fluid mech & machinery

7/29/2019 Fluid Mech & Machinery

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Prepared By: Dr. Sumit Gandhi & M.L. Rathore,Civil Engg Dept, JUET Guna (M.P.): 1

DEPARTMENT OF CIVIL ENGINEERING, JUET GUNA

FLUID MECHANICS & MACHINERY LAB

(COURSE CODE: 10B17CE372)

CONTENTS

EXP. NO. NAME OF THE EXPERIMENT PAGE NO

-- Report writing 2 3

1. Verification of Bernoullis Theorem 4 6

2. Determination of Frictional Losses in Pipes 7 8

3. Determination of Minor Losses in Pipe 9 12

4. Reynolds Dye Experiment for Flow

Characterization

13 14

5. Calibration of Venturimeter 15 17

6. Calibration of V- Notch and Rectangular Notch 18 20

7. Calibration of Orifice meter 21 23

8. Calibration of Pitot Tube 24 25

9. Determination of Metacentric Height 26 28

10. Determination of Cc, Cv and Cd of an Orifice 29 32

11. Verification of the impulse momentum equation 33 35

ADDITIONAL/DEMONSTRATION TYPE EXPERIMENT

12. Experiments on open channel 36 38

13. Experiments on wind tunnel 39 41

14. Performance characteristics of a centrifugal

pump

42 45

15. Study of various types of pump cut section

models and turbines

--

-- References 46


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INSTRUCTIONS FOR LABORATORY REPORT WRITING

A full report is an extensive account of experiment, such as may be required for external

readers. It should be a standalone document and so is likely to include a description of the

apparatus and a summary of the experimental procedure.

A full report is not to exceed 1500 words (excluding Tables and Diagrams). It is to be

organized under the following headings:

OBJECTIVE/OBJECTIVES

EXPERIMENTAL SETUP WITH DIAGRAM

THEORY TO BE USED FOR EXPERIMENT

EXPERIMENTAL METHOD

OBSERVATIONS/DATA COLLECTED

SAMPLE CALCULATIONS

EXPERIMENTAL RESULTS

DISCUSSION/CONCLUSIONS (Including that of errors)

ERROR ANALYSIS

COMMENTS

OBJECTIVES

It contains the aim of the experiment and how the author is going to achieve his aim.

EXPERIMENTAL SETUP WITH DIAGRAM

Write every experimental setup and instruments you used with their dimensions. Draw a

neat sketch of experimental setup.

EXPERIMENTAL METHOD

It should contain a brief description of experimental method, a neat sketch of experimental

setup.

THEORY TO BE USED FOR EXPERIMENT

Write theory behind your experiment briefly.

OBSERVATIONS/DATA COLLECTED

Write down all data collected by you and also attached the signed lab data sheet.


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SAMPLE CALCULATIONS

Give the sample calculations.

EXPERIMENTAL RESULTS

Represent experimental results in tabulated form and diagrams.

DISCUSSIONS/ CONCLUSIONS

Compare your results with available reported results from standard literature. Give the

reason of departure of your results from reported results.

The conclusions contains a summary (what has been done and what are the main results)

and in addition to that some future prospective.

ERROR ANALYSIS

Analyze error associated with your experiment.

COMMENTS

Substantiate the error associated with your experiment.

Note:

Failure to submit the report and at tend the viva voce wi ll result in a zero mark.


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Experiment No - 1

VERIFICATION OF BERNOULLIES THEOREM

Objective

To Verify the Bernoullis theorem.

Introduction

The Bernoulli theorem is one of the most important equations of fluid mechanics. The

theorem is based on the law of conservation of energy. According to the Bernoulli theorem,

in an ideal, incompressible, steady and continuous flow, the sum of the pressure energy,

potential energy and the kinetic energy per unit weight of the fluid is constant.

The energy per unit weight of the fluid (N.m/N) has got the dimensions of length (L) and can

be expressed in meters of the fluid column, commonly called head. Thus according to the

Bernoulli theorem, the sum of the pressure head ( /p ) datum head (Z) and the velocity

head ( g2/V 2 ) is constant, i.e.

g

VZ

p

2

2

Constant

In case of real fluids, because some energy is always lost in overcoming frictional resistance,

the Bernoulli equation for real fluids is

L2

2

221

2

11 HZg2

VpZ

g2

Vp

Where LH is the loss of head from sections 1 to 2

Theory

Bernoullis theorem states that the total energy of an ideal fluid for steady irrotational flow

remains constant along a stream line. The total energy in the flowing fluid is the sum of the

flow energy, the potential energy and the kinetic energy. In fluid mechanics energy of unit

weight of fluid is expressed as head. The pressure head, datum head, and velocity head are

represented as p/, z, and v2/2g, respectively. Therefore the Bernoullis theorem can be

represented by the following equation-

H = g

VZ

p

2

2

constant

H = total head

p/ = pressure per unit weight or pressure head

z = potential energy per unit weight or datum head

v2/2g = kinetic energy per unit weight or velocity head

= specific gravity of fluid

p, is the pressure at a point in fluid, v is the velocity at that point and z is the height of that

point above any arbitrarily selected datum.


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Apparatus

Supply water tank, discharge measuring tank, variable area duct with minimum area at the

middle with connections to piezometric tubes at different sections, stop watch, meter scale.

Fig. 1 Experimental setup

Procedure

1. Measure the distances from an end to locate the position of piezometers andcalculate the area of cross section of duct at all piezometric points, also measure the

area of discharge measuring tank.

2. Open the supply valve and adjust the outlet so that the water level in the inlet tankremains stable

3. Remove air bubbles from the piezometric tubes with the help of rubber pipe.4. Measure the height of water level in different piezometers above an arbitrarily

selected horizontal plane.

5. Measure the discharge passing through the duct by measuring the volume of watercollected in the tank for a selected period t seconds.

6. Repeat step 3, 4, 5 for one more discharge value.


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Observations and Calculations

Area of Tank (A) = Length X Width = cm2

Width of the duct = cm

Table 1. Height of duct at various piezometric points

Piezometric

point1 2 3 4 5 6 7 8 9 10 11

Height (cm)

Table 2. Discharge calculation

Table 3. Observations for determination of various heads

Run

No.

Piezometer

No.

Distance

(cm)

Area of

duct a

(cm2)

Piezometric

head

p/ + z (cm)

Velocity

v = Q/a

(cm/s)

v2/2g

(cm)

Total

Head

H (cm)

1. 1

2

3

4

5

67

8

9

10

11

2. -Do- -Do- -Do- -Do- -Do- -Do- -Do-

Results

Plot the graphs, taking piezometric points along X-axis and velocity head, piezometric head,

total energy head along Y-axis.

Discussion

Precautions

1. At the time of observation, ensure that water level in the supply tank has becomestable.

2. Air should not be present in the piezometric tubes and duct.3. Maintain the water level in the tank above the suction point of pump to avoid the

entry of air into the system.

Run no.Initial Level h1

(cm)

Final Level h2

(cm)

Time t

(sec)

Discharge

Q = A (h2 - h1) / t

(cm3/s)

1.

2.

3.


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Experiment No - 2

FRICTIONAL LOSS IN PIPES OF DIFFERENT DIAMETERS

Objectives

To determine the friction factor for pipes of different sizes,

a. 1.7cm diameterb. 2.7cm diameter

Introduction

The Darcys Weisbach equation commonly used for the computation of the loss of head in

pipes is given below.

g2

V.

D

L.fh

2

f

For accurate determination offh a suitable value of f should be known. Moodys charts are

commonly used in practice for the estimation of the value of f. however, for the turbulent

flow; the value of f depends upon the height of roughness projections. It is very difficult to

estimate the value of the roughness projection, as it depends not only on the material but

also on the age and use of the pipe. Therefore, the value of f is sometimes determined in

the laboratory for estimation of the value of fh

Theory

Transportation of fluids through pipes is frequently dealt with by engineers. Distribution of

water and gas for domestic consumption through pipes is an example. Experimental

observations by Froude on long, straight and uniform diameter pipes on the flow of water

indicated that head losses due to friction h f between two sections of pipes varied in direct

portion with the velocity head V2/2g, the distance between the two sections L, and inversely

with the pipe diameter, d. By introducing a co-efficient of proportionality f, called the

friction factor. Darcy and Weisbach proposed the following equation for head loss due to

friction in a pipe.

g2

V

d

Lfh

2

f Or, 2f

LV

gdh2f

Experimental setup

The experimental setup consists of:

1. Pipes of different diameter, 1.7cm, 2.1cm, 2.7cm2. Two pet-cocks on each side with the help of which flow is regulated3. A valve fitted to each pipe with the help of which flow is regulated4. An U tube manometer connected to the pressure tapping of each pipe5. A discharge measuring tank fitted with a piezometer tube and a graduated scale to

measure the depth of water collected.


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Procedure

1. Record the diameterd of the pipe and the length L between the sections attachedto the limbs of U-tube manometer.

2. Open the supply valve to allow water to flow in one pipe only.3. Record the initial water level in the piezometer fitted to the discharge measuring

tank and starts the stop watch and finds the depth of water collected for a particular

time by recording the final reading of the piezometer.

4. Knowing the area of the measuring tank, flow rate through the pipe can be obtained.5. Record the readings of the two limbs of the manometer, difference of which gives

the head loss hf .

6. Repeat the procedure at least ten times at different fluid flow rate.7. Repeat the above procedure for other pipes.

Observations

Density of the manometer fluid m = 13.6 g/cc

Density of water f = 1g/cc

Area of measuring tank A = 50 cm X 40cm =2000 cm2

Length of the test pipe L = 90 cm

Diameter of the test pipe d = 1.7cm, 2.1cm

Area of pipe a =

Observation Table

S.No Measuring Tank Reading

Initial Level y1 Final Level y2 Difference y = y1 - y2 Time t (sec)

1.2.3.

Manometer Reading Manometer Difference Manometer difference cm of

water

h1 h2 h = h1- h2 hf= h (m - f)

S.No. Discharge, Q = y x A/t Velocity of water = Q/a2

f

LV

gdh2f

Calculate friction factor for each experiment and also Reynolds number. Plot Reynolds

number with friction factor in a log graph paper.

Results

Discussion

Concluding Remarks


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Experiment No - 3

MINOR LOSSES IN PIPE DUE TO FITTINGS

Objective

To determine form (minor) losses in a pipe.

Introduction

In most of the pipe flow problems, the flow is steady and uniform, and the loss of head due

to friction is predominant. In addition to the loss of head due to friction, the loss of head

also occurs whenever there is a change in the diameter or direction, or when there is any

obstruction in the flow. These losses are called from losses or minor losses.

The form losses are usually small and insignificant in long pipes of small length; they are

quite large compared to the frictional loss. In some small length pipes, they may be even

more predominant than that due to friction.

Experimental setup

The set-up consists of a small diameter pipe which suddenly changes to a large diameter.

After a certain length, the large diameter suddenly reduces to a small diameter. The small

diameter pipe has a 90o

bend. Suitable pressure tapping points are provided to measure the

loss of head with an inverted U- tube manometer. The loss of head can be determined by

connecting the manometer across the sections where the changes occur in the flow.

The pipe is connected to a constant-head supply tank. The water is collected in a measuring

tank for the determination of the discharge.

Theory

The form losses are usually expressed as

Where,

V is the mean velocity of flow,

K is the form loss factor, which depends upon the type of obstruction or change, the

type of the loss off head due to sudden expansion is usually determined by the Borda -

Carnot equation

g2

VVH

2

21L

(a)

Where,

V1 is the velocity in the smaller pipe and

V2 is the velocity in the larger pipe.

g

VKHL

2

2


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Eqn. (a) can be expressed as

g2

VKH

2

1eL

Where,

eK is the coefficient for sudden expansion. The value of eK depends upon

21 d/d ratio.

For gradual expansion (diffusers), the value of eK depends upon the 21 d/d ratio and

the angle of divergence.

The loss of head due to sudden contraction is usually expressed as

g2

VKH

2

1cL

Where 1V is the velocity in the smaller pipe

The value of Kc is usually about 0.3 to o.5

For gradual contractions, the loss of head is considerably small.

The loss of head at a bend can be expressed as

g2

VKH

2

bL

The value of Kb depends upon the angle of bend, the ratio of the radius of curvature of the

bend to the diameter of the pipe (i.e. r/D ratio), and the roughness of the pipe.

For a 900 bend, the value of Kb usually varies between 0.60 and 0.90.

Procedure

1. Measure the diameters of pipes. Also measure the dimensions of the collecting tank.2. Open the inlet valve.3. Connect the manometer across the sections for which the loss of head due to

sudden expansion is to be measured.

4. Gradually adjust the exit valve. When the flow becomes steady, measure themanometeric deflection (h)

5. Take the initial reading of the measuring tank and start the stop watch. Note the risein water level for a suitable time period.

6. Repeat steps 4 and 5 for different discharges.7. Repeat steps 3 to 6 for the loss of head due to sudden contraction.8. Repeat steps 3 to 6 for the loss of head due to bend.


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Observations and calculations

Diameter of the smaller pipe, D1 = 1.7 cm

Area of smaller pipe, A1 = 2.269 cm2

Diameter of the larger pipe, D2 = 2.8 cm

Area of Larger pipe, A2 = 6.157 cm2

Density of mercury, S2 = 13.6 g/cm3

Density of water, S1 = 1 g/cm3

Dimension of the measuring tank

Length L = Width B = Area A =

(a) Sudden Expansion

S.N Discharge measurement Loss of head1V

g2

V21

2V

g2

V22

eK

Initiallevel

Final

level

Rise

In

level

Volume Time Q Deflection

(h)fh

S/S1 12

1.

2.

3.

(b) Sudden contraction


g2

V21

2V

g2

V22

cK

Initial

level

Final

level

Rise

In

level


(h)

fh

S/S1 12

1.

2.

3.

(c) 900

bend


g2

V21

2V

g2

V22

bK Initial

level

Final

level

Rise

In

level


(h)fh

S/S1 12

1.

2.

3.


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Result

Average values of factor K for

(a) Sudden Expansion, eK =(b) Sudden contraction, cK =(c) 900 bend, bK =

Precautions

1. There should be no air bubble in the inverted U- tube and its tapings.2. Readings should be taken when the flow is steady.3. Collect adequate quantity of water for the determination of discharge.

Discussion

Concluding Remarks


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Experiment No - 4

CRITICAL REYNOLDS NUMBER

Objectives

1. To study the laminar, transition and turbulent flow characteristics.2. To determine the critical Reynolds number.

Introduction

Laminar flow occurs in a pipe at low velocities when the Reynolds number Re is less than

about 2000. Viscosity plays an important role in a laminar flow, the fluid moves in layers. If a

dye is injected, it appears as a straight line.

As the velocity in the pipe is increased, the flow changes from laminar to turbulent, with a

transition stage between two types of flow. In the transition stage, the dye thread gradually

starts breaking and becomes ill-defined. The dye streak appears wavy and disturbed.

Finally, at high velocities, the dye mixes completely and the whole pipe is filled with the

coloured fluid, and the flow becomes turbulent. In the turbulent flow, the momentum

transfer plays an important role.

If the flow is now gradually decreased, a stage is reached at which the flow changes back

from turbulent to laminar and the dye thread again appear as a straight line.

The velocity at which the flow changes from laminar to turbulent is called the upper critical

velocity and the corresponding Reynolds number as the upper critical Reynolds number.

The velocity at which the flow changes back from turbulent to laminar is called the lower

critical velocity and the corresponding Reynolds number is known as the lower critical

number.

The upper critical number is not a fixed quantity as it depends upon a number of factorssuch as initial disturbance of flow, the shape of the entry to the pipe etc. on the other hand,

the lower critical Reynolds number is well established, and its value is usually about 2000.

There is a transition stage for the Reynolds number between 2000 to 4000, and the flow is

gradually turbulent when the Reynolds number is greater than 4000. However, the flow

may not become turbulent in some cases even at a higher value of the Reynolds number.

Theory

The Reynolds number Re is defined as follows

dv

forceViscousforceInertialRe

If Re < 2000 The flow is laminar.

2000 < Re 4000 The flow is turbulent.


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The velocity at which the flow changes from laminar to transition is called lower critical

velocity and the velocity at which the flow changes from transition to turbulent is called

upper critical velocity.

Apparatus

A perplex tube of diameter 2.5 cm fitted at the bottom of a reservoir tank, die injector,

measuring tank, piezometer, stop watch, dye pot.

Procedure

1. Fill the tank with water.2. Open the control valve so that water can flow through the tube.3. Inject the dye into the fluid stream.4. Collect fluid for some particular time interval.5. See the dye filament characteristics.6. Change the flow rate of fluid and repeat the same procedure.

Observations

Area of measuring tank = 50 cm X 40 m = 2000 cm2

Diameter of Glass tube (d) = 2.5 cm.

dv

Re

v = average velocity of fluid in m/s

= density of fluid in kg/m3

= 1000 kg/m3 for water

= viscosity of fluid in pa-s= 8 X 10

-4Ns/m

2for water.

Observation Table

Discharge Calculation

Sl. NoInitial reading

(h1)

Final reading

(h2)

Time of collection

(t)

Volumetric flow

rate Q = {A x (h2-

h1)}/t (m3/s)

Results

Discussion

Conclusions


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Experiment No - 5

VENTURIMETER TEST

Objectives

1. To calibrate venturimeter.2.

To determine the co-efficient of discharge.

Introduction

A venturimeter is commonly used to measure discharge in closed conduits having pipe flow.

It consists of a converging cone, a throat section and a diverging cone. An expression for the

discharge is derived by applying the Bernoulli equation to the inlet and the throat and using

the continuity equation, discharge is given by:

gH

AA

AACQ

dth2

2

2

2

1

21

Where Cd is the coefficient of discharge, A1 and A2 are the area of cross section at the inlet

and throat, respectively; H is the difference of the peizometeric heads expressed as the

height of the liquid column.

The converging cone has an angle of convergence about 200, the flow in the converging

cone is accelerating and the loss of head is relatively small. The coefficient C d takes into

account this loss of head. The value of Cd is usually between 0.97 and 0.99.

In the diverging cone, the flow is decelerating. To avoid excessive head loss, it is essential to

keep the angle of divergence small, usually 50 to 70.

Generally the diameter at the throat D2 is between to times the inlet diameters D1. The

smaller the D2 / D1 ratio, the more is the pressure difference. However, the pressure at the

throat should not be allowed to drop to the vapour pressure to prevent cavitation.

For accurate results, the venturimeter should be preceded by a straight and uniform length

of about 30 D1 or so. Alternatively, straightening vanes can be used in the pipe.

Theory

Venturimeter: It is a device for measuring rate of flow in a pipeline. Its theoretical analysis is

based on (1) Bernoillis equation and (2) Continuity equation


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Procedure

1. Record the inlet pipe diameter (D1) throat diameter (Dt) and the densities ofmanometer fluid and hat of flowing fluid

2. Open the regulation valve and under steady state condition note the readings h1 andh2 in the two limbs of the mercury differential manometer.

3. Note the initial level of water in measuring tank. Collect the water in the measuringtank for certain time and note the final level of water in measuring tank. Calculate

the actual discharge.

4. Vary the flow rate through the system with the regulation valve and take thedifferent readings.

Observations

Densities of manometer fluid mercury at room temperature = 13.6 g/cm3

Density of water at room temperature = 1 g/cm3

Area of measuring tank = 40 cm x 50 cm

= 2000 cm2

Diameter of pipe D1 = 2.8 cm

Diameter of throat Dt = 1.4 cm

Area of Pipe A1 = D12/4 = 6.15 cm2

Area of Throat A2 = Dt2/4 = 1.54 cm

2


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Observation Table


Initial Level y1 Final Level y2 Difference y = y1 - y2 Time t (sec)

Manometer Reading Manometer

Difference

Manometer difference cm of

water

h1 h2 h = h1- h2 H = h (m - f)/ f

Calculation Table

Results

Co-efficient of Discharge Cd =

The fluid flow rate =

Discussions

Concluding Remarks

S.No Volumetric flow rate

Qact= A(y2-y1)/t

Volumetric flow rate at throat

gH

AA

AAQ

th2

2

2

2

1

21

Cd = Qact/Qth


18/46


Experiment No - 6

NOTCH AND WEIR EXPERIMENT

Objective

To study the flow over a notch or a weir and to find the coefficient of discharge for it along

with to calibrate it for discharge measurement in a free surface flow

Introduction

AV-notch is commonly used for the measurement of small discharges in an open channel. A

V-notch is of the shape of a triangle with its apex down and base at top. A V-notch usually

consists of a metal plate with a sharp crest having a bevel edge on the downstream so that

the liquid springs off the notch with only a line contact. The stream of liquid is called the

nape. The nape should be fully ventilated so that the pressure below it is atmospheric.

A rectangular notch consists of a thin metallic plate placed across a channel so that the

water flows over it with a free surface. Rectangular notch is used for the measurement of

discharge in an open channel. The discharge Q is computed from the head H over the crest,as there is a unique relationship between the discharge Q and the head H.

The crest of the notch is sharp-edge with a bevel edge on the downstream surface so that

the sheet of water (nape) has only a line contact with the crest. Ventilation holes are usually

provided on the side walls on the downstream of the crest so that the nape has atmospheric

pressure below it.

Theory

A weir is an obstruction placed across a free surface of a stream flow such that the flow

takes place over it. Notches are opening cut in a metallic plate and installed in flumes orsmall channels. Installation of a notch is exclusively for the purpose of measuring the

discharge in the steam.

A sharp crested weir or notch for the measurement of discharge generally have a regular

geometrical shape i.e. triangular, rectangular. The free surface flow taking place over it

acquires steady state conditions such that the discharge is uniquely related to the head H

over the crest of the notch, measured at a distance about 3 to 4 times H from the crest

towards upstream.

The discharge over a Triangular or V-Notch is given by the formula

2

5

d H2

tang2C15

8Q

The discharge over a Rectangular Notch is given by the formula

2

3

dBHg2C

3

2Q


19/46


Where,

is the angle of Triangular Notch

B = Width of Rectangular Notch

H = Head over the Notch

Cd = Discharge Coefficient

Discharge Coefficient (Cd) is the ratio of actual volumetric flow rate to theoretical volumetric

flow rate i.e.,

ltheoretica

actuald

Q

QC

In actual practice, the discharge over a notch is considerably less than indicated by the

above formula without considering Cd i.e., the formula is derived on the basis of frictionless

one dimensional flow. The discrepancy arises due to real flow effects like viscosity, end

contractions, nappe suppression, ventilation of weirs etc. So the actual discharge is obtained

by multiplying the theoretical discharge by Cd, as given in the above formula.

Apparatus

A tank fitted with a notch, Perforated plates, discharge measuring tank fitted with a

piezometric tube and a graduated scale, Triangular notch with varying angles, Stop watch,

hook gauge with a vernier scale.

Experimental Set Up

The set up consists of-

1. A tank on the raised platform.2. A water inlet pipe with a regulating valve.3. Vertical perforated plates (Baffle plates) are fitted in the tank having the notch to

decrease the turbulence and thereby velocity of approach.

4. A hook gauge with vernier scale.5. A discharge measuring tank fitted with a piezometric tube and graduated scale to

measure the flow through/over the notch.


20/46


Procedure

1. Record the geometrical features of the notch.2. Allow the water into the tank till it just starts passing over the notch.3. Stop the supply of water and record the level of water by hook gauge when no water

passes over the notch. This gives level of still of crest (H1).

4. Increase the supply of water till the head over the still of notch becomes constant.Record the level H2 of free liquid surface. Difference of the two readings (H2-H1) gives

the head over the still causing flow.

5. Measure the flow rate (Q) with the help of discharge measuring tank and stop watch.6. Vary the flow rate through the system with a regulating valve and take eight

different readings.

7. Repeat the experiment for different type of Notches.Observation

Area of measuring tank (A) = 50 cm X 40 cm = 2000 cm2

Angle of V-Notch = 600

Width of Rectangular Notch (B) =

Observation Table

S.

No.

Initial water

Level above

notch

H1 (cm)

Final water

level above

notch

H2 (cm)

Initial level of

tank

h1 (cm)

Final level of

tank

h2 (cm)

Time for water

collection in

tank t (sec)

1

2

Calculation Table

Sl. No. Qact = A (h2 h1) / t

QtheCd = Qact/ QtheFor V-

notch

For Rect.

notch

1

2

Results



Discussions

Concluding Remarks


21/46


Experiment No - 7

ORIFICE METER TEST

Objective

Calibration of orifice meter.

Introduction

An orifice meter consists of a thin circular plate with a central hole. The plate is inserted in a

pipe for the measurement of discharge. The orifice plate is clamped between flanges of the

pipe. The beveled edge of the orifice is kept on the downstream side. As the fluid flows

through the orifice, there is a pressure difference between an upstream section and the

vena-contracta. The vena-contracta forms at a distance of about d1/2 from the plane of the

orifice, where d1 is the diameter of the pipe. The pressure difference between the upstream

section and the vena-contracta is used for the measurement of discharge.

Theory

Orifice-meter: It is a device for measuring rate of flow in a pipeline.

gHAA

AACQ dth 2

2

2

2

1

21

A1 = Area of Pipe

A2 = Area of Orifice

H = Difference in Manometer height cm of water.

Q = Theoretical discharge

Cd = Qact/Qthe

Fig: Sectional View


22/46


Procedure

1. Record the inlet pipe diameter (d1) orifice diameter (do) and the densities ofmanometer fluid and that of flowing fluid.

2. Open the regulation valve and under steady state condition note the readings h1and h2 in the two limbs of the mercury differential manometer.

3. Note the initial level of water in measuring tank. Collect the water in themeasuring tank for certain time and note the final level of water in measuring

tank Calculate the actual discharge.

4. Vary the flow rate through the system with the regulation valve and take thedifferent readings.

Observations

Densities of manometer fluid mercury at room temperature = 13.6 gm/cm3

Density of water at room temperature = 1 gm/cm3

Area of measuring tank = 40 cm x 50cm

= 2000 cm2

Diameter of pipe d1 = 2.8 cm

Diameter of orifice do = 1.4 cm

Area of Pipe a1 = d12/4 = 6.15 cm

2

Area of Orifice a2 = dt2/4 = 1.54 cm2

Observation Table


Initial Level

y1

Final Level

y2

Difference y =

y1 - y2

Time t

(sec)

Manometer Reading Manometer Difference Manometer difference cm of

water

h1 h2 h = h1- h2 H = h (m - f)


23/46


Calculation Table

S. No Volumetric flow rate

Qact= A(y2 - y1)/t

Flow rate at Vena-contracta

gHAA

AAQth 2

2

2

2

1

21

Cd = Qact/Qthe

1

2

3

Results



Discussions

Concluding Remarks


24/46


Experiment No - 8

PITOT TUBE CO-EFFICIENT DETERMINATION TEST

Objectives

To calibrate the pitot tube and determine the pitot tube co-efficient.

Theory

A pitot tube is used to find the velocity of an open stream at any point. The tube bent at its

end and drawn out into a nozzle may be used to find the velocity at point nozzle axis is

aligned toward the direction of flow. The water of stream will rise in the tube at a height

equal to stagnation pressure head which will project out of the free surface by the amount

of velocity head. Thus the velocity at tip of nozzle can be calculated.

If Vth is the theoretical velocity and Cp is the coefficient of Pitot tube, hm is the difference in

the levels of manometric liquid (mercury).

gHVth 2

1

w

m

mhH

hm = manometric difference (h2 - h1)

ccgm

/6.13

ccgw /1

the

act

p

V

VC

Apparatus

Pitot tube,

Differential Manometer,

Stop watch.

Fig: Sectional View of Pitot tube


25/46


Procedure

1. Start the pump and adjust the flow.2. Note the initial reading of water H1 in the tank and collect water for certain timet

and note the reading H2 calculate discharge Qact and mean velocity Vm.

3. Now take the reading of manometer at different test run.4. Calculate the velocity at different place.

Observations

Area of measuring tank a = 50 X 40 = 2000 cm2

Diameter of pipe = 2.7 cm

Area of pipe (a) = D2 / 4 = 5.72 cm2

Observation Table

Sl.

No.

Water level of measuring

tank

Time Volumetric

flow rate,Q

m3/sec

Average

velocityV= Q/a

(m/s)

Manometer

readingInitial (m) Final (m) h1 (m) h2 (m)

Plot pressure average velocity versus pressure drop in a log-log graph paper and determine

the value of pitot co-efficient.

Results

Discussion

Concluding Remarks


26/46


Experiment No - 9

METACENTRIC HEIGHT DETERMINATION TEST

Objective

To determine the metacentric height of floating body (flat bottomed vessel).

Introduction

A floating body should not only be in equilibrium but it also should be stable. Te floating

body is in equilibrium when the resultant up thrust (U) is equal to the weight of the body

( sW ) and the two forces act in the same line.

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 the floating body to be stable it is essential that the

metacentre (M) is above the center of gravity (G).In other words, the metacentric height

(MG) should be positive. For most of the actual ships, MG is between 0.3 and 1.20 m. The

greater the metacentric height, the greater is the stability. However, very large metacentric

heights cause undesirable oscillations in the ships and are avoided.

Theory

When a body is immersed in a fluid two forces act on it; the gravitational force (weight) and

the buoyant force. The buoyant force is equal to the weight of displaced fluid, and it acts

through the center of gravity of the displaced fluid.

For a body to be in equilibrium on the liquid surface as shown in Fig.1, the weight (W) and

the buoyant force must lie in the same vertical line. On rotating the body as shown in Fig.2

through an angle (), the center of gravity G is usually unchanged in this position but the

center of buoyancy B0 shifts towards the new position. Therefore W and B will make couplethat will try to balance the disturbance.

The line of action of FB in this new position cuts the axis of symmetry at M, which is called

metacentre and the distance GM is called the metacentric Height.

G = Center of Gravity

B0 = Centre of Buoyancy

B = New center of Buoyancy

GM = Metacentric height

m = Weight of hangers

w = Weight applied

W = Weight of vessel

(Including m, w)

x = Distance from the center

= Angle of tilt Fig. 1 Fig. 2


27/46


Theoretically, GM is determined by equation

GM = I00/V - BG

I00 = Area moment of inertia of the water line area about the axis of rotation.

V = volume of the submerged portion of vessel.

BG = distance between center of gravity and center of buoyancy

Experimentally, GM is determined by equation

GM = {(w1 + m) x1 - (w2 + m)x2}

W tan

Apparatus

Small steel tank (50 cm x 50 cm x 50 cm), metal vessel with hangers, adjustable weights,

plumb bob, scale, and steel rule.

Procedure

1. Determine the weight of vessel (W), including the weight of the hangers and weights.For determining the W, water level in the tank before floating the vessel is noted (h1)

and water level after floating the vessel is noted (h2).

2. Shift the moveable weights by unequal distances x1 and x2 from the center of thecrossbar.

3. Note down x1, x2 and angle of heel .4. Repeat steps from 2 to 3 for different positions of moveable weights.

Observation(s) and Calculation(s)

Area of Tank = A =

Initial Water Level (without vessel) = h1 =

Final Water Level (with vessel) = h2 =

Weight of vessel = W= w x A x (h2 - h1)

Table 1. Observation table for determination of metacentric height.

S.

No.w1 w2 x1 x2

Angle of

Heel tan

GM =

{(w1 + m) x1 - (w2 + m) x2}

W tan

(1) (2) (3) (4) (5) (6) (7) (8)

1.

2.

3.


28/46


Results

Mean meta-centric height of flat-bottomed vessel is = m.

Discussion

Precautions

1. Ensure that the pendulum moves freely about the pivot and there is no friction.2. Start the experiment and record the readings when water in the tank becomes still.3. Reading of angle of heel should be taken when the pendulum becomes steady and

does not fluctuate.

4. Initially needle of pendulum must be at zero if not, and then take account of theerror in calculations


29/46


Experiment No - 10

VARIOUS CO-EFFICIENT DETERMINATION TEST

Objective

To determine the values of cC vC and dC of a sharp-edged, circular orifice discharge free.

Introduction

An orifice is an opening in the side wall of a tank or a vassal. The liquid flows out of the tank

when the orifice is opened. In a sharp edged orifice, there is a line contact of the liquid as it

flows out. An orifice is called the orifice discharging free when it discharges into

atmosphere. The jet issuing from the tank forms the vena contracta at a distance of d/2,

where d is the diameter of the orifice. The orifices are commonly used for the

determination of discharges.

From the Bernoullis Theorem, it can be shown that the discharge is given by:

cCQ vC a gH2 gH2aCd

Where, Cc is the coefficient of contraction, which equal to the ratio of the area of the jet at

the vena contracta to the area of the orifice (a). The value of Cc generally varies between

0.61 and 0.65.

vC is the coefficient of velocity, which is equal to the ratio of the actual velocity of the vena

contracta to the theoretical velocity (a gH2 ). The value of vC usually varies between 0.95

and 0.99.

dC is the coefficient of discharge, which is equal to the ratio of the actual discharge (Q) to

the theoretical discharge ( gH2a ). The value of dC usually varies between 0.59 and 0.64.

H is the head causing flow, which is equal to the vertical distance between the free surface

in the tank and the center of the orifice. H should be comparatively large with respect to

diameter of orifice. a is the area of the orifice of diameter d.

Experimental Set-up

The set-up consists of a constant head supply tank with a circular orifice on in its side wall. A

measuring tank is provided to collect the water for the measurement of discharge.A micrometer contraction gauge can be held across the water jet at the vena contracta for

the measurement of diameter of the jet at the vena contracta in two perpendicular

directions. For the measurement of the coordinates of the jet, a horizontal scale to which a

vertical scale is fitted is attached to the tank. A hook gauge is mounted on the vertical scale.

The hook gauge can be moved vertically as well as horizontally so that its tip touches the

lower surface of the jet. The distances x and y can be read on the horizontal and vertical

scales respectively.


30/46


Theory

The coefficient of contraction Cc is equal to the ratio aa /c , where ca is the area of cross

section at the vena contracta. The readings of the micrometer gauge give the mean

diameter cd of the jet at the vena contracta at two sections perpendicular to each other.

Thus,

2

2

c

2

2

cc

d

d

d4/

d4/C

, where d is the diameter of the orifice.

By applying the equations of motion to the trajectory of the jet, it can be shown that the

actual velocity of the jet is given by

y2

gxV

2

Therefore,yH4

x

ygH4

gx

gH2

VC

22

v

Where x and y are the coordinates of the jet, measured with respect to the center of the

vena contracta.

The coefficient of discharge ( dC ) is given bygH2a

t/

gH2a

QCd

Where is the volume of water collected in time t.

Since it is difficult to determine the diameter of the jet at the vena contracta accurately, it

can also be determined indirectly from the relation

v

dc

C

CC

The value of dC depends upon the nominal Reynolds number RN given by

v

gH2d

v

VdNR

Procedure

1. Measure the diameter of the orifice and fit it to the side opening of the constanthand supply tank and close it with a rubber plug.

2. Open the inlet valve of the supply tank to fill water to the required level. Note thehead H.

3. Remove the plug. The water flows out of the orifice and the water level in the tankdrops. Adjust the inlet valve till the water level becomes constant.

4. Hold the micrometer contraction gauge across the venacontracta. Adjust the screwson its ring so that the points of all the four screws just touch the periphery of the jet.


31/46


5. Take the micrometer contraction gauge away from the jet and measure the diameterin the two perpendicular directions.

6. Bring the hook gauge to the vena contracta. Note the horizontal scale and verticalscale readings ( 00andyx ) when the point of the hook gauge just touches the lower

surface of the jet.

7. Slide the hook gauge to a point some distance away from the vena contracta andmeasure the x' and y' coordinates.

8. Determine the actual discharge by collecting the volume of water ( ) for a period oftime (t).9. Repeat steps 2 to 8 for 5 to 7 different heads H.

Observations and Calculations

Diameter of the orifice d = a =

Dimensions of the measuring tank;

L = B = A =

The coordinates of the center of the vena contracta:

0x = 0y =

Sl.

No

Head

H

Discharge measurement

x' y' x =

x'- 0x

y =

y- 0y

vC =

yH4

x 2

dC =

gH2a

Q

cC =

v

d

C

C

cC

2

2

c

d

d

Initial

level

Final

level

Rise

in

level

Volume

Time

t

Q=

/t


32/46


Graph

Plot Q versus H on an ordinary graph, with Q as ordinate, and determine the value of

dC from the slope of the line.

Results

vC ..

dC (Analytically) = ..

dC (Graphically) =

cC (From dC and vC values) = .

cC (By direction measurement) = .

Precautions

1.

Make sure that the head remains constant for one set of observations.2. The head over the orifice should be fairly large so that the orifice acts as a small

orifice.

3. While measuring the coordinates of the jet, take care to ensure that the point of thehook gauge just touches the lower surface of the jet without any splash.

4. The micrometer contraction gauge should be kept axial with the orifice. The screwsshould just touch the periphery of the jet at the vena contracta.

5. The hook gauge should not be moved to and fro to avoid backlash error.


33/46


Experiment No - 11

IMPACT OF JET EXPERIMENT

Objective

To determine the force exerted by a jet of water on a stationary vane, and to verify the

impulse momentum equation.

Introduction

Curved vanes are used in turbines. The force exerted by a jet of water on a vane is

determined from the impulse-momentum equation. The net force acting on the fluid in a

control volume is equal to the rate of change of momentum in that direction, according to

the impulse- momentum equation. For incompressible, steady flow, the components of the

force in x and y directions are:

1x2x

'

x VVQF

1y2y

'

yVVQF

Where suffixes 1 and 2 indicate the inlet and exit sections, respectively.

The force components acting on the boundary are equal and opposite and are given by:

2x1xx

VVQF

2x1xy

VVQF

The main advantage of the impulse-momentum equation over the energy equation is that

only the flow conditions at the inlet and exit sections are required. The changes within the

control volume need not be known.

Experimental set-up

The set-up consists of a transparent cylinder, with an axial vertical rod which can move up

and down. A vane is fixed at the lower end of the rod. A nozzle, through which a water jet

emerges and strikes the vane, is located just below the vane so that the jet strikes at the

center of the vane. The water after striking the vane falls at the bottom of the cylinder and

is collected in a measuring tank.

A spring is fixed at the top of the vertical rod on which a loading pan is placed. The force

exerted by the jet on the vane can be measured by the weights placed on the loading pan to

counteract the reaction of the jet. Vanes of different shapes can be used for the

measurement of the force. After the impact, the rod tends to move upward but the weights

bring it downward.

A vertical scale is fixed to the top of the cylinder for setting back the rod to its original

position. The water is supplied to the nozzle from a constant-head tank


34/46


Theory

When a vertical jet with a velocity V strikes a symmetrical horizontal vane, the vertical

components of the force on the vane is given by,

cosVVQFv

or, Vcos1AVFv

or, cos1AVF 2v

Where,

is the mass density = 1000 kg/m3

A is the cross sectional of the jet

V is the velocity of the jet

is the angle by which the jet is deflected by the vane.

( is usually greater than 90)

The net horizontal component of the force is zero in this case because of vertical symmetry

of the vane.

Because of losses, the actual force acting on the vane is less than the theoretical force. The

vane coefficient (K) is equal to the ratio of the actual force to the theoretical force.

Procedure

1. Measure the angle of the vane. Also measure the exit diameter of the nozzle.2. Fix the vane at the bottom end of the vertical rod so that it is exactly above the

nozzle and is symmetry.

3. Regulate the inlet valve of the supply pipe so that the jet issuing from the nozzlestrikes the vane axially.

4. Place the required weights on the pan to counteract the upward force due to impactof jet.

5. Take the initial reading of the water level in the measuring tank, and start the stopwatch. Note the rise in the water level after a suitable time period for the

measurement of discharge.

6. Repeat steps 3 to 5 for different flow rates.7. Close the inlet valve. Repeat steps 1 to 6 for another vane.


Exit angles, Vane No. 1

Vane No. 2

Diameter of the nozzle, D = A =

Dimensions of the measuring tank;

L = . B = Area =


35/46


S.

No.

Discharge Measurement Appliedmass M

(kg)

Applied

weight W

(N) = Mg

Theoretical

force (N)

Vane

coefficient

(K)Initial

level

Final

level

Rise in

level

Volume Time Q

Vane No. 1

1

2

3

4

5

6

Vane No. 2

1

2

3

4

5

6

Result

Vane coefficients:

Vane No. 1 =

Vane No. 2 =

Precautions

1.

Make the sure that the vanes are smooth and symmetrical.2. The jet should strike at the center of the vane.3. The weights should be placed on the loading pan gently, starting with smaller

weight.

4. The vertical rod should be set to the original position after every observation.


36/46


Experiment No - 12

OPEN CHANNEL EXPERIMENT

OBJECTIVE

Verification of sequent depth ratio and relative energy loss in hydraulic jump for horizontal

rectangular channel.

INTRODUCTION AND THEORY

When supercritical flow changes to subcritical flow hydraulic jump forms which is

accompanied by violent turbulence, eddy formation, air entrainment, and surface

undulations. Hydraulic jump is a very useful means to dissipate the excess energy of flowing

water which otherwise, would cause damages downstream. Consider the flow situation as

shown in fig. 1, in which section 1 is in supercritical zone and section 2 is in subcritical zone.

Assuming the channel bed to be horizontal, friction forces to be negligible and flow to be

two dimensional, one can write using the momentum equation;

1221 VVqPP (1)

Where, q = Q/B in which B is width of channel, Q is discharge and P represents the

hydrostatic force per unit width of channel. Substituting the values of P1 and P2 for

rectangular channel in eq. (1),

122

2

2

1

22VVq

ghgh

(2)

Where, is the mass density of water. From the continuity equation,

hVhVq 122 (3)

Combining eqs. (2) and (3) and then solving for h2/h1, obtains the following Belangers

equation:

211

2 8112

1rF

h

h (4)

1

11

gh

VFr is known as Froude number of the incoming flow at section 1. The depths h2and

h1, as related by eq. (4) are known as conjugate or sequent depths. A jump forms in a

rectangular channel when eq. (4) is satisfied.

Because off eddies and flow decelerations that accompany the jump, considerable head loss

occurs. This head loss hL may be calculated by using the energy equation.


37/46


Thus,

g

Vh

g

VhEEh

L22

2

22

2

1121 (5)

From Eqs. (2), (3) and (5),

21

3

12

4 hh

hhhL

(6)

Height of jump hj is defined as the difference between the depths of flow after and beforethe jump, hj= h2 h1.

EXPERIMENTAL SET UP

It consists of a glass walled rectangular flume about 5 m long, 0.20 m wide, and 0.4 m deep

having a sluice gate at the inlet end, a tail gate at the downstream end top rails for the

movement of pointer gauge. A sluice valve is provided near the outlet end of the supply

pipe.

PROCEDURE

1. Adjust the supply valve. Sluice gate and the tail gate, so that there forms a stablehydraulic jump in the flume.

2. Take the pointer gauge reading for the gate valves and water surface elevations atpre-jump section (1) and post - jump section (2).

3. Measure the discharge by volumetric method.4. Repeat steps (1) to (3) for other positions of valve, sluice gate and tail gate.

OBSERVATION

Width of flume B = m

Exp

No

Area of

tank A

Height

of water

in tank

h

Time

t

Discharge

Q

(A x h)/t

h1 h2v1 =

Q/(Bxh1)

v2 =

Q/(Bx h2)Frl E1 E2 hj/E1

hL/E

1

(m2) (m) (sec) (m

3/s) (m) (m) (m/s) (m/s) (m) (m)

1

2

3

4

5

6


38/46


FIGURES TO BE PREPARED

1. Plot h2/h1 Vs Frl on a simple graph paper. On the same plot also draw the linerepresented by eq. (4). Note the scatter of the observed data points.

2. Mark the data points ofhL/Eland for hj/Elfor various values ofFrl. Note the scatter ofthe experimental data points from the standard curve as shown in fig. 2 and discuss

with reason.

RESULTS AND DISCUSSION

1. Before taking the observation, ensure that water level in the channel attains uniformflow with no surface rollers.

2. Ensure that water level in the supply tank has become constant head at all openingof sluice gate during experimentation.

3. Take the pointer gauge reading accurately to avoid further error, if possible takeaverage value by taking minimum two to three reading across the width of channel

at a point.


39/46


Experiment No - 13

WIND TUNNEL EXPERIMENT

OBJECT

To study the boundary layer velocity profile and determine boundary layer thickness &

displacement thickness.

INTRODUCTION AND THEORY

Because of viscous characteristics of a fluid flowing past a stationary body, the fluid has a

tendency to adhere to the body. As a result no slip condition prevails and the fluid at the

boundary has zero velocity and away from the boundary, the velocity increases gradually.

Thus, there is a thin layer in the vicinity of the boundary within which has been affected

because of the boundary and viscous effects. This thin layer is termed the boundary layer.

Consider a fluid flow past a flat plate which is placed parallel to the flow. At the

leading edge, x = 0, of the plate, the thickness of the boundary layer zone is zero. Thickness

of this zone increases with increase in x. in the initial portion of the flat plate (i.e. small

values of x), the flow within the boundary layer is termed the laminar boundary layer. After

some distance downstream of the leading edge, the flow within the boundary layer is,

however, turbulent (i.e., the fluid does not move in parallel layers but moves in the way that

the fluid particles have transverse motion as well) and accordingly, the boundary layer is

called the turbulent boundary layer. In the turbulent boundary layer zone, there still exists a

very thin layer near the boundary in which the flow is laminar. This thin layer is called

laminar sub layer. In between the laminar boundary layer zone and turbulent boundary

layer zone, there exists a transition zone. Velocity distribution in the laminar boundary layer

zone follows parabolic variation while in the turbulent boundary layer zone the velocity

variation is logarithmic.The extent of viscous effects near a boundary is measured in terms of boundary layer

thickness. Two commonly used thicknesses are the nominal thickness and displacement

thickness of the boundary layer. The nominal thickness of a boundary layer, is defined as

that value of y at which the velocity of flow is 99% of the free stream velocity. In other

words, at y = , u = 0.99 Uo. Here, u represents the velocity of flow at a distance y from the

boundary and Uo is the free stream velocity.

Displacement thickness, * is defined as the distance by which the boundary should be

shifted so that the resulting volume of fluid flowing with uniform velocity distribution is the

same as that of the actual flow. Obviously,

oU

AreaABC*

Here, area ABC represents the reduction in flow rate (per unit width of plate) due to the

boundary effects.

Velocity variation in a turbulent boundary layer is often expressed as:n

o

y

U

u

(1)

In which n varies from 1/7 to 1/10.


40/46


EXPERIMENTAL SET-UP

It consists of a wind tunnel (open circuit type) having a test section of size 400 mm X 300

mm (approx.). A longer test section will result in large thickness of the boundary layer and is,

therefore, desirable. A Prandtl tube fitted to a suitable manometer is provided at the

downstream end of the test section for measuring the velocities at different points along a

vertical. Alternatively, a total head tube fitted to a pointer gauge and a pressure point on

the tunnel bottom (to measure static pressure) may be used. Instead of using lower wall of

the wind tunnel as a flat plate, one may, alternatively, place a metallic plate in the wind

tunnel and measure the velocity profile near the downstream end of the plate.

PROCEDURE

1. Start the wind tunnel and let the Prandtl tube touch the bed of the plate.2. Take manometer readings h1 and h2.3. Raise the Prandtl tube by 1 to 2 mm and repeat step (2).4. Repeat step (3) till the centre of the tunnel is reached or when no change in

manometer readings is observed for three different successive positions of the

Prandtl tube.

FIGURES TO BE PREPARED AND FURTHER CALCULATION

Plot y v/s u (with u on x - axis) on a simple graph paper. Fit-in a smooth curve to the plotted

data points. This is the velocity profile. Determine Uo i.e. the free stream velocity. Find out

the value of y at which u = 0.99 Uo. This value of y is the boundary layer thickness . Thus,

= ..

Estimate the area ABC, as marked in Fig. 2, on the plotted velocity profile. Then,

* = Area ABC/Uo = .

Using the value of Uo and complete the last two columns of the observations andcomputations sheet for y . Now plot u/Uov/s y/ (with y/d on x-axis) on a log-log graph

paper. Fit-in a straight line to these plotted points. The slope of the line is the exponent in

Eq. (1). Thus, n = .

OBSERVATION AND COMPUTATIONS

Diameter of Prandtl tube, d =

Slope of the inclined manometer, sin = ..

Mass density of the manometer liquid, m = .

Mass density of air, air = ..

Conversion factor for converting manometer liquid head into equivalent air head,

C= (m/air) =

Intial reading of the pointer gauge when Prandtl tube touches the tunnel bottom or the

plate, Gi = .


41/46


Sl.

No.

Pointer

Gauge

reading,

Gf

Y =

Gf - Gi

+ d/2

Manometer ReadingsU

= hg2 u/Uo y/Limb 1,

h1

Limb 2,

h2

h =

C (h1-h2) Xsin

RESULTS AND COMMENTS


42/46


Experiment No - 14

CHARACTERISTICS OF CENTRIFUGAL PUMP

Objective

To obtain the performance characteristics of a centrifugal pump and to determine its

specific speed.

Introduction

Centrifugal pumps are used extensively in practice. The wheel of the centrifugal pump on

which the vanes are fixed is called an impeller. The centrifugal pump has radially outward

flow. The liquid enters as its center. The impeller applies a centrifugal head to the liquid

which leaves the impeller at the outer periphery with high pressure and velocity. The

velocity is converted into useful pressure head, to a large extent, by the casing. The pump is

driven power from an external source, usually an electric motor.

The effective head H developed by the centrifugal pump is given by

g2

VZ

p

g2

VZ

pH

2

s

s

s

2

d

d

d (1)

Where,

dp is the pressure indicated by the pressure gauge on the delivery side and sp is the

pressure indicated by the suction gauge on the suction pipe ( sp is negative).

andZd sZ are the heights of the delivery and suction gauge above the axis of the

pump, respectively ( sZ is negative in the figure)

andVd sV are the velocities in the delivery and suction pipes, respectively.

H is also called the manometric head.

Experimental set-up

The set-up consists of a centrifugal pump coupled to an electric motor. The suction pipe is

provided with a strainer and a non-return valve at its lower end dipped in a sump. The valve

on the delivery pipe controls the discharge. The pressure gauges are provided on the

delivery and suction pipes. A venturimeter is installed on the delivery pipe for the

measurement of discharge.

The input power to the electric motor is measured by means of an energy meter.

Alternatively, a mechanical dynamometer, such as a rope brake, can be used.

The water from the pump is discharged into a tank, from which it can again be re-circulated.


43/46


Theory

A Centrifugal pump is usually designed to work at a particular set of head H, discharge Q and

speed N. However; it may be required to run at the conditions different from those for

which it is designed. The behavior of the pump under different conditions can be predicted

by conducting tests and obtaining the performance characteristics.

The operating characteristics curves are obtained by running the pump at the designed

speed but the discharge is varied by means of the delivery valve. The head H and the shaft

power are measured for each discharge.

The discharge is calculated from the relation

dCQ 1S/Sgh2AA

AA12

2

2

2

1

21

(2)

Where h is the manometer deflection.

The power input in kw to the pump ia calculated as

3Pi mK Where,

K is the energy meter reading.

m is the efficiency of the electric motor (note power factor = 3 )H is calculated from eq. (1)

The power input 0P of the centrifugal pump is calculated as

QHP0

Where = 9.81 kN/m3, Q is in s/m3 and H in meters.

The overall efficiency of the pump is then calculated asi

00

P

P

The specific speed sN is calculated as:

4/3s H

QNN

Where sN is the speed, and Q and H are the discharge and head at the maximum efficiency.

Q is in liters per second.

Procedure

1. Close the delivery valve of the pump. Prime the pump by filling water in it by a funnelprovided for this purpose.

2. Start the electric motor by moving the starting lever gradually till the full speed isattained.

3. Wait for some time for the pump to develop sufficient centrifugal head.4. Note the readings of the pressure gauge and the energy meter.


44/46


5. Measure the speed of the pump with a tachometer. The speed of the motor shouldbe kept constant by using a rheostat.

6. Take the manometer reading for the computation of discharge.7. Repeat steps 3 to 6 for various discharges.8. Close the delivery valve first and then switch off the supply to the electric motor.


Speed of the electric motor (or pump), N =

Efficiency of the electric motor, m =

Diameter of the suction pipe ds =

Diameter of the delivery pipe dd =

Height of the pressure gauge on the delivery side, Zd =

Height of the pressure gauge on the suction pipe, Zs =

Venturimeter parameters

D1 = Cd =

D2 = S2 =

S.

No.

Discharge Head Energy

K (kW)

Input

power

iP

Output

power

0P

0 Manometer

deflection

(h)

Q

(Eq.) 2/ps g2/V

2

s

H (m)

(Eq. 1)

1.

2.

3.

4.

5.

6.

Graphs

Plot the operating characteristics (a). H Vs Q

(b). Po Vs Q

and (c). o Vs Q

On the same graph, with Q as abscissa.


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Specific speed

Draw a vertical line through the point of the maximum efficiency and determine the values

of h and Po where the vertical line cuts H vs Q and Po vs Q curves, respectively.

Calculate specific speed,4/3s H

QNN

Where, Q is in liters per second.

The value of sN usually varies between 300 and 5000 for the centrifugal pumps with oneimpeller (i.e. single stage pumps).

Result

Specific speed =

Precautions

1. The delivery valve must remain closed when the pump is either started or closed.2. Move the starter of the electric motor very gradually while starting the pump.3. Before starting the pump, make sure that the pump is fully primed and there is no air

anywhere in the system.


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REFERENCES

1. Asawa, G.L. Laboratory work in Hydraulic Engineering. 1 st Edition, New AgePublication, 2006.

2. Geankoplis, C. J., Transport Processes and Unit Operations 3rd Ed., Prentice Hall ofIndia Pvt. Ltd., 2002.

3. McCabe, Smith, Harriott, Unit Operations of Chemical Engineering 6th Ed.,McGraw-Hill International Edition, 2001.

4. Bansal R.K. Fluid Mechanics and Hydraulic Machines, Laxmi Publication, New Delhi,2005.

5. Garde, R. J. and Mirajgaoker, A. G. Engineering Fluid Mechanics: Including HydraulicMachines, Nem Chand & Bros., Roorkee, 1983.

6. Modi. P. N. and Seth. S. M., Hydraulics and Fluid Mechanics Including HydraulicMachines, Standard Book House, New Delhi, 2004.

fluid mech & machinery

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