total pressure head

-

Republic of Iraq

Ministry of Higher Education

and Scientific Research

University of Technology-Electromechanical

Department

1436 2014

August 28 2014 Lab. of Fluid Mechanics Electromechanical Eng. Dept .

[2]

Experiment No. 1 Calibration of Bourdon Gauge

Description: Figure (1) shows the photography and schematic of bourdon gauge

device, this device consist of:

Figure (1) shows the photography and schematic of bourdon gauge device.

1. Piston

2. Weights Weights may be added to the piston so that a number of

predetermined pressures may be set up within the cylinder.


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3. Baseboard The cylinder is mounted on a baseboard which is supported on

leveling screws and fitted with a spirit level.

4. Gauge Connection The gauge under test is linked to the cylinder connection by a

flexible tube.

5. Waste Water Leakage of water past the piston is taken to waste through

connection to a second flexible tube. This tube is connected to a

tapping which is drilled into the cylinder and is opposite a n

annular recess in the cylinder.

6. Technical Data The following dimensions from the equipment are used in the

appropriate Calculations. Required these values may be checked as part

of the experimental procedure and replaced with your own

measurements.

Mass of piston Mp = 498 g

Diameter of piston D = 0.05767 m


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Nomenclature:

Column

Heading

Units Nom. Type Description

Mass of Piston g Mp Measured Given piston mass

Diameter of Piston

m D Measured Given piston diameter

Area of Piston m2 A Measured A =

D4

Mass of Load Kg Mw Measured Weights applied to the calibrator.

Total Mass Kg M Measured = +

Gauge Reading

KN/m2 G Measured The reading taken from the Bourdon Gauge.

Cylinder Pressure

KN/m2 P Measured =

Absolute Gauge Error

KN/m2 EA Measured =

%o Gauge Error

% EA Measured % = × 100

Objective: 1. To calibrate a pressure gauge Bourdon type in to determine the gauge error.

2. To determine the measurement errors in the reference pressure source used

for calibration.


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Method: To calibrate a pressure gauge by applying predetermined pressures generated

by loading weights on to a piston of known cross-sectional area (a "dead-weight

calibrator").

Equipment Required: In order to complete the demonstration of the Bernoulli apparatus we need a

number of pieces of equipment.

The Hydraulics Bench.

The Dead Weight Calibrator.

Weights.

Weigh-balance.

Pressure gauge.

Filling tube or Measuring Cylinder.

Theory: The use of the piston and weights with the cylinder generates reference pressure

(P):

=

Where :

=

And

F is the force applied to the liquid in the calibrator cylinder, M is the total mass

(including that of the piston), A is the area of piston.

The area of the piston can be expressed in terms of its diameter, D, as:


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=4

Readings and Results:- All readings should be tabulated as follows:

Mass of Piston (Mp) Kg Diameter of Piston (D) m Area of Piston (A) m2 Mass of Load (Mw) Kg Total Mass (M) Kg Gauge Reading(G) KN/m Cylinder Pressure (P) KN/m2 Absolute Gauge Error KN/m2 % Gauge Error

Plot a graph of gauge reading against absolute and % gauge error .

Conclusions: Comment on the accuracy of the gauge.

Comment on the size of gauge errors in relation to the errors in the reference

pressure measurements.

Is the relative height between the dead-weight calibrator and the gauge

important in the calib Discussion:-

1- What is the effect of rotation of piston on gage reading?

2- Will you obtain the same reading if you change the liquid?

3- Explain the effect of Hysteresis on the reading of the gage?

4- List the causes of reduces the percentage of error, when the pressure

increases?


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[8]

Experiment No. 2 Convergent-Divergent Tube

Objective:- To investigated the validity of the Bernoulli equation when applied

to the steady flow of water in a tapered duct.

Method:- To measure flow rates and both static and total pressure heads in a

rigid convergent/divergent tube of known geometry for a range of steady

flow rates.

Equipment:- In order to complete the demonstration of the Bernoulli apparatus we

need a number of pieces of equipment.

1. The Hydraulics Bench which allows us to measure flow by timed

volume collection.

2. The Bernoulli's Apparatus Test Equipment.


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3. A stopwatch for timing the flow measurement. As shown in figure

below.

Technical Data:- The following dimensions from the equipment are used in the

appropriate calculations. If required these values may be checked as part

of the experimental procedure and replaced with your own

measurements. The dimensions of the tube are detailed below:-

Tapping Position Manometer Legend Diameter (mm)

A h1 25.0

B h2 13.9

C h3 11.8

D h4 10.7

E h5 10.0

F h6 25.0


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Nomenclature:- Column

Heading

Units Nom. Type Description

Volume collected

m3 V measured Taken from scale on hydraulics bench The volume collected is measured in liters. Convert to

cubic meters for the calculations (divide reading by 1000).

Time to collect

s t measured Time taken to collect the known Volume of water in the hydraulics

bench. Flow rate m3/s calculated qv =V/t =volume/time to collect.

Manometer Legend

hx given Manometer identi cation labels

Distance into duct

m given Position of manometer tapping given as distance from the datum

at tapping h1.see test section dimensions.

Area of duct m2 A given The areas of the duct at each tapping see test section

dimension. Static head m h calculated Measured value from the

appropriate manometer. The manometer readings are taken in

(mm) water. Convert to (m) water for calculation?

velocity m/s v calculated Velocity of uid in duct= Qv/A

Dynamic head m calculated V2/2g see theory Total head m ho calculated h+V2/2g see theory

Distance into duct

m measured Position of the total head probe from the datum at tapping h1 .

Probe reading h8

m measured Measured value taken from h8.this is head recoded from the total

head probe.


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Theory - The Bernoulli Equation

The Bernoulli equation represents the conservation of mechanical energy

I for a steady, incompressible, frictionless ow:-

+ + = + +

Where

p = static pressure detected at a side hole, v = uid velocity.

z = vertical elevation of the uid, hence,

z1= z2 for a horizontal tube.

The equation may be derived from the Euler Equations b integration. it may

also be derived from energy conservation principles. Derivation of the Bernoulli

Equation is beyond the scope of this theory.

Other Forms of the Bernoulli Equation:- If the tube is horizontal, the difference in height can be disregarded

Hence:

+2

= +2

With the apparatus, the static pressure head p, is measured using a

manometer directly from a side hole pressure tapping. The manometer actually

measures the static pressure head, h , in meters which is related to p using the

relationship:

= /


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This allows the Bernoulli equation to be written in a revised form, i.e:

+ +

The velocity related portion of the total pressure head is called the dynamic

pressure head.

Total Pressure Head

The total pressure head, h°, can be measured from a probe with an end hole

facing in to the ow such that it brings the flow to rest locally at the probe end.

Thus, h° = h + (meters) and, from the Bemoulli equation, it follows, that

= .

Velocity Measurement The velocity of the ow is measured by measuring the volume of the ow, over a

time period, t. This gives the rate of volume ow as:

Qv = which in turn gives the velocity of ow through a de ned area A,ie. V=

Continuity Equation:- For an incompressible uid, conservation of mass requires that volume is

also conserved,

A1v1, =A2v2 (m3/s)


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Procedure - Equipment Set Up:- Level the apparatus

Set up the Bernoulli equation apparatus on the hydraulic bench so that its

base is horizontal; this is necessary for accurate height measurement from I the

manometers.

Set the direction of the test section.

Ensure that the test-section has the 14° tapered section CONVERGING in

the direction of ow. If you need to reverse the test-section, the total pressure head

probe must be withdrawn before releasing the mounting couplings.

Connect the water inlet and outlet.

Ensure that the rig out ow tube is positioned above the volumetric tank, in

order to facilitate timed volume collections. Connect the rig inlet to the bench ow

supply; close the bench valve and the apparatus ow control 1 valve and start the

pump. Gradually open the bench valve to full the test rig with water.

Bleeding the manometers

In order to bleed air from pressure tapping points and manometers, close I

both the bench valve, the rig ow 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

ow through the manometers to purge all air from them; then, tighten the air bleed

screw and partly open the bench valve and test rig ow control valve. Next, open

the air bleed screw slightly to allow air to enter the top of the manometers (you


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may need to adjust both valves in order to achieve this); re-lighten the screw when

the manometer levels reach a convenient height. The maximum volume ow rate

will be determined by the need to have the maximum (hl) and minimum manometer

readings both on scale.

If required, the manometer levels can be adjusted further by using the air

bleed screw and the hand pump supplied. The air bleed screw controls the air ow

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.

Procedure - Taking a Set of Results:-

Readings should be taken at 3 flow rates. Finally, you may reverse the test

section in order to see the effects of a more rapid converging section. Setting the

flow rate.

Take the rst set of readings at the maximum ow rate, then reduce the

volume flow rate to give the h1- h5 head difference of about 50 mm. Finally repeat

the whole process for one further ow rate, set to give the difference

approximately half way between that obtained in the above two tests.

Reading the static head

Take readings of the h1 — h5; manometers when the levels have steadied.

Ensure that the total pressure probe is retracted from the test-section.


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Timed volume collection

You should carry out a timed volume collection, using the volumetric tank,

in order to determine the volume ow rate. This is achieved by closing the ball

valve and measuring (with a stopwatch) the time taken to accumulate a known

volume of uid in the tank, which is read from the sight glass. You should collect

uid for at least one minute to minimize timing errors. Again the total pressure

probe should be retracted from the test-section during these measurements. If not

using the Fl-l5-301 software, enter the test results into the data entry form, and

repeat this measurement twice to check for repeatability. If using the software,

perform the collection as described in the walkthrough presentation.

Reading the total pressure head distribution

Measure the total pressure head distribution by traversing the total pressure

probe along the length of the test section. The datum line is the side hole pressure

tapping associated with the manometer hi. A suitable starting point is 1 cm

upstream of the beginning of the 14° tapered section and measurements should be

made at l cm intervals along the test-section length until the end of the divergent

(2l°) section.

Reversing the test section

Ensure that the total pressure probe is fully withdrawn from the test-section

(but not pulled out of its guide in the downstream coupling). Unscrew the two

couplings, remove the test-section and reverse it then re-assemble by tightening the

coupling.


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Readings and Results -:

Volume

collected

V (m3)

Time to

collect

t(sec.)

Flow

rate Qv

(m3/s)

Distance

into

duct (m)

Area

of duct

A (m2)

Static

head h

(m)

Velocity

v

(m/s)

Dynamic

head

(m)

Total

head

ho (m) h1 0.00

h2 0.0603

h3 0.0687

h4 0.0732

h5 0.0811

h6 0.1415

Discussion:-

Comment on the validity of the Bernoulli equation for

convergent ow

divergent ow

State clearly the assumptions made in deriving the Bemoulli equation and

justifications for all your comments.

Comparison of the total heads obtained by the two methods you have carried

out.


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[18]

Experiment No. 3 Flow through an ori ce apparatus

Objective:- 1. To determine the coefficient of discharge, velocity and contraction of a small ori ce.

2. Determine the losses in head, ow rate, and energy.

Method:- - Determination of coefficient of discharge by measurement of volume flow rate

from the ori ce. Determination of coefficient of velocity by measurement of total

head at the ori ce using pitot tube.

Determination of coefficient of contraction by measurement of jet diameter and the

vena contract diameter.

Description :- The ori ce Discharge accessory consist of a cylindrical tank which has a hole in

the base to accept one of ve ori ces, each with a different pro le. The exible

inlet pipe is connected to the quick release connector on the hydraulics bench.

Water is delivered to the tank via an inlet pipe which is adjustable in height and

tted with a diffuser to reduce disturbances in the tank. An over ow pipe maintains

the water at a xed level in the tank and excess water is returned to the sump tank

of the hydraulics bench as shown in the figure.


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An traverse assembly mounted beneath the base of the tank enables a pitot tube to

be positioned anywhere in the jet of water. Attached to the pitot is a ne Wire

which can be traversed a cross the jet to measure the diameter of the jet at the vena-

contract and so determine the contraction coefficient. The traverse assembly in

corporate a graduated knob which moves the pitot tube a distance of l mm for each

full rotation of the knob. Each graduation on the knob corresponds to a movement

of 0.1mm.

The pitot tube and a tapping in the base of the tank are connected to

monometer tubes adjacent to the tank. These allow the head over the ori ce and the

total head of jet to be measured and compared. The volumetric ow rate of the

water discharging from the ori ce on test can be determined using the volumetric

tank on the hydraulics bench.


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The different sharp edged of orifice plate shown in the figure below:

Theory:- Determination of Coefficients with constant head out ow:-

From the application of Bernoulli's Equation (Conservation of mechanical energy for a steady, incompressible, frictionless ow ):

The ideal orifice outflow velocity at the jet vena contract at (narrowest diameter)

V0 = 2

Where h is the height of fluid above the orifice.

The theoretical ow rate is

Qt = V0A0

The actual velocity is

V = CV 2

CV is the coefficient of velocity, which allows for the effects of viscosity


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and, therefore CV < 1

For the pitot tube hc =

V= 2

Hence, Cv=

The actual ow rate of the jet is de ned as:

Qact = Acv

Where Ac is the cross- sectional area of the vena contracta given by:

Ac = CcA0

Where

Cc= =

A0 is the ori ce area and Cc is the coefficient of contraction and therefore,

Cc < 1

Hence

Qact = Cc Ao Cv 2

But Cd = Cc * Cv

So finally,

Qact = Cd Ao 2

If Cd is assumed to be constant, then a graph of Qt plotted against will be linear and the slop, S = Cd A0 2

The losses as head:

hL = ho _ hc


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The losses in ow rate:

QL = Qth _ Qact

The losses in energy is:

Plost= QLhL

Procedure- Equipment set up:-

Position the apparatus across the channel on the top of the hydraulic bench

and level it using the adjustable feet and the spirit level on the base connect the

exible in let pipe to the hydraulics bench snop connector in the top channel. Place

the end of the over ow tube directly in to the hydraulics bench overflow, and adjust

the inlet pipe to the approximate level of the head required for the experiment.

Turn on the pump and open the bench valve gradually. As the Water level

rises in the reservoir towards the top of the over ow tube. The bench valve to give

a water level of 2 to 3 mm above the over ow level, with the end of inlet tube fully

submerged. This will ensure a constant head produce a steady flow through the

ori ce.


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Processing Results:- All reading should be tabulated as follows:

Orifice Dia. (m)

Vena Contracta Dia. (m)

Orifice Head (m)

Pitot Head (m)

Volume (m3)

Time (s)

Flowrate (m3/s)

Cv Cc Cd

Discussion:-

- Is it justi alble to assume that Cd is Constant over the range of steady ow tested?

- Why are the Cd values signi cantly less than 1.0? - Comparing the Cd value for the steady and falling head tests, which value is

likely to be more reliable?


[24]


[25]

Experimental No (4) Discharge over weirs

Objective:-

The purpose of the experiment:

1- Calculate the rate of ow through a rectangular gap.

2- Finding coefficient of discharge.

3- Calculate the loss of the energy while water passes the gap.

Equipment:-

Figure (1) shows the outline of the device use in this exp.

Figure (1) discharge over weirs


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The experiment theory:-

We take two points showing the water molecules uidity. Point (1) before

the gap, point (2) at the vertical axis of the middle of the gap, by neglecting the loss

of the energy and applying the rule of Bernoulli between two environments (1) and

(2)

+2

+ = +2

+

Since that the area of the tank section is larger than the area of gap section. We can

neglect water motion in point (1).

And since point (1) is open to the atmosphere which means (P1=0). And also we

can assume that the pressure equals to the atmospheric pressure

+ = =

u2= The theoretical speed of the water falling over the gap.

The area of the slice at the depth dh is ( dA=bdh) where b= the hole width.

Then,


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dQ= uzbdh = 2 .

with integration we can calculate the theoretical ow rate through the

gap

Qth = 2 .

Qth = 2 . (1)

Notice that there is at retraction in the water bundle while it passes through the gap.

The retraction occurs with the vertical direction from the Top and the bottom of the

sharp end. Also there is a retraction occurs in the bundle with the horizontal

direction.

Now we can calculate the real water ow by the tank weight

Qact= (2)

Cd= (3)

Qact= Cd × Qth

= Cd. 2 . (4)


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Working steps:-

1- Leveling device with the horizontal situation

2- We operate the pump and open the processing value to fill the tank with Water

until the water begins to full on the weir

3- We close the water supply value. Allow the excess water to fall until its level

equals with the level of the weir lower edge

4- Nut is rotated to move the hook until the applicability of its top with water level

consider it the zero readings of the device.

5- Now we open the supplying valve so that water passes over the weir, and

measure the total pressure column (H). Then we calculate the spent time by

collecting a certain amount of water tank. We open a larger gap in the valve than

the rst reading to increase the ow and measure the reading eight times by

gradually increase the ow.

b=30 mm

H=Reading of martin

m= mass of water

t= time

H(m) M(kg) T(s) Log h Log Qact

Qth (m3/s)

Qact (m3/s)

Cd


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And also the mean value of (Cd) can calculated from the Figure by using the

relationship between (log H) and (log Qact )

The equation (4 ) is wrote as follows:

Qact = KHn

And take a logarithm to each side of this equation.

Log( Qact) = log(K) + n log(H)

K = Cd 2 .

Cd =

From this sketch we can speci cation the value (n) which means the slope, and (log

K) means the vertical distance for the cutting part.


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Discussion:-

1- Discuses the value Cd that obtained from gure (log Qact) (log H) and compare

them with those from table.

2- Plot the relationship between Qact .H

3- Compare between value of Cd which is obtained for weirs with the applied

values for venturi tube and hole.

4-" give a conclusion for the relationship between'(log Qact)(l0g H)?

Is the values of (n) (k) exist with the theoretical values.


[31]


[32]

Experiment No. 5 Impact of Jet

Object:- 1. Measure the momentum of water fountain clashes with a flat or curved

Plate (hemispherical).

2. Compare this force with the rate momentum after and before clash.

Equipment:-

Figure (1) shows the outline of the device use, consists of transparent glass

cylinder ( s ),put in the middle a tube with a jet at the end allows the water to come

out of t in the form of a fountain clashes with the plate attached with a holder , the

holder attached with the arm that is hanged in the rotation center and free from the

other edge. The arm is balanced with the horizontal when the mass is(m)at the zero

mark on the arm, by rotating it at the end of the spring until it touches the guide

balance attached the arm with the surface of the cylinder without pushing it, when

you move the mass with a distance (x) the balance arm deviates to the lower to put

the guide back we pump the water from the processing system to come out of the

jet in the form of fountain , we can control the water by a valve until the

strengthening of the balance arm.


[33]

Figire (1)


[34]

Theory of experience:-

The momentum equation for fixed blade with assumptions :

- Steady

- Incompressible

- Frictionless

F = Q(V V )

Then,

F = Q(U COS U COS ) (1)

According to Newton's third law (For every action, there is an equal and opposite reaction)

=

= ( ) Assuming that there are no losses on the surface and the surface is open(open system)

U1= U2

And the jetting is vertical = 0

= ( ) (2)

To account the speed (U) by using Bernoulli's equation.

U1=U2- 2gs (3)

(s) is the distance between the jet and the surface of the blade

Notice:-

1. Flat plate = 90°


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2. Hemispherical plate = 180°

Way of Working:- 1- Put the device in a setting situation that the arm is in a

balanced situation. 2- Make the water ow through the supplying water and put

the jet towards the central of the plate by adjusting the springs of the base.

3- Change the flow then the weight place until it balance. 4- Took a series of readings with an equal increasing of the

weight place. 5- Return the steps (1-4) for each place.

Readings and Results:- S=37mm, L=15.25 Cm, d=l0Cm

R N

U m/s

U m/s

X m

Q m/s

T Sec


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Discussion:- l. plot the relationship between R and Q for each type of surface plate .

2. Plot the relationship between R and X for each type of surface plate .

3. Discuss the relationship between F and S. ‘

4. Explain from Bernoulli equation that U=U and are those values are equals I J or not.

5. At any angle the force will be maximum? Explain this from the mathematical equations.


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total pressure head

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