b)
(………………………)
c) (………………………)
d)
(………………………)
2) The following data are recorded for Bernoulli experiment, if 20 Liters of water
was collected at 330 second.
a) Plot Hydraulic Gradient Line (HGL) and Energy Gradient Line (EGL).
b) Find degree of recovery pressure. Comment
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25 30 35
H.G.L & E.G.L
H.G.L
E.G.L
Tapping No. 1 2 3 4 5 6 7 8 9 10 11
S (cm) 4.3 6.8 9.3 11.8 14.3 16.8 19.3 21.8 24.3 26.8 29.3
A (mm2) 102.56 90.11 77.66 65.22 52.77 40.32 52.77 65.22 77.66 90.11 102.56
H (m) 0.47 0.459 0.443 0.419 0.376 0.296 0.31 0.364 0.381 0.39 0.396
Hydraulics Lab - ECIV 3122 Appendix B
105
Useful Formula For Hydraulics Laboratory (ECIV 3122)
g = 9.81 m2/s, ρ = 1000 kg/m
3 , 1 bar = 10.2 m water
Hydrostatic Force Experiment
a = 10 cm, b = 7.5 cm, L = 27.5 cm, d = 10 cm
When the surface is fully submerged y>100mm
) 2
d -(y d b g F ( Theoretical)
H 12
d
2
d a
L g M F
2
(Practical)
)2
d -(y
H 12
d H
2
P (Centre of pressure)
When the surface is partially submerged 0<y<100mm
y b g 0.5 F 2 ( Theoretical)
3
y d a
L g M F (Practical)
y 3
2 H P (Centre of pressure)
Buoyancy & Floatation - Metacentric Height Experiment
PART (1): unloaded and loaded pontoon PART (2): changing the center of gravity
Impact of Jets
θ - ρ Q V
R
i
cos1 , A
QVn ,
t
VQ , g hVV ni 2 - 22 ,
g mR , 2
4 dA
, x
yS
lope
Flow Measurement
1. Sudden Enlargement
g
Vkehe
2
2
1 , Where
22
2
2
1 11
A
Ake
2. Venturi Meter, Orifices
421
2
gHACQ dact
4. Elbows
g
Vkh bb
2
2
1
5. Rotameter
2
dyH
2
yH
LD
VOB
2
1
radianin
WWW
mmx
W
xPGMExp
bVM
123
.
..
W
XWbOGWOG
OGOBBMGM
VMVMtotal
totalth
1**
ebiVMtotal
displacedfluidtotaltotal
mmm
VggmW
V
DL
V
IBM
lg
3
**
**)12/1(
W
OGWOGWOGWOGWOG
OGOBBMGM
mmbbbbVMVM
total
totalth
**** 11
radianin
gmW
WWWWW
W
xP
W
xPGMExp
mbbVM
3500
.
.
sin.
..
1
D*L
V-OGGMM
21
2
12
2
1
)12(2
A
A
A
A
hhgV
time
VolumeQactual
Hydraulics Lab - ECIV 3122 Appendix B
106
Flow Through Orifice
thdact QCQ
ghAQth 2 , thCact ACA ,
thvact vCv , ,
ghVth 2
Flow Over Weirs
(Rectangular)
2
3
23
2HgBQth
, 2
3
23
2HgBCQCQ dthdact
gB
eC
ercept
d
23
2
int
In British Code 2
3
)001.0](2716.05461.0[ HHQact
(Vee Notch)
Investigation of Bernoulli Theorem
fHzg
v
g
pz
g
v
g
p 2
2
221
2
11
22 , fHHH 111 ,
61
611
hh
hhR
, A
QV
Minor losses
, A
QV
Minor Head Losses Loss Coefficient
Enlargement Δh +V12/2g- V2
2/2g
Contraction Δh +V32/2g- V4
2/2g
Long Bend Δh = h5-h6
Short Bend Δh = h7-h8
Elbow Δh = h9-h10
Mitre Bend Δh = h11-h12
Gate Valve Δh = P1-P2 (bar)
time
VolumeQactual
Cv
CdCc
gA
SlopeCd
2
H
SlopeCv
2
time
VolumeQactual
time
VolumeQactual
time
VolumeQactual
g
V
g
v
g
vhK
222
22
2
2
1
g
V
g
v
g
vhK
222
22
4
2
3
g
VhK
2/
2
g
VmhK
2)(
2
Hydraulics Lab - ECIV 3122 Appendix B
107
Other suggested questions:
Question 5 ( 25 points)
1) What is the difference between orifices and notches?
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
2) The following graph is for a rectangular notch with width = 30mm.
a) Find the actual flow rate.
b) Find the theoretical flow rate.
c) Find the intercept from graph and calculate the coefficient of
discharge.
d) Comment on the results.
1 2 3 4 5 6 7 8
H (mm) 8.5 12.5 20 26 32 37 45.5 51
V (L) 6 10 23 27 40 40 40 40
T (sec) 162.08 134.4 158.3 123.77 132.47 105.11 75.75 63.43
…………………………………………………………………………………………
…………………………………………………………………………………………
-11-10
-9-8-7-6-5-4-3-2-10
-5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
....
....
....
....
....
....
....
...
............................. Rectangular Notch
Hydraulics Lab - ECIV 3122 Appendix B
108
Question 6 ( 15 points) - each branch 3 points -
1) Draw H.G.L for the given flow through Venturi meter. Explain the results.
………………………
………………………
………………………
………………………
………………………
………………………
………………………
………………………
………………………
………………………
………………………
2) Draw a relationship shows the shape of trajectory through side orifice. (write axis
titles)
3) Draw the shape of the nappe in flow over weirs. How does it effect on fluid height?
And where the height of fluid over notch can be measured?
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
Hydraulics Lab - ECIV 3122 Appendix B
109
4) Complete the following Comparison by determining the sign (positive or
negative) and draw them.
∆h
∆h
Drawings
Enlargement
Contraction
5) The following plot gives the relation between dynamic head and head loss in gate
valve when it was 50% , 70% & 80% opened. Which figure expected for each case,
Why?
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
With my best wishes