EXPERIMENT – 1 - · Web viewh – Height differences in piezo meter in cm t – Time to collect water for a height difference of h cm, measured in seconds And Now calculate coefficient

Fluid Mechanics LaboratoryLab code- ME-405MECH. ENGG. DEPARTMENT

Fluid Mechanics Laboratory(CM-405)

List of experiments prescribed by RGPV, Bhopal

1. To determine the local point pressure with the help of pitot tube..

2. Calibration of Venturimeter.3. Calibration of Open channel Flow Measuring Devices4. Calibration of Orifice Meter.5. Calibration of Nozzle meter and Mouth Piece.6. Reynolds experiment for demonstration of stream

lines & turbulent flow.7. Determination of metacentric height.


EXPERIMENT NO.1

Pitot tube

Date of conduction:-Date of submission:-Submitted by other members:-

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Signature

Name of faculty incharge:

Name of Technical Assistant:


Objective: - Calibration of Pitot tube and measurement of air velocity.

Theory: - A Pitot tube is a pressure measurement instrument used to measure fluid flow velocity. The Pitot tube is used to measure the local velocity at a given point in the flow stream and not the average velocity in the pipe or conduit. As this tube contains fluid, a pressure can be measured; the moving fluid is brought to rest (stagnates) as there is no outlet to allow flow to continue. This pressure is the stagnation pressure of the fluid, also known as the total pressure.Bernoulli's equation states:Stagnation pressure = static pressure + dynamic pressure

Which can also be written

Solving that for velocity we get:

(1)Where:

is fluid velocity; is stagnation or total pressure; is static pressure; and is fluid density.The value for the pressure drop – or due to , the reading on the manometer:

(2)Where:

is the density of the fluid in the manometer is the manometer reading

And from equations (1) and (2)V=√2 g ∆ h (3)Equation (3), can be used to measure fluid velocity, but For Pitot tube measurement, measurement error could be resulted due to certain reasons, errors may introduce in the measurement; that the probe is not aligned with the flow direction. At low Reynolds number, validity of

http://www.wikipedia.org/wiki/Velocity

http://www.wikipedia.org/wiki/Fluid


applying Bernoulli equation should be investigated further. The geometry of the probe sting support affects the accuracy of measurement.

Therefore, calibration of pitot tube required, which can be done using a hot-wire anemometer. Considering the linear law

V ∝ f (∆ h)The pitot tube equation;

V=K √2 g ∆ hHere, K is pitot tube coefficient and needs to determine by calibration.

A heated wire of micro-meters in diameter and mini-meters in length is inserted in the flow field. The flow velocity can be sensed based on the principle of convective heat transfer concerning flow over a heated 2-D circular cylinder. In anemometer, the circuitry consists of a feedback loop of a Wheatstone bridge and a series of amplifiers which directly flow velocity.

Pitot tube is basically for time-mean velocity measurement (very low frequency response. It is low cost, easy to use. Hot-wire is basically for real-time velocity fluctuations measurement (high frequency response).

Procedure:

1. Adjust air intake with the help of a valve, fix anemometer probe at the discharge of channel.

2. Connect manometer to the Pitot tube and piezo-meter tube.3. Start the blower.4. Take the flow rate reading anemometer and pressure drop in

manometer.5. Repeat the step 3 & 4 for unknown flow rate & record the

reading in the tube and draw the graph.6. The above procedure may also be repeated for difference in

depth of Pitot tube.

Observation Table:-S. no. Anemometer

reading, VManometer reading, ∆h

Actual velocityV

1234

Calculation:- Plot a graph velocity Vs head as shown and determine the slope of the line and coefficient of


velocity of Pitot tube. Use linear regression to fit the equation.

K = slope/2g

Results: - The pitot tube coefficient K =

Conclusion:-

Precautions:-

1. Do not close air regulating valve fully to avoid over loading at blower meter.

2. Use only mild detergents to clean the instruments do never use any organic solvent and strong acid or alkali.

3. Ground the instrument properly to avoid electric shock.4. The density of fluid in manometer is one.

Suggestion

Further reading resources:

Book: Lab experiment related theory available in following books: Book Name Author Page No.

1. Fluid mechanics Streeter 130-132,457-4582. Fluid mechanics S.G Gupta 165-180

Web resources: 1. www.wikipedia.com

2. www.tmh.co.in


EXPERIMENT NO.2

Calibration of Flow Measuring Devices


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Objective: - To calibrate following flow measuring devices.

Venturi meter, Orifice meter and Rotameter

.Theory:

The flow rate in a closed channel is usually measured by creating a constriction in the cross-section of the channel and measuring the pressure drop caused by it. The drop in the pressure across the constriction depends on the flow rate and thus is a measure of the flow rate.

In case of a venturi meter, the flow cross-section of the channel rapidly decreases to a minimum at the venturi throat, and then gradually increases to the original cross-section. The difference of pressure between the pressure tapping 1 at the inlet to the device and the pressure tapping 2 at vena contract of slow stream which occurs almost at the venturi throat is measured by a U- tube mano-meter.

In case of the orifice meter the vena-contract occurs at approximately half a pipe diameter drown stream the orifice plate. Assuming the flow to be incompressible and in-viscid between the inlet section 1 and the vena contract section 2, and assuming the flow be one dimensional, use of the continuity equation and the Bernoulli’s equation leads to the flow expression as

Qth=Cd ¿ ¿Cd ¿

WhereA1 – The area at inlet side in cm2

A2 – The area at throat in cm2

∆h – Head difference in the manometer, g – Acceleration due to gravity (9.81m/sec²)

Coefficient of dischargeCd=

Q a

Qth

Calibration of flowmeters- Equations derived above relating flow rate to the differential

pressure cannot be applied directly in practical applications. All the flowmeters need calibration a priori where a known quantity of fluid is passed through the flowmeter and the differential pressure across the


flowmeter related to the actual mass flowrate through a discharge coefficient given as the ratio of actual to theoretical mass flowrate. Two methods of knowing the actual mass flowrate are- measurement of time for collection of a finite volume of fluid and measurement of mass collected in a certain amount of time.

Description of Equipment:-SPECIFICATIONS OF VENTURI METER:

Pipe Dia : 25 mm IDThroat Dia : 12 mmDistance of upstream pressure tap from the throat : ___mm Distance of upstream pressure tap from the throat : ___mm

SPECIFICATIONS OF ORIFICE METER:

Pipe Dia : 25 mm IDOrifice Dia : 12.7 mmDistance of upstream pressure tap from the throat : ___mm Distance of upstream pressure tap from the throat : ___mm Size of collecting tank : 24x24x40

Procedure:

1. Make a neat sketch of the experimental set-up and note/measure the necessary dimension on it.

2. Clean the storage tank fill with fresh water.3. Open the bypass line and close the delivery line.4. Keeping the valves to the venturi meter and the orifice meter

closed, open the discharge line.5. Slowly open the supply to the venturi meter. After the steady

state is reached, read the manometer reading and determine


the flow rate volumetrically. Also read the Rota meter reading. Repeat the experiment for higher flow rates, by increasing the supply slowly.

6. Lose supply to the venturi meter and slowly open supply to the orifice meter. Repeat the experiment as done In the case of venturi meter.

7. Repeat the procedure for at least ten mass flow rates for both venturimeter and orifice meter.

Observation Table:- for coefficient of discharge

Sl.No

Time for 10cm rise of water level (s )

Actual discharge Qa.cm3/s

Differential head in cm. of mercury

Differential head in cm. of water

Theoretical discharge Qth, cm3/s

Coefficient of discharge Cd

t1 t2 tm h1 h2 h1-h2

=hHg

Calibration TableSl.No

HHg in cm

Hw in cm

Qa in cm3/s

Log Qa

Log HHg

Actual dischargeQa =KHHg

n

HHg in cm


Calculation:-

1. Calculate actual discharge through flow meter

Qa=aht

cm3

tWherea – Area of measuring tank in cm2

h – Height differences in piezo meter in cmt – Time to collect water for a height difference of h cm, measured in secondsAnd Now calculate coefficient of discharge for each run

Cd=Q a

Qth

2. Calculations for Calibration curve

The equationQa = Cd x Qth can be written asQa=K . H Hg

n cm3/ sWhere

k=Cd( A1 A2

√A12−A2

2 ¿¿√2 g(ρm−ρ)/ ρ)

Use linear regression to fit the equation Qa=K . H Hgn and show on

calibration curve, logQa vs logHHg and determine the slope of the line and coefficient.

Results: -

Conclusion:-


Precautions:-1. Do not close air regulating valve fully to avoid over loading at

blower meter.2. Use only mild detergents to clean the instruments do never use

any organic solvent and strong acid or alkali.3. Ground the instrument properly to avoid electric shock.4. The density of fluid in manometer is one.

Suggestions:-




Web resources:1. www.wikipedia.com2. www.engineersedge.com3.


EXPERIMENT NO.3

Calibration of Open channel Flow Measuring Devices


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Calibration of V notch and Rectangular notch

Objectives:- (i) To determine the coefficient of discharge (Cd) of the given

notch for different rates of flow

(ii) To calibrate the notch (by determining the constants K and n, assuming the actual discharge Qa = K.H)

Theory: - Flow rate through open channels is measured by weirs and notches. A weir is an obstruction placed in open channel over which the flow occurs. The weir is generally in the form of a vertical wall with a sharp edge at the top, running all the way across the cross section of the open channel. When the liquid flows over the weir, the height of the liquid above the top of the sharp edge bears a relationship with discharge across it.

A notch is a sharp-edge device which permits the liquid to go through it, the liquid being exposed to the atmospheric pressure. Notches may be rectangular, triangular, circular or trapezoidal in shape. A triangular notch is also called a V-notch. Volume flow rate across a notch is given by

Qtheoretical=b√2g∫0

H

h13 dh

Where, H: height of the liquid over the notch while crossing the tip of the notch.h: is the depth of the liquid at a horizontal strip below the liquid level.b: width of the strip at the level.

1. RECTANGULAR NOTCH

Total theoretical discharge = Qtheoretical=b . 23 √2g . H2/3

However, in actual case the area of cross-section of flow is less than the area of flow across the notch, and there are frictional losses due to the presence of solid boundaries and eddy formation, the actual flow rate can be approximated as

Qactual=2/3 Cd b √ 2 g H3 /2


Where, the correction factor Cd is called coefficient of discharge which depends on the geometry of notch and Reynolds number of flow.

2. V-NOTCH or TRIANGULAR NOTCH

For a V-notch with an included angle θ, liquid flowing through it with the level H above the base point.

The breadth of element b=2(H−h) tanθ /2This gives, Total discharge

Qth=8

15. tan( θ

2 )√2 g H❑5/2

3. TRAPEZOIDAL NOTCHDischarge over trapezoidal notch = discharge over rectangular portion + discharge over rectangular portion

Qth=( 23

L+ 815

. tan( θ2 ) . H)√2g Hw

3 /2

Description of Equipment:-

a) The given rectangular and triangular notches fitted on the open channel of the experimental setup. The channel has steadying arrangement with baffles and provision for fixing interchangeable notch plates. The steadying zone is filled with 25mm or 40mm ballets to get steady flow.

b) Hook gauge is fixed on the notch tank’s top edge, which should be kept in horizontal position with the help of spirit level. It is used to measure the depth of water

c) Measuring tank Size 20 x 59 x 14.5 (LWH) meters with overflow arrangement, gauge glass, scale arrangement and a drain valve to measure the actual discharge.

SPECIFICATION of NOTCHES1. Rectangular notch : 5 cms width x 4 cms H2. Triangular of V-Notch : Angle of Notch 900, Hieght 4.7 cms3. Trapezoidal Notch : Angle of Notch 450, Hieght 3.0

cms

Procedure:

1. Make a neat sketch of the experimental set-up and note/measure the necessary dimension on it.


2. Clean the storage tank fill with fresh water.3. Open the bypass line and close the delivery line.4. Keeping the valves to the Notches open the discharge line.5. Allow the Water to flow over the notch at different rates ranging

from zero to the maximum possible level and the corresponding head over notch shown in the hook gauge are noted.

6. Now close the supply. Note the width and height of the rectangular notch. Slowly open the supply to the channel to which the rectangular notch is attached. After the steady state is reached, measure the height of the liquid over the tip of the notch.

7. Collect the water in tank for definite time interval and measure the level of water inside tank.

8. Repeat the step 7 for different flow rates, till the entire range of the flow rate is covered.

9. Note the included angle of the V-notch and perform the experiment as done in the steps 7 and 8 for the rectangular notch, noting each time the height of the liquid above the tip of the V- notch.

Observation Table:- for coefficient of discharge

Sl. No

hook gauge reading

Time for 10 cms raise of water in sec.

TheoreticaldischargeQth

Actual dischargeQa

Cofficient of dischargeCd= Qa/QthInitial

hFinal

hDepth

∆ht1 t2

Meantm

Calibration TableSl.No Hw in

cmQa in cm3/s

QthLog HHg

Actual dischargeQa =KHHg

n


Calculation:-

1. Calculate actual discharge through flow meter

Qa=ahtm

cm3

tWherea – Area of measuring tank in cm2

h – Height differences in piezo meter in cmt – Time to collect water for a height difference of h cm, measured in secondsAnd Now calculate coefficient of discharge for each run

Cd=Q a

Qth

2. Calculations for Calibration curve

The equationQa = Cd x Qth can be written as

Qa=K . H Hgn cm3/ s

Where

k=Cd((23

L+ 815

. tan( θ2 ) . H)√2 g)

Use linear regression to fit the equation Qa=K . H Hgn and show on

calibration curve, logQa vs logHHg and determine the slope of the line and coefficient.

Results: -

Conclusion:-


Precautions:-

1. Do not close air regulating valve fully to avoid over loading at blower meter.

2. Use only mild detergents to clean the instruments do never use any organic solvent and strong acid or alkali.

3. Ground the instrument properly to avoid electric shock.4. The density of fluid in manometer is one.

Suggestions:-




3. Fluid mechanics Modi and seth 700-703

Web resources:1. www.wikipedia.com2. www.engineersedge.com3.www.tmh.in


EXPERIMENT NO.4

Losses due to pipe fittings


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Objective:- (i) To determine the loss of head in the fitting at the various water

flow rates.

(ii) To determine the loss coefficient for the pipe fittings.

Theory:- Loss of head due to change in cross section, bends, elbows, valves and fittings of all types fall into the category of minor loss in pipeline. In long pipe lines the friction losses all much longer than this minor losses and hence the fleeter and often neglected. But in shorter pipelines their consideration is necessary for the correct estimate of losses. The minor loss in contraction can be express.

hL=KLV 1

2

2 gThe minor loss due to enlargement can be expressed as.

hL=KL(V 1

❑−V 2❑ )2

2 gWhere,

h1 = minor loss or head lossK1 = Loss coefficient V1 = Velocity of fluid in pipe of small diameterV2 = Velocity of fluid in pipe of larger diameter

Description:-The apparatus consist of a ½” bent and elbow. A sudden

expansion from ½ ” to 1” and a sudden contraction from 1” to ½ ” ball value and gate value pressure taping are provided at inlet and outlet of these fitting at suitable dust. A differential manometer in the lines gives pressure gauge due to fittings supply to the pipeline is made through centrifugal pump which deliver water from sump tank. The flow of water in pipeline is made through centrifugal pump which deliver water from is regulated by means of central valve and by pass valve discharge is measured with the beep of measuring tank and stop watch.

Utilities Required:1. Power supply: single phase 220 volts, 50 Hz, 5 AMP. With earth


2. Water supply3. Drain STANDARD DATA:A → Area of measuring tank = 98.059 × 10-3m2

S → Specific gravity of Hg= 13.6g → Acceleration due to gravity = 9.81 m/sec2

d → Diameter of small pipe = 0.016 m.d2 → Diameter of large pipe = 0.028 m.a1 → Area of cross section of small diameter pipe = 2.0106 × 10-4m2.A2 → Area of cross section of large diameter pipe = 6.1575 × 10 -4m2.

Δh = 12.6 × h

Procedure:

A) STARTING PROCEDURE

1. Clean the apparatus and make all tanks from dust.2. Close the drain.3. Fill sump tank ¾ with clean water and ensure that no foreign

particles an there.4. Close all flow controls valves given on the water line and open

bypass valve.5. Check the valve of Hg in manometer tube. It showed be to half.

It is used then fills it.6. Close all pressure tapes of manometer connected to different

pipe fitting.7. Ensure that ON/OFF switch given on the panel is at OFF position.8. Now switch on the main power supply.9. Switch on the pump.10. Operate the flow control valve to regulate flow of water in the

desired test section.11. Open the pressure taps of manometer of related test section

very slowly to avoid the blow of water on manometer fluid.12. Now open the air release valve provided on the manometer.

Slowly to release the air to manometer.13. When there is no air in the manometer close the air release

valves.14. Adjust water flow rate in the manometer close the air release

valves.15. Record the manometer reading.16. Measure the flow of water, discharge through desired test

section using stop watch and the measuring tank.


17. Repeat same procedure for different flow rates of water, operating control valve and by pass valve.

18. When experiment is over for one desired test section, open the by-pass valve fully. The close the flow control valve of running test section and open the control valve of desired test section.

19. Repeat same procedure for selected test section and so on.B) CLOSING PROCEDURE:

1. When experiment is over close all manometers tops first.2. Switch off pump.3. Switch off power supply.

Calculation:-

1. Loss of head (for contraction):

hc=KLV 1

2

2g

2. Loss coefficient (for contraction and bend):

K L=hL2 gV 1

2

¿hL=12.6h

Loss of head (for expansion):

K L=hL2g

(V 1−V 2 )2

¿hL=12.6 h

3. Change in kinetic energy:e = V12 – V22 / 2g.

4. Discharge. Q = v / t, V = A × R cm3.

Observation Table:-S. no. Pressure diff., h (cm) Rise of water level in

measurement tank, R (cm)

Time taken for R, t sec


Calculation tableS. no. Discharge,

QVelocity, V1 Velocity,

V2hL=12.6 h Loss coefficient,

KL

Results: -

Conclusion:-

Precautions:-1. Do not run the pump at low voltage i.e. less than 180 volts.2. Never fully close the delivery line and by pass line valves

simultaneously.3. Always keep apparatus free from dust.4. To prevent the clogging of moving parts. Run pump at least once

in fortnight. 5. Frequently grease the rotating parts. Once in three months.6. Always use clean water.7. If apparatus use for more than one month drawn the apparatus

completely and fill pump with cutting drill.

Trouble shootings:1. If pump cuts join open the back cover of pump and rotate the

shaft manually.2. If pump cuts heat up switch off the main power off 15 min and

avoid closing the flow control valve and by pass valve simultaneously during operation.


Suggestions:-



1. Fluid mechanics Indrajeet 6.2-6.502. Fluid mechanics S.G Gupta 165-180

Web resources:1. www.wikipedia.com2. www.engineersedge.com


EXPERIMENT NO.5

Reynolds Experiment


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Objective:- To perform the Reynolds experiment for determination of different regimes of flow

Theory:- The flow of real fluids can basically occur under two very different regimes namely laminar and turbulent flow. The laminar flow is characterized by fluid particles moving in the form of lamina sliding over each other, such that at any instant the velocity at all the points in particular lamina is the same. The lamina near the flow boundary move at a slower rate as compared to those near the center of the flow passage. This type of flow occurs in viscous fluids, fluids moving at slow velocity and fluids flowing through narrow passages.

The turbulent flow is characterized by constant agitation and intermixing of fluid particles such that their velocity changes from point to point and even at the same point from time to time. Thistype of flow occurs in low density Fluids flow through wide passage and in high velocity flows.

Reynolds number is defined as, the ratio of inertia force to the viscous force .Where viscous force is shear stress multiplied area and inertia force is mass multiplied acceleration.

ℜ=VDρµ

=VDv

(v=µ ρ)

WhereRe-Reynolds numberV - Velocity of flowD - Characteristic length=diameter in case of pipe flowΡ - Mass density of fluid =1000 µ - dynamic viscosity of fluid = 0.55x 103 v - Kinematic viscosity of fluid

Reynolds observed that in case of flow through pipe for values of Re<2000 the flow is laminar while offer Re>40000 it is turbulent and for 2000<Re<4000 it is transition flow.

Description:-


A stop watch, a graduated cylinder, and Reynolds apparatus which consists of water tank having a glass tube leading out of it. The glass tube has a bell mouth at entrance and a regulating valve at outlet, a dye container with an arrangement for injecting a fine filament of dye at the entrance of the glass tube. Potassium permanganate (to give brightly reddish color streak) thermometer and measuring tank.

Procedure:

Start the experiment by pressing start button with default values of temperature of water and time taken and diameter of pipe. Then pass the experiment with few cycles and note the observation.Observation1:

1) Start the experiment and allow the water to flow in to the tank of the apparatus. Water level in the pyrometer is slightly rising along with rise in tank. Control valve of the glass tube should be slightly opened for removing air bubbles.

2) After the tank is filled outlet valve of the glass tube and inlet valve of the tank should be closed, so that water should be at rest.

Observation2:1) Keeping the velocity of flow is very small and inlet of the die injector is

slightly opened, so that the die stream moves at a straight line throughout the tube showing the flow is laminar.

2) Again measure the discharge and increase the velocity of flow.

Observation3:1) Note the observations till the die stream in the glass tube breaks up

and gets diffused in water.2) Repeat the experiment by decreasing the rate of flow and by changing

the temperature and diameter of pipe.

Observation Table:-Inner diameter of glass tube, D =Cross - sectional area of glass tube, A=π

4D ²

Mean temperature of water – t - =Kinematic viscosity of water-ν- =


S.No Discharge‘q’ in (liters)

Time taken forDischarge ‘t’ in (sec)

Discharge‘Q’ in(cm3/sec)

Velocity‘V’(cm/sec)

Reynold’sNumber‘Re’

Type offlow

Calculation:- 1) Discharge – Q=A h/ t

2) Velocity of flow – V=Q . π4

D ²

Results: - 1. Reynolds number –Re = VD/ ν2. Regime of flow =

Conclusion:-

Suggestions:-



1. Fluid mechanics Streeter 228-2742. Fluid mechanics S.G Gupta 263-308

Web resources:


1. www.wikipedia.com2. www.tmh.in

EXPERIMENT NO.6

Bernoulli’s Theorem Apparatus


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Objective: - To verify the Bernoulli’s theorem experimentally i.e. conservation of mechanical energy

Theory:- Bernoulli’s equation states as follows:

“In an ideal, incompressible fluid flow when the flow is steady and continuous, the sum of pressure energy, kinetic energy and potential energy is constant along a stream line”.

Mathematically,pw

+ V 2

2 g+ z = Cons tan t

For two sectionsp1

w+

V12

2 g+ z1 =

p2

w+

V22

2g+ z2

This is called Bernoulli’s equation.

Assumptions: It may be mentioned that the following assumptions are made in the derivation of Bernoulli’s equation.

1. The liquid is ideal and incompressible.2. The flow is steady and continuous.3. The flow is along the streamline, i.e. it is one-dimensional.4. The velocity is uniform over the section and is equal to the mean

velocity.5. The only forces acting on the fluid are the gravity forces and the

pressure forces.

Rate of flow or Actual Discharge (Q):

The water flowing through the section of a pipe or a channel under the steady state conditions is collected in a collecting tank for a known time t. The rise of water level in the collecting tank is noted down. The actual discharge is


Q = area of the collecting Tank x rise of water level in the collecting Tanktime ( t )

Description:-The experimental set up consists of a horizontal Perspex duct of smooth variable cross-section of convergent and divergent type. The section is 40 mm x 40 mm at the entrance and exit and 40 mm x 20 mm at middle. The total length of duct is 90 cm. The piezometric pressure P at the locations of pressure tapping is measured by means of 11 piezometer tubes installed at an equal distance 7.5 cm along the length of conduit. The duct is connected with supply tanks at its entrance and exit end with means of varying the flow rate. A collecting tank is used to find the actual discharge.

Data: area of collecting tank, A= 0.1 m2

Procedure:

1. Clean the apparatus and make all tanks free from dust2. Close the drain valve provided.3. Fill sump tank ¾ with clean water and ensure that no foreign particles are

there.4. Close all control valves given on the water line and open by-pass valve.5. Ensure that ON/Off switch given on the panel is at OFF position.6. Now switch on the main power supply.7. Switch ON the pump.8. Operate the flow control valve to regulate the flow of water.9. Measure the height of water level in tubes.10.Measure the flow rate using measuring tank and stop watch11.Repeat steps the same procedure for different flow rates of water

operating control valves and By-pass valve.12.When experiment over switch OFF pump.13.Switch off power supply to panel.

Observation Table:-S.No

Discharge Measurement

DischargeQ, cm3/sec

Diameter of passage

mm.

Area of c/s of passage

A, cm2

V2 / 2gcm

P/w + Zcm

P/w+ Z + V2/2gcm

Rise of water level (h2-h1)

Timesec


Calculation:- 1. Compute the area of cross section ‘a’ at a given section

a=π d2/4

2. Calculate Discharge:Q=A(h2−h1 )

t3. Velocity of flow: V=Q/a4. Velocity head= V2 / 2g

Results: -

Conclusion:-

Precautions:-1. Apparatus should be in leveled conditions.2. Reading must be taken in steady or nearby steady conditions

and it should be noted that water level in the inlet supply tank should reach the overflow condition.

3. There should not be any air bubble in the piezometer and in the Perspex duct.

4. By closing the regulating valve, open the control valve slightly such that the water level in the inlet supply tank reaches the overflow conditions. At this stage check that pressure head in each piezometer tube is equal. If not adjust the piezometers to bring it equals.

.

Suggestions:-




1. Fluid mechanics Streeter 208-2102. Fluid mechanics modi and seth 293-300

Web resources:1. www.wikipedia.com2. www.engineersedge.com3 www.tmh.in


EXPERIMENT NO.7

Meta-centric Height


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Objective:- Determination of meta-centric height.

Theory:- Buoyancy: When a body is immersed in a fluid either wholly of partially, it is buoyed or lifted up by a force, which is equal to the weight of fluid displaced by the body.

Centre of Buoyancy: The point of application of the force of buoyancy on the body is known as the centre of buoyancy. It is always the centre of gravity of the volume of fluid displaced.

Meta-centre: Figure shows a body floating in a liquid in a state of equilibrium. When it is given a small angular displacement, it starts oscillating about some point M. The point, about which the body oscillates, is called meta-centre.

The meta-centre may also be defined as a point of intersection of the axis of body passing through centre of gravity G and original centre of buoyancy B and a vertical line passing through the centre of buoyancy B1 of the tilled position of the body.

Meta-centric height: The distance between the centre of gravity of a floating body and the meta-centre is called meta-centric height. For stable equilibrium, the position of meta-centre M remains higher than centre of gravity of the body G.For unstable equilibrium, the position of meta-centre M remains lower than G.For neutral equilibrium, the position of meta-centre M coincides with G.Determination of Meta-centric Height: A known weight W1 is shifted by a distance Z across the axis of tilt. The change in momentum due to this shift is W1 Z. Let the angle of tilt be θ. The change in moment due to this tilt is equal to (Wc + W1) GM tanθ.

GM =W 1 Z

(W c+W 1) tanθ Wc = weight of the vessel


W1 = weight of unbalanced massZ = distance of the unbalanced mass from the centre of the cross bar.

Description:-The experimental set up consists of a pontoon (flat bottomed vessel) which is allowed of float in a M.S. tank having a transparent side. Removable steel strips are placed in the model for the purpose of changing the weight of the vessel. By means of a pendulum (consisting of a weight suspended to a longer pointer), the angle of tilt θ can be measured on a graduated arc. For tilting the ship model a cross bar with two movable hangers is fixed on the model. Pendulum and graduated arc are suitably fixed at the centre of the cross bar.

Procedure:

1. Note down the relevant dimensions as area of collecting tank, mass density of water etc.

2. Note down the water level in the tank when pontoon is not in the tank.

3. Pontoon is allowed to float in the tank. Note down the reading of water level in the tank. Mass of pontoon can be obtained by the help of Archimedes’s principle.

4. Position of unbalanced mass, weight of unbalanced mass and the angle of heel can be noted down. Calculated the meta-centric height of the pontoon.

5. The procedure is repeated for other positions and value of unbalanced mass.

6. Also the above procedure is repeated while changing the weight of the pontoon by changing the number of strips in the pontoon.

Observation Table:-Water level without pontoon, Y1 (cm) =

S.No. Reading on tank with

pontoon Y2

cm

Mass of pontoon

Wc=(Y2-Y1)Awgm

Unbalanced mass W1

gm

Angle of heel θdegree

Distance of unbalanced mass Z, cm

Meta-centric Height


Calculation:-

Results: - The metacentric height of a flat bottom pontoon =

Conclusion:-

Precautions:-1. Apparatus should be in leveled conditions.2. Reading must be taken in steady condition of water.3. Unbalanced mass should be measured by taking care that water

disturbance should be minimum.

Suggestions:-



1. Fluid mechanics Streeter 65-702. Fluid mechanics Indrajeet 4.2-4.7


Web resources:1. www.wikipedia.com2. www.engineersedge.com

Documents

EXPERIMENT – 1 - · Web viewh – Height differences in piezo meter in cm t – Time to collect water for a height difference of h cm, measured in seconds And Now calculate coefficient