Fluid Mechanics Lab

Prepared By: Dr Sumit Gandhi & M.L. Rathore, Civil Engg Dept: 1

DEPARTMENT OF CIVIL ENGINEERING, JUET GUNA

FLUID MECHANICS LABORATORY

(COURSE CODE: 10B17CE372)

CONTENTS

Exp. No. DESCRIPTION PAGE NO

-- Report writing 2 – 3

1. Verification of Bernoulli’s 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

-- References 36


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.


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 attend the viva voce will result in a zero mark.


Experiment No - 1 VERIFICATION OF BERNOULLIE’S THEOREM

Objective To Verify the Bernoulli’s 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

VZp2

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

222

1

211 HZ

g2Vp

Zg2

Vp

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

Theory Bernoulli’s 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/γ, z, and v2/2g, respectively. Therefore the Bernoulli’s theorem can be represented by the following equation-

H = g

VZp2

2

constant

H = total head p/γ = 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 γ = 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.


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 and calculate 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 tank remains 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 water collected in the tank for a selected period ‘t’ seconds.

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


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 point

1 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/γ + z (cm)

Velocity v = Q/a (cm/s)

v2/2g (cm)

Total Head

H (cm) 1.

1 2 3 4 5 6 7 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 become stable.

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.


Experiment No - 2 FRICTIONAL LOSS IN PIPES OF DIFFERENT DIAMETERS

Objectives To determine the friction factor for pipes of different sizes,

a. 1.7cm diameter

b. 2.7cm diameter

Introduction The Darcy’s Weisbach equation commonly used for the computation of the loss of head in pipes is given below.

g2

V.DL.fh

2

f

For accurate determination of fh a suitable value of f should be known. Moody’s 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 hf 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.

g2V

dLfh

2

f Or, 2f

LVgdh2f

Experimental setup

The experimental setup consists of:

1. Pipes of different diameter, 1.7cm, 2.1cm, 2.7cm 2. Two pet-cocks on each side with the help of which flow is regulated 3. A valve fitted to each pipe with the help of which flow is regulated 4. An U tube manometer connected to the pressure tapping of each pipe

5. A discharge measuring tank fitted with a piezometer tube and a graduated scale to measure the depth of water collected.


Procedure

1. Record the diameter‘d’ of the pipe and the length L between the sections attached to 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 ρm = 13.6 g/cc Density of water ρf = 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 (ρm - ρf)

S.No. Discharge, Q = y x A/t Velocity of water = Q/a 2f

LVgdh2f

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


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

g2VVH

221

L

(a)

Where, V1 is the velocity in the smaller pipe and V2 is the velocity in the larger pipe.

Eqn. (a) can be expressed as

gVKH L 2

2


g2VKH

21

eL

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

g2VKH

21

cL

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

g2VKH

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 the manometeric deflection (h)

5. Take the initial reading of the measuring tank and start the stop watch. Note the rise in 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.


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 head 1V

g2V2

1

2V

g2V2

2

eK Initial

level Final level

Rise In level

Volume Time Q Deflection (h)

fh hS/S1 12

1.

2.

3.

(b) Sudden contraction


g2V2

1

2V

g2V2

2

cK Initial level

Final level

Rise In level


fh hS/S1 12

1.

2.

3.

(c) 900 bend


g2V2

1

2V

g2V2

2

bK Initial level

Final level

Rise In level


fh hS/S1 12

1. 2. 3.


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


Experiment No - 4

CRITICAL REYNOLD’S 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 Reynold’s 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 factors such as initial disturbance of flow, the shape of the entry to the pipe etc. on the other hand, the lower critical Reynold’s number is well established, and its value is usually about 2000. There is a transition stage for the Reynold’s number between 2000 to 4000, and the flow is gradually turbulent when the Reynold’s 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

dvforceViscousforceInertialR e

If Re < 2000 The flow is laminar. 2000 < Re<4000 The flow is in transition state


Re > 4000 The flow is turbulent. 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.

dvR e

v = average velocity of fluid in m/s ρ = density of fluid in kg/m3 = 1000 kg/m3 for water µ = viscosity of fluid in pa-s = 8 X 10-4 Ns/m2 for water. Observation Table Discharge Calculation

Sl. No Initial reading

(h1) Final reading

(h2) Time of collection

(t)

Volumetric flow rate Q = {A x (h2-

h1)}/t (m3/s)

Results Discussion Conclusions


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:

gHAA

AACQ dth 222

21

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 Cd 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 ¼ to ¾ 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) Bernoilli’s equation and (2) Continuity equation


Procedure

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

2. Open the regulation valve and under steady state condition note the readings h1 and h2 in the two limbs of the mercury differential manometer.

3. Note the initial level of water in measuring tank. Collect the water in the measuring 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 the different 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 = πD12/4 = 6.15 cm2


Area of Throat A2 = πDt2/4 = 1.54 cm2

Observation Table

S.No Measuring Tank Reading 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 (ρm - ρf)/ ρf

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

gHAA

AAQth 222

21

21

Cd = Qact/Qth


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 A V-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 or small 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

25

d H2

tang2C158Q

The discharge over a Rectangular Notch is given by the formula


23

d BHg2C32Q

Where, θ 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.

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 Qthe

Cd = Qact/ Qthe For V-notch

For Rect. notch

1

2

Results Co-efficient of Discharge Cd = The fluid flow rate =


Discussions Concluding Remarks

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 222

21

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

Procedure

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

2. Open the regulation valve and under steady state condition note the readings h1

and h2 in the two limbs of the mercury differential manometer.

3. Note the initial level of water in measuring tank. Collect the water in the measuring 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 the

different 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 = πd12/4 = 6.15 cm2

Area of Orifice a2 = πdt2/4 = 1.54 cm2

Observation Table

S.No Measuring Tank Reading 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 (ρm - ρf)

Calculation Table

S. No Volumetric flow rate Qact= A(y2 - y1)/t

Flow rate at Vena-contracta

gHAA

AAQth 222

21

21

Cd = Qact/Qthe

1

2

3

Results Co-efficient of Discharge Cd = The fluid flow rate = Discussions Concluding Remarks


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

mmhH

hm = manometric difference (h2 - h1)

ccgm /6.13

ccgw /1

the

actp V

VC

Apparatus


Pitot tube, Differential Manometer, Stop watch.

Fig: Sectional View of Pitot tube

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 time‘t’

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 velocity V= Q/a (m/s)

Manometer reading

Initial (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

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 couple that 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 F F

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) B B

x = Distance from the center

= Angle of tilt Fig. 1 Fig. 2

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 θ

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 the crossbar.

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= γw x A x (h2 - h1)

Table 1. Observation table for determination of metacentric height.

S. No.

w1 w2 x1 x2 Angle of Heel θ

tan θ

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

W tan θ

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

1.

2.

3.

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 the

error in calculations


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 Bernoulli’s 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.


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

2c

2

2c

c dd

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

gxV2

Therefore, yH4x

ygH4gx

gH2VC

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 by gH2at/

gH2aQCd

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

vgH2d

vVdNR

Procedure

1. Measure the diameter of the orifice and fit it to the side opening of the constant hand 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 the head H.

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

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


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

6. Bring the hook gauge to the vena contracta. Note the horizontal scale and vertical scale 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 and measure the x' and y' coordinates.

8. Determine the actual discharge by collecting the volume of water ( ) for a period of time (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 =

yH4x 2

dC =

gH2aQ

cC =

v

d

CC

cC

2

2c

dd

Initial level

Final level

Rise in

level

Volume

Time t

Q=

/t


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 the hook 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 screws should 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.


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'y VVQF

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


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, ρ is the mass density = 1000 kg/m3 A is the cross sectional of the jet V is the velocity of the jet θ is the angle by which the jet is deflected by the vane. (θ is usually greater than 90º) 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 θ 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 nozzle strikes the vane axially.

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

5. Take the initial reading of the water level in the measuring tank, and start the stop watch. 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. Observations and calculations Exit angles, Vane No. 1 Vane No. 2 Diameter of the nozzle, D = A = Dimensions of the measuring tank;

L = …………………………. B = ………………………… Area = ………………………


S. No.

Discharge Measurement Applied mass 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.


REFERENCES

1. Asawa, G.L. “Laboratory work in Hydraulic Engineering”. 1st Edition, New Age

Publication, 2006. 2. Geankoplis, C. J., “Transport Processes and Unit Operations” 3rd Ed., Prentice Hall of

India 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 Hydraulic Machines”, Nem Chand & Bros., Roorkee, 1983.

6. Modi. P. N. and Seth. S. M., “Hydraulics and Fluid Mechanics Including Hydraulic

Machines”, Standard Book House, New Delhi, 2004.

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Fluid Mechanics Lab