mekflud modul 2 & 5

8/10/2019 Mekflud Modul 2 & 5

1/27

Modul H-02 Hydrostatic Pressure

Determining a hydrostatic force magnitude on the vertical p Determining the correlation between water level and mass


2/27

Data ObservationFILLING TANK

DRAININ

Mass (m)

(gram)

Height of Water (y)

(mm)

Mass (m)

(gram)

50 45 50

70 56 70

90 68 90

110 69 110

130

76 130

150

82 150

170 87 170

190 93 190

210

98 210

230 103 230

250 109 250

270 114 270

290 118 290

310 122 310

330

127 330

350 133 350

370 137 370

a = 10 cm

b = 7.5 cm

d = 10 cm

L = 27.5 cm

m.g

b

yd

ar

r

L


3/27

Partially Submerged ExperimentFILLING TANK DRAINING TANK Average

y (x) m/y2(y) x2 y2 xyMass Height

of water

(cm)

Mass

(g)

Height

of water

(cm)

M H

(g)

50 4,6 50 4,6 50 4,6 4,6 2,36294896 21,16 5,583527789 10,86956522

70 5,6 70 5,6 70 5,6 5,6 2,232142857 31,36 4,982461735 12,5

90 6,3 90 6,3 90 6,3 6,3 2,267573696 39,69 5,141890467 14,28571429

110 6,9 110 6,8 110 6,85 6,85 2,344291118 46,9225 5,495700847 16,05839416

130 7,6 130 7,6 130 7,6 7,6 2,250692521 57,76 5,065616823 17,10526316

150 8,2 150 8,2 150 8,2 8,2 2,230814991 67,24 4,976535524 18,29268293

170

8,7 170 8,7 170 8,7 8,7 2,246003435 75,69 5,04453143 19,54022989

190 9,3 190 9,3 190 9,3 9,3 2,196785756 86,49 4,825867656 20,43010753

210 9,8 210 9,8 210 9,8 9,8 2,186588921 96,04 4,781171111 21,42857143

66,95 20,31784226 522,3525 45,89730338 150,5105286

Table 1. Regression Linear, relationship between /

=

=

=

=9 150,5105286

9 522,3525= 0.0259

=522,3525 20,31784226

9 522,3525= 2.450750717

y= -0.02597x + 2.450


4/27

. /

y = -0.026x + 2.4508

R = 0.5657

y = -0.045x + 2.727

R = 1

0

0.5

1

1.5

2

2.5

3

0 5 10 15

m/y2(y)

Height of water (cm)

Graph of y and m/y2

Partially Submerged Experiment

m/y2

Theory

=

6 =

1

6

=

2=

= 2.727

Relative Mistake

=

= 10.13%

=

= 42,28 %


5/27

Calculating F-Hydrostatic

Mass Height of Water (m) F-Hydrostatic

50

0,046 1,037898

70

0,056 1,538208

90 0,063 1,9467945

110

0,0685 2,301548625

130 0,076 2,833128

150

0,082 3,298122

170

0,087 3,7125945

190 0,093 4,2423345

210

0,098 4,710762

F-Hydrostatic: 0,5gby2

0,510009,810,1y2

Table of Hydrostatic Pressure for partially submerged

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1 2 3

Heightofwater(m)

Hydrostatic Force (

Hydrostatic Force

Partially Submerged

Graph of Hydrostatic Force (Partially S


6/27

Fully Submerged ExperimentFILLING TANK DRAINING TANK Average

x2

y2

xy

Mass

Height

of water(cm)

Mass(g)

Height

of

water(cm) M (y) H (x)(g)

230 10,3 230 10,3 230 10,3 106,09 52900 2369

250 10,9 250 10,8 250 10,85 117,7225 62500 2712,5

270 11,4 270 11,3 270 11,35 128,8225 72900 3064,5

290 11,8 290 11,8 290 11,8 139,24 84100 3422

310 12,2 310 12,3 310 12,25 150,0625 96100 3797,5

330 12,7 330 12,8 330 12,75 162,5625 108900 4207,5

350 13,3 350 13,3 350 13,3 176,89 122500 4655

370 13,7 370 13,7 370 13,7 187,69 136900 5069

2400 96,3 1169,08 736800 29297

=

=

=

=8 29297 96,3 2

8 1169,08 927

=1169,08 2400

8 1169,08= 191.44

= .

Table 1. Regression Linear, relationship between


7/27

y = 40.655x - 189.38

R = 0.9994

y = 40.909x - 181.82

R = 1

0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20

Mass(g)

Height of water (cm)

Graph of h and m

Fully Submerged Experiment

M (y)

Theory

.

=

2

=

1

= 40.909

= 3

6

= 1 7.5 1

= 181.8181

Relative Mistake

=

= 5,293%

=

= 0,81227%


8/27

Calculating F-HydrostaticF-Hydrostatic:

1000 9,81 0,1 0,1 ( ,

)

Mass Height of Water (m) F. Hydrostatic

230

0,1035,1993

250

0,10855,73885

270 0,1135 6,22935

290

0,1186,6708

310

0,12257,11225

330

0,12757,60275

350

0,1338,1423

370 0,1378,5347

Table of Hydrostatic Pressure for fully submerged

0

0.020.04

0.06

0.08

0.1

0.12

0.14

0.16

4 5 6 7

Heightofwater(m)

Hydrostatic Force

Hydrostatic Force

Fully Submerged


9/27

Analysis Partially submerged is measured at the water level below 100 mm and lo

starting from 50 grams to 210 grams. For fully submerged it is measured

mm and loadings starting from 210 grams all the way to 370 grams. The vand b are determined for both sections and then compared to the theorTo find a and b, we used least square

For partially submerged experiment, ( = 0.025973326 and = 2.45We then used the equations =

and =

+

to f

theoretical values.

Relative mistake for a = 42.28% and b = 10.13%. The coefficient of correlobtained is R2= 0.565, which means that the x and y are not closel

For fully submerged experiment, ( = 41.24129196 and = 191.44Relative mistake for a = 5.29% and b = 8.12%. The coefficient of correlatiois R2= 0.999, which means that the x and y are very closely related.

We also obtain the value of hydrostatic force at each of the water level bformula = 0,5 for partially submerged and = for fully submerged.


10/27

Conclusion

The magnitude of hydrostatic force is perpendicular to the surface of tapparatus. As more volume of the object is submerged, the more hydforce will act on it.

As the weight of the load increases, the height of the water also increbecause more water is needed to balance the scales arm.

The values of a and b obtained from experiment and theory show a linrelationship between the relationship of mass and water level.

The weights that are added to the apparatus are able to be balanced water to the tank because there is hydrostatic force acting on the vertof the apparatus.

The sum of moments and hydrostatic force acting on the surfaces thatvertical is zero because the directions point straight to the hinge. The because it is not perpendicular


11/27

Modul H-05 Flow Rate Measuremen

Demonstrating various type of basic flow rate measurementprinciples


12/27

Data ObservationNo Manometer Reading (cm) Volume

(mL)

Time

(s)

Orifice Pipe Venturimeter Pitot Pipe

3 4 5 6 7 8

5 19,7 19,4 19,4 18,8 18 18,5 215 3,05

7,5 13,2 12,3 12 10,8 9,5 10,5 350 3,30

10 12,5 10,5 9,8 7,7 4,5 6,3 430 3,00

12,5 16,7 13,5 13,8 9,5 6 8,9 570 3,28

15

19,3 14,7 15,2 8,7 4 8,5 750 3,08

17,5 22,3 15,9 16,2 7,5 2,5 8,5 800 3,00

20 26,8 18,5 19,5 8 2 9,8 940 3,12

22,5

34,5 24 26 11,5 4 14 1050 3,03

d1 d2 A1

(m) (m) (m2)

Orifice

Pipe

0,029 0,02 0,00066

Venturi

meter

0,029 0,017 0,00066

Pitot - 0,019 -


13/27

Determining Flow Rate Coefficien(Cd)

Orifice Pipe = .

h3

h4

|h3-

h4|

Qorifice(X) Volum

e

Time

(m)

(m) (m3/s) (m3) (s)

0,197

0,194 0,003 0,000076179

8

0,0002

2

3,05 0

0,132 0,123 0,009 0,000131947 0,0003

5

3,3 0

0,125 0,105 0,02 0,000196695 0,0004

3

3 0

0,167

0,135 0,032 0,000248802 0,0005

7

3,28 0

0,193

0,147 0,046 0,000298303 0,0007

5

3,08 0

0,223 0,159 0,064 0,000351859 0,0008 3 0

0,268 0,185 0,083 0,000400699 0,0009

4

3,12 0

0,345 0,24 0,105 0,000450685 0,0010

5

3,03 0


14/27

y = 0.8664x

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0 0.0001 0.0002 0.0003 0.0004 0.0005

Qreal(m3/s)

QOrifice (m3/s)

Graph of QOrifice and Qreal

Graph of Linear Regression of Or

y = m . x Qreal= Cd . QORegression line obtained, y = 0,86

Value of Flow rate coefficient (Cd

Manual method

=

b = Cd = 0,8466784960

So, value of Cdorifice= 0


15/27

Venturi meter = .

h5

h6

|h5-h6|

Qventuri(X) Volume Time Qreal (Y)

(m) (m) (m3/s) (m3) (s) (V/t)

(m3/s)

0,194 0,188 0,006 0,0000778379 0,000215 3,05 0,0000704

0,12

0,108 0,012 0,00011008 0,00035 3,3 0,0001060

0,098 0,077 0,021 0,00014562 0,00043 3 0,0001433

0,138 0,095 0,043 0,00020838 0,00057 3,28 0,000173

0,152

0,087 0,065 0,0002562 0,00075 3,08 0,0002435

0,162 0,075 0,087 0,0002964 0,0008 3 0,0002666

0,195 0,08 0,115 0,00034077 0,00094 3,12 0,0003012

0,26 0,115 0,145 0,00038265 0,00105 3,03 0,0003465


16/27

y = 0.9617x

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0 0.0001 0.0002 0.0003 0.0004

Qreal(m3/s)

QVenturi (m3/s)

Graph of QVenturi and Qreal

Graph of Linear Regression o

y = m . x Qreal= Cd

Regression line obtained, y =

Value of Flow rate coefficient

Manual method

=

b = Cd = 0.9383930

So, value of Cdventur


17/27

Pitot Pipe

= .

h7 h8 |h7-h8| Qpitot(X) Volume Time Qreal (

(m) (m) (m3/s) (m3) (s) (V/t

(m3/

0,18 0,185 0,005 0,0000887589 0,000215 3,05 0,000070

0,095

0,105

0,01

0,00012552

0,00035

3,3

0,00010

0,045 0,063 0,018 0,00016841 0,00043 3 0,00014

0,06 0,089 0,029 0,00021376 0,00057 3,28 0,00017

0,04 0,085 0,045 0,00026628 0,00075 3,08 0,00024

0,025 0,085 0,06 0,00030747 0,0008 3 0,00026

0,02 0,098 0,078 0,00035057 0,00094 3,12 0,00030

0,04 0,14 0,1 0,00039694 0,00105 3,03 0,00034


18/27

y = 0.8654x

0

0.000050.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0 0.0001 0.0002 0.0003 0.0004 0.0005

Qreal(m3/s)

QPitot (m3/s)

Graph of QPitot and Qreal Graph of Linear Regression of Pity = m . x Qreal= Cd . QORegression line obtained, y = 0.86

Value of Flow rate coefficient (Cd

Manual method

=

b= Cd = 0.89246526639

So, value of Cdpitot= 0.8


19/27

Determining Head Loss Coefficie

Orifice Pipe =

, =

2

=

2

Variable Area

h3

h4

h=|h3-h4|

Qorifice (Y) V (Q/A2) (m/s) h =V2/2g

(m) (m) (Y) (X)

(m3/s)

5 0,197 0,194 0,003

0.00006707242

0,2243818

0.002321

7,5

0,132 0,123 0,009

0.00011617283

0,3376019

0.006964

10 0,125 0,105 0,02

0.00017318024

0,4562420

0.015476

12,5 0,167 0,135 0,032

0.00021905760

0,5531576

0.024761

15 0,193 0,147 0,046

0.00026264083

0,7751019

0.035594

17,5

0,223 0,159 0,064

0.00030979423

0,8488254

0.049522

20 0,268 0,185 0,083

0.00035279496

0,9590081

0.064224

22,5 0,345 0,24 0,105

0.00039680577

1,1030526

0.081247


20/27

y = 1.2924x

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000

hprkatikum(

m)

h' theory (m)

Graph of h' and h (Orifice)

Graph of head loss coefficient

y = m . x h = k.h |Regression line obtainedy = 1,

Value of head loss coefficient

Manual method

=

m = k = 1.2

So, value o


21/27

Venturi meter =

, =

2=

2

Variable Area

h5

h6

h=|h5-h6|

Qventuri (Y) V (Q/A2) (m/s) h =V2/2g

(m) (m) (Y) (X)

(m3/s)

5 0,194 0,188 0,006

0.000073164500,310563926

0.00529

7,5 0,12 0,108 0,012

0.000103470220,467270244

0.0105810

0,098 0,077 0,0210.00013687824

0,6314785440.01852

12,5

0,138 0,095 0,0430.00019586597

0,7656181160.03792

15 0,152 0,087 0,0650.00024081384

1,0728081770.05732

17,5 0,162 0,075 0,087

0.000278602101,174848004

0.07672

20 0,195 0,08 0,1150.00032031235

1,3273504270.10141

22,5 0,26 0,115 0,145

0.00035967376

1,526720416

0.12787


22/27

y = 1.1339x

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.00000 0.05000 0.10000 0.15000

hprkatikum(

m)

h' theory (m)

Graph of h' and h (Venturi meter)Graph of head loss coefficient of Ve

y = m . x h = k.h |h4-h3

Regression line obtained y = 1,13398

Value of head loss coefficient (kventu

Manual method

=

m = k = 1.133899256

So, value of kventuri= 1.133


23/27

Pitot Pipe =

, =

2=

2

Variable Area h7 h8 h=|h7-h8| Qpitot (Y) V (Q/A2) (m/s) h =V2/2g

(m) (m) (Y) (X)

(m3/s)

5 0,18 0,185 0,005

0.00008883955

0,248622015

0.005000

7,5 0,095 0,105 0,01

0.00012563810

0,37407329

0.010000

10 0,045 0,063 0,018

0.00016856120

0,505530279

0.018000

12,5 0,06 0,089 0,029

0.00021395397

0,612915741

0.029000

15 0,04 0,085 0,045

0.00026651865

0,858836807

0.045000

17,5 0,025 0,085 0,06

0.00030774923

0,940524812

0.060000

20

0,02 0,098 0,078

0.00035088811

1,062610658

0.078000

22,5

0,04 0,14 0,1

0.00039730255

1,222216344

0.100000


24/27

y = x

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.000 0.020 0.040 0.060 0.080 0.100 0.120

hpraktikum(

m)

h'theory (m)

Graph of h' and h (Pitot Pipe)

Graph of head loss coeffi

y = m . x h = k.h

= m

Regression line obtained

Value of head loss coeffic

Manual method

=

m = k = 1

So, value of kpit


25/27

Table Results

Flow Rate Coefficient

Graph Method Manual Method

Orifice pipe 0,8664 0.846678496044

Venturimeter

0,9617 0.938393092725

Pitot pipe

0,8654 0.892465266392

Head Loss Coeff

Graph Method

Orifice pipe 1,2924

Venturimeter 1,1339

Pitot pipe 1


26/27

Analysis flow rate coefficient formula for orifice pipe and venturimeter :

= . 2 1 2

1

determine the regression line (y = mx + a). Q is the value of y,

2 1 2

1

is the value of x, the flow rate coefficient (Cdvalue of m.

for the pitot pipe, the equation is: = . 2 1 2

because the diopening and end of pitot pipe is the same, so there is no difference in the areof x is 2 1 2

, the y is obtained from the values of Q. The manua

determined by using least square To determine the head loss coefficient (k), =

=

and h = k.h =

V which is the volume of the outflow that is measured for 3 seconds. The valuobtained by Q/A. The gravitational acceleration is 9,8 m/s2. The graphical metto find the linear regression (y = mx +a). The value of the x is h, the value of and the value of m is k. For the manual method, the value of k is determined bleast square


27/27

Conslusion

The value of flow rate coefficient (Cd) and head loss coefficient (k) can be de

experimentally and calculated by using the graphical and manual method. From Bernoullis equation, one can obtained the formulas to find the value o

coefficient: = . 2 1 2

1

for orifice and ventu

= . 2 1 2

for pitot pipe.

Flow rate can be determined by using the formula: Q =V (mL)

t (s)

The coefficient of head loss for orifice pipe is 1,2924. For venturimeter the v1,1339. And the value for pitot pipe is 1, all according to the graphs

The coefficient of flow rate for orifice pipe is 0,8664. For venturimeter the va0,9617. And the value for pitot pipe is 0,8654.

Orifice pipe has the least value flow rate coefficient than venturimeter and palso has the largest value of head lost compared to venturimeter and pitot p

mekflud modul 2 & 5

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