fluid mechanics lab manual

7/17/2019 Fluid Mechanics Lab Manual

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ME-234 FLUID MECHANICS LAB

DEPARTMENT OF MECHANICAL ENGINEERING



ME 234: Fluid Mechanics LAB (0,1)

1. Introduction to the lab equipment and safety precautions.2. To understand the working of hydraulic bench and to measure the flow rate.3. (a) To determine the contraction, velocity and discharge coefficients (Cc , Cv and Cd)

for a sharp edged orifice.(b) To determine the relationship between flow rate and head drop across the orifice

and to demonstrate that the discharge coefficient is constant over a range of flowconditions.4. (a) To determine the coefficient C of a venture meter by comparing the measured

flow rate with the ideal flow rate. b) To measure the pressure distribution along the meter and compare it with theideal pressure distribution

5. (a) To determine the discharge coefficient C for rectangular and vee notch bycomparing the measured flow with the ideal flow.(b) To determine the relationship between head H and flow rate Q over rectangularand vee notches (weirs)

6. (a) To measure the force produce by a water jet when it strikes two types of vane: a

flat plate and a hemispherical cup.(b) To compare the results with the theoretical values calculated from the momentflux in the jet.

7. Determination of torque produced using a Pelton wheel.8. (a) To demonstrate the existence of laminar and turbulent flow and to establish the

value of Reynolds number for transition from laminar to turbulent flow.(b) For the laminar flow regime, to use Poiseuille‟s equation to calculate thecoefficient of viscosity .(c) To determine the variation of friction factor „f‟ in the laminar and turbulent flowregimes

9. To determine the relationship between total head loss and flow rate for pipe bendsand other common fittings. To determine the loss coefficient K for each fitting and to

compare the results with standard data.10. To visualization the difference between laminar and turbulent flow.11. To determine how the stability of a rectangular pontoon is affected by altering the

vertical position of its center of gravity.(b) To demonstrate how the metacentric height can be used as a measure of thestability.(c) To determine the height of the metacentric and compare this with the theoreticalvalue

12. To determine the hydrostatic pressure13. Calibration of a pressure gage.14. To study the surface profiles and shapes of free & forced vortexes and to plot the

relation between surface profiles and speed under different conditions.15. To understand the working of the wind tunnel.

Fluid Mechanics



EXPERIMENT # 1: INTRODUCTION

In first week of the lab, An Introduction of the lab equipment and experiments will begiven. List of equipment which will be used in lab experiments is given below:

S/No Equipment

1 H1-Hydraulics bench2 H4-Flowthrough an orifice

3 H5-Flow through a Venturi meter4 H2-Stability of a Floating body5 H-6 Discharge over a notch6 H-8 Impact of a Jet7 FM-108 Friction Loss along a pipe8 FM-112 Reynolds number & Transitional flow910 H-13 Free and Forced Vortex11 H-16 Losses in pipe bends12 H-19 Pelton Turbine13 AF81-Wind Tunnel

H3-Calibration of a pressure gauge

The above mentioned equipment will be used in the respective experiments as mentioned in thelab manual.



EXPERIMENT # 2: Description of Hydraulic Bench

The Hydraulic bench provides facilities for performing a number of experiments. A smallcentrifugal pump, drawing water from the water sump, which lies below the pump, delivers toapparatus placed on the top of the bench. The flow rate is controlled by the valve, and ismeasured by collecting water in the weigh tank. The weigh tank is supported beneath the bench to

one end of the weigh beam. The other end of the weigh beam projects slightly from the benchsupport, and carries a weight hanger, sufficient to balance the dry weight of the tank, plus a smallamount of water. An operating lever, adjusted to weigh hanger, may be set in either the stand bymode or the weighing model. In the stand by mode, a drain valve at the base of the weigh tank isopened automatically, so alloying the contents to be emptied back to the sump.

Hydraulic Bench

To find the rate of discharge, the liver is moved to the weighing mode. This allows the free end ofthe weighing beam to drop to its lower stop, there by closing the drain valve. Water then starts toaccumulate steadily in the weigh tank, so there comes a time when the weighing beam rises to itsupper stop. A stop clock is started at this instant. A known weigh is then added to hanger, soreturning the beam to its lower position. The stop watch is stopped when the beam rises to itsupper stop for a second time. The lever ratio of the weighing beam is 3: 1, so the weight of thewater collected in the time interval is three times the added weight. The flow rate(Kg/Sec) can be

calculated by dividing that weight by the time measured by the stop watch.

Observations and Calculations:

S No Weight on Hangar (kg) Mass of Water (kg) Volume (m3) Time (s) (Q = V/t)

(m3/s)

1

2

3

4

5



S No

Volume (Liters) Volume (m3) Time (s) (Q = V/t)(m3/s)

1

2

3

4

5



EXPERIMENT # 3: Flow through an Orifice

Objective:

1. To determine the contraction, velocity and discharge coefficients (Cc , Cv and Cd) for a

sharp edged orifice.2. To determine the relationship between flow rate and head drop across the orifice and todemonstrate that the discharge coefficient is constant over a range of flow conditions.

Applications of orifice:

There are several reasons you might want to install a restrictive device or orifice in a pipingsystem.

To create a false head for a centrifugal pump, allowing you to run the pump close to itsBEP.To increase the line pressure.

To decrease the flow through a line.To increase the fluid velocity in a line.

Apparatus:- Orifice meter.



Theory:-

An Or if ice is an opening in a vessel th rough which the li quid f lows out . Orifice meter is used to measure the discharge through pipe. An orifice meter, in its

simplest form consists of a plate having a sharp edge circular hole known as an orifice. This plateis fixed inside a pipe as shown.

Vena Contracta:-

It has been observed, that the jet, after leaving the orifice, gets contracted. Themaximum contraction takes place at a section slightly on the downstream side of the orifice,where the jet is more or less horizontal. Such a section is known as Vena Contracta as shown.

Section 1 Section 2

HYDRAULIC COEFFICIENTS:-

a) Coefficient of Contraction:- Cc = Area of jet at Vena Contracta

Area of Orifice

b) Coefficient of Velocity:- Cv = Actual velocity of jet at Vena Contracta

Theoretical velocity of jet

c) Coefficient of Discharge:-Cd = Actual Discharge

Theoretical Discharge



= Actual Velocity x Actual Area .

Theoretical Velocity x Theoretical Area

= Actual Velocity x Actual area

Theoretical Velocity Theoretical area

Cd = Cv x Cc

We can predict the velocity at the orifice using the Bernoulli equation. Apply it along thestreamline joining point 1 on the surface to point 2 at the centre of the orifice.

P 1+ρ (u12 /2) + ρgz 1 = P 2+ρ (u2

2 / 2) + ρgz 2 _____(1)

At the surface velocity is negligible (u1 = 0) and the pressure atmospheric ( p1 = 0).At the orificethe jet is open to the air so again the pressure is atmospheric ( p = 0).The eq1 will becomethen_________________

ρgz 1 = ρ (u2

2

/ 2) + ρgz 2

The density ρ will be cancelled .If we take the datum line through the orifice then z 1 = h and z 2

=0, putting all these values in the above equation we will get_______________

___________(2)

This is the theoretical value of velocity. Unfortunately it will be an over estimate of the real

velocity because friction losses have not been taken into account. To incorporate friction we usethe coefficient of velocity to correct the theoretical velocity,

Each orifice has its own coefficient of velocity, they usually lie in the range (0.97 - 0.99)

To calculate the discharge through the orifice we multiply the area of the jet by the velocity. Theactual area of the jet is the area of the vena contracta not the area of the orifice. We obtain thisarea by using a coefficient of contraction for the orifice

So the discharge through the orifice is given by



Where C d is the coefficient of discharge, and C d = C c C v



Method:-

1. Stand the apparatus on the top of the hydraulics bench and connect the bench supply hoseto the inlet pipe diffuser to about 30mm below the top of the overflow pipe.

2. Connect a hose to the overflow pipe and push the other end of the hose into the drain holein the bench top.

3. Position the apparatus so that the orifice is directly above the pipe leading to the benchweighing tank.

4. Switch on the bench pump and open the flow control valve to supply water to theapparatus.

5. When the water level has risen to the top of the overflow pipe, adjust the flow controlvalve to obtain a overflow pipe. This will ensure a constant water level in the tank..

6. Determination of Cc and Cv. Set the traverse mechanism so that the sharp blade will pass through the water jet emerging from the orifice.

7. Traverse the blade to intersect one edge and then the opposite edge of the jet. Record thelead screw reading at each point (the lead screw has I thread per mm and each division onthe hand nut represents 0,1mm)

8. Now set the pitot tube in the center of the water jet. From the manometers on the side ofthe tank, read the pitot head h p and the head h across the orifice.

9. Measure the flow rate through the orifice by quantity of water in the bench weighingtank.

10. Record the diameter d of the orifice (this is given on the apparatus)11. Carefully reduce the flow rate to the tank so that the head h is reduced by about 10%

Adjust the inlet pipe to keep the diffuser about 30mm below the water.12. When the water in the tank has settled to a constant level, read the exact value of head

and measure the flow rate through the orifice.Repeat (11) and (12) until you have about 8 sets of readings over a range of flow rates.



Results:

Diameter of the orifice (d) = mm = m

Area of orifice (A orifice ) = ¶d2 / 4 = m

Tank piezometer reading (∆h) = mm m

Coefficient of contraction:

Lead screw reading on left side of the jet ( L1) = mm

Lead screw reading on right side of the jet (L2) = mm

Difference = diameter of jet (L1 – L2) = mm

Coefficient of contraction( Cc ) = (dc / d) 2 =

Cc =Coefficient of Velocity:As from equation 2 we have____________U2 = (2gh) ½So we will take the readings of velocity in terms of water head.U2 actual = ( 2g∆h p ) ½U2 theoretical = ( 2g∆h ) ½Coefficient of velocity = Cv = (U2 actual / U2 theoretical ) = ( 2g∆h p ) ½ / ( 2g∆h ) ½By simplifying the above equation we get____________

________Cv =√ (∆h p / ∆h)

Pitot tube reading = ∆h p = m __________

Coefficient of Velocity = Cv = √ (∆h p / ∆h)Cv

Coefficient of Discharge:Mass of water collected = M KgVolume of water collected = V = M/ ρ = M / 1000 m3 Time taken = t secVolume Flow rate = Q = V / t = m3 / sFrom the equation Q = Cd A orifice √ 2g∆hWhere Cd = ( Q ACT / Q TH)Then by rearranging the above equation we get__________

Cd = Q .A orifice √ 2g∆h



Variation of Flow Rate with Head:

M(Kg)

V(m3)

T(s)

∆h(m)

Q x 10-4 (m3 / s)

√∆hm ½

Cd

Avg Cd =

Actual Coefficient of discharge = Cd ACT =

Theoretical coefficient of Discharge = Cd TH = Cv x Cc

=

% Error = ( Cd TH - Cd ACT / Cd TH ) x 100

Now write a brief summary of what you have learnt from the experiment. When writingyour conclusions, it may help you to think about the following questions:

i. Do your results show that Bernoulli‟s equation can be applied with reasonable accuracy?ii. Is the approach velocity really negligible?

iii. Is Cd constant over the range of flow rate?iv. How accurate are your results?

Draw a graph between√∆h and Q x 104 (m3 / s)



√∆h

Q x 104 (m3 / s)

VARITION OF ∆h Q



EXPERIMENT # 4: Flow through a Venturi Meter

Objective.

1. To determine the coefficient C of a Venture Meter by comparing the measured flow ratewith the ideal flow rate.2. To measured the pressure distribution along the meter and compare it with the ideal

pressure distribution.

Apparatus:- Venturi Meter.

Theory:-

A Venturi meter is an apparatus for finding out the discharge of a liquid flowing in a pipe. A venture meter, in its simplest form, consists of the following three parts:(a). Convergent cone (b). Throat (c). Divergent cone.



A Venturi meter

Applying Bernoulli along the streamline from point 1 to point 2 in the narrow throat of theVenturi meter we have

By the using the continuity equation we can eliminate the velocity u2,

Substituting this into and rearranging the Bernoulli equation we get



To get the theoretical discharge this is multiplied by the area. To get the actual discharge taking into account the losses due to friction, we include a coefficient of discharge

This can also be expressed in terms of the manometer readings

Thus the discharge can be expressed in terms of the manometer reading::

Notice how this expression does not include any terms for the elevation or orientation ( z 1 or z 2) ofthe Venturimeter. This means that the meter can be at any convenient angle to function.

The purpose of the diffuser in a Venturi meter is to assure gradual and steady deceleration afterthe throat. This is designed to ensure that the pressure rises again to something near to the originalvalue before the Venturi meter. The angle of the diffuser is usually between 6 and 8 degrees.Wider than this and the flow might separate from the walls resulting in increased friction andenergy and pressure loss. If the angle is less than this the meter becomes very long and pressurelosses again become significant. The efficiency of the diffuser of increasing pressure back to theoriginal is rarely greater than 80%.



Method.

1. Stand the apparatus on top of the hydraulics bench. Connect the bench supply hose to theinlet pipe and secure to with a hose clip. Connect a hose to the outlet pipe and put theother end of the hose into the hole leading to the bench weighing tank.

2. Open the outlet valve, then switch on the bench pump and open the bench supply valve toadmit water to the apparatus.

3. Partly close the outlet valve so that water is driven into the manometer tubes. Thencarefully close both valves so that you stop the flow whilst keeping the levels of ware in

the manometers somewhere within the range of the manometer scale.4. Level the apparatus by adjusting the leveling the screws until the manometers each read

the same value.5. Open both valves and carefully adjust each one in turn until you obtain the maximum

differential reading (h1-h2) whilst keeping all the water levels within the range on themanometer scale. If necessary, adjust the general level by pumping air into the reservoiror releasing air from it

6. Record all of the manometer readings and measure the flow rate by timing the collectionof water in the bench weighing tank.

7. Partly close the outlet valve to reduce the differential reading (h 1-h2) by about 10%.Adjust the supply valve to keep all of the readings within the range on the manometerscale.

8. Repeat (8) and (9) until you have about 8 sets of readings over a range of flow rate. Forone of these conditions, again record all of the manometer reading.



RESULTS AND CALCULATIONS

CALCULATION OF C

Q = Ca2 2g(h1-h2)/ 1-(a2/a1)2

Rearranged to express C we have

C = 1/a2 1-(a2 /a1)2 /2g Q/ h1 – h2

Now d1 = 26,00 mm a1 = 531 mm2 = 5,31 10 – 4 m2

(a2/a1)2 = 0.143 1- (a2/a1)

2 = 0.857

Q

C = 1039h1-h2

TABLE1. DIMESIONS OF VENTURI TUBE

Piezometer

Tube No. n

Diameterdn (mm)

d2/dn a22/an (a2

2/a1-a22/an)

A(1)BCD(2)

EFGHJKL

26.0023.2018.4016.00

16.8018.4720.1621.8423.5325.2426.00

0.6150.6900.8691.00

0.9530.8670.7870.7300.6800.6330.615

0.1440.2260.5751.000

0.8300.5650.4000.2890.2150.1680.144

0.0000.0820.4310.856

0.6860.4210.2560.1450.0710.0240.000



TABLE 2 MEASUREMENTS OF (h1 – h2) AND Q

Qty

( kg )

.t

(s)

h1

( mm)

h2

(mm)

Q x 10-4

(m3 / s)

.h1-h2

(m)h1-h2

m

C

Avg C

TABLE 3. MEASUREMENT OF PRESSURE DISTRIBUTION ALONG VENTURI

METER

Piezometertube No.

Q = m3 / sU2

2/ 2g = mQ = m3 / sU2

2/ 2g = m

.hn (mm)

.hn-h1 (m)

.hn-h1 u2

2/2g.hn

(mm).hn-h1 (m)

.hn-h1 u2

2/2g

A (1)BC

D(2)

EFGHJKL



√ h1-h2

Q x 104 (m3 / s)

VARITION OF h1-h2 WITH Q



VARITION OF C WITH Q

C

Q x 104 (m3 / s)

VARITION OF C WITH Q



EXPERIMENT # 5: Flow over Weirs

Objectives;

1. To determine the relationship between head H and flow rate Q over rectangular and veenotches (weirs)

2. To determine the discharge coefficient C for each notch by comparing the measured flow

with the ideal flow.Apparatus:-

Theory:-

a. Flow Over Notches and Weirs:-

A notch is an opening in the side of a tank or reservoir which extends above the surface of theliquid. It is usually a device for measuring discharge. A weir is a notch on a larger scale - usuallyfound in rivers. It may be sharp crested but also may have a substantial width in the direction offlow - it is used as both a flow measuring device and a device to raise water levels.

b. Weir Assumptions:-

We will assume that the velocity of the fluid approaching the weir is small so that kinetic energycan be neglected. We will also assume that the velocity through any elemental strip depends onlyon the depth below the free surface. These are acceptable assumptions for tanks with notches orreservoirs with weirs, but for flows where the velocity approaching the weir is substantial thekinetic energy must be taken into account (e.g. a fast moving river).

c. A General Weir Equation

To determine an expression for the theoretical flow through a notch we will consider a horizontal

strip of width b and depth h below the free surface, as shown in the figure below.

Elemental strip of flow through a notch

integrating from the free surface, , to the weir crest, gives the expression for thetotal theoretical discharge



This will be different for every differently shaped weir or notch. To make further use of thisequation we need an expression relating the width of flow across the weir to the depth below thefree surface.

d. Rectangular Weir

For a rectangular weir the width does not change with depth so there is no relationship between b and depth h. We have the equation,

A rectangular weir

Substituting this into the general weir equation gives

To calculate the actual discharge we introduce a coefficient of discharge, , which accounts forlosses at the edges of the weir and contractions in the area of flow, giving

'V' Notch Weir

For the "V" notch weir the relationship between width and depth is dependent on the angle of the"V".



"V" notch, or triangular, weir geometry.

If the angle of the "V" is then the width, b, a depth h from the free surface is

So the discharge is

And again, the actual discharge is obtained by introducing a coefficient of discharge



Method.

1. Carefully slide the rectangular notch plate into the groove on the apparatus and check thatthe rubber seal makes contact with the plate along all three edges.

2. Switch on the bench pump and open the bench supply valve. The apparatus with wateruntil the level reaches the bottom (crest) of the notch.

3. Using a beaker, add or remove water until the water surface is just level with the notchcrest. Use a steel rule to check that the level is correct

4. Set the hook gauge dial to zero and slide the hook up or down until the point of the hook

just coincides with the water surface. Subsequent readings of the water level will than berelative to the true datum at crest level.

5. Set the hook gauge to a reading of 60mm. Then adjust the bench supply valve until thewater level corresponds roughly to the hook gauge setting.

6. Wait until the water level has settled to a constant value, then adjust the hook to this leveland read the exact value of head.

7. Measure the flow rate by timing the collection of water in the bench-weighing tank.Again use the hook gauge to measure the water level and record a mean value of head.

8. Now decrease the head by about 5mm and take another set of head and flow ratereading. Repeat this procedure until you have about 8 sets of reading over a range ofheads down to about 15mm.

9. Close the bench supply valve and fit the vee notch to the apparatus. Set the water level to

the base of the vee by adding or removing water. Check that the level is correct byobserving the notch from close to the water surface. The point of the vee and itsreflection should just coincide.

10. Repeat the procedure given in steps (5) to (9), but this time obtains reading over a rangeof heads between 80mm and 30mm.

11. Switch off the bench pump. Record the witch b of the rectangular notch the semi-angleof the vee notch.



RESULTS AND CALCULATIONS:-

Results for Rectangular Notch:-

Width of the rectangular notch b = mm = m

For Rectangular Notch:

Cd = Q 3 (1/√2g) 1/2 H -3/2 1/B

2RESULTS FOR RECTANGULAR NOTCH

H(mm)

Qty(kg)

.t(s)

Q x 10 -4 (m3/s)

Log Q(m3/s)

Log H(m)

CLCULATION FOR THE DISCHARGE COEFFICIENT

H -3/2 Cd = Q 3 1/√2g H -3/2 1/b2



Results for V Notch:-

Angle θ = 30o Tan θ = 0.57735For V- Notch: Q = C 8 √ 2 g tan θ H 5/2

15C = Q 15 1/√2g 1/tanθ H -5/2

8RESULTS FOR V- NOTCH

H(mm)

Qty(kg)

.t(s)

Q x 10 -4 (m3/s)

Log Q(m3/s)

Log H(m)

CLCULATION FOR THE DISCHARGE COEFFICIENT

H -5/2 C= Q 15 1/√2g 1/tanθH -5/2

8

Avg Cd



Q x 10( 4m3/s)H (m)

VARITION OF Q WITH H FOR RECTANGULAR AND VEE NOTCHES



Log Q (m3/s)LOG H (m)

VARITION OF LOG Q WITH LOG H FOR RECTANGULAR AND VEE NOTCHES



EXPERIM ENT # 6: Impact of a jet

INTRODUCTION:

Water turbines are widely used through the world to generate power. In the type of waterturbine referred to as a Pelton wheel, one or more water jets are directed tangentially onto vanes generated to the rim of the turbine disc. The impact of the water on the vanesgenerates a torque on the wheel, causing it to rotate and to develop power. Such turbinescan generate considerable output at high efficiency. Power in excess of 100 MW, andhydraulic efficiencies greater than 100%, are not uncommon. It may be noted that thePelton wheel is best suited to conditions where the available head of water is great, andthe flow rate is comparatively small.Objectives:

1. To measure the force produce by a water jet when it strikes two types of vane: aflat plate and a hemispherical cup.

2. To compare the results with the theoretical values calculated from the moment flux in the jet.

Apparatus

Fig No: 1

Method

1. Fit the flat plate to the apparatus.2. Set the weighing beam to its datum position. Set the jockey weight on the beam so that datum

groove is at zero on the scale. Turn the adjusting nut above the spring until the grooves on the tallyare in line with the top plate.

3. Switch on the bench pump and open the bench supply valve.

4. Fully open the supply valve and slide the jockey weight along the beam until the jockey return toits datum position. Record the reading on the scale corresponding to the grove on the jockeyweight.

5. Measure the flow rate by timing the collection of water.6. Move the jockey weight inwards by 10 to 15 mm and reduce the flow rate until the beam is

approximately level position.7. Repeat the step 6 until you have 6 sets of readings over the range of flow. For the last set, the

jockey should at about 10mm from the zero position.8. Switch off the bench pump and fit the hemispherical cup to the apparatus using the same method

as of flat plat take another set of readings.



Switch off the bench pump and record the mass m of the jockey weight, the diameter ofthe nozzle and the distance of the vanes from the outlet of the nozzle.



RESULTS AND CALCULATIONS:

TABLE # 1 RESULTS FOR A FLAT PLATE

Qty

(kg)

t (s) ∆x

(mm)

m∙

(kg/s)

U (m/s) Uo

(m/s)

m∙ Uo

(N)

F

(N)

TABLE # 2 RESULTS FOR A HEMISPHERICAL CUP

Qty(kg)

t (s) ∆x(mm)

m∙ (kg/s)

U (m/s) Uo

(m/s)2 m∙ Uo

(N)F(N)

Plots:

1. Force on a Vane (F) versus Momentum Flux (m∙ Uo) for a Flat Plate

2. Force on a Vane (F) versus Momentum Flux (2m∙ Uo) for a

Hemispherical Cup



EXPERIM ENT # 7: Pelton Wheel

Objective

Determination of torque produced using a Pelton wheel.

Equipment required

1. A suitable stroboscope for measurement of rotational speed.2. Pelton Wheel apparatus.

Fig No: 2

Procedure for calibration of dynamometer scale

a) Set the quadrant arm (carrying the scale graduated 0-35) horizontal with weight hangersuspended from the pointer at the 100mm radius

b) Turn the loading knob (at the top) anti-clockwise to lower the pivot of the lever from thelever arm until the friction cord is slackened off.

c) Remove the friction cord by unhooking it from the lever arm. In this configuration thetension in the spring should be adjusted by turn the knurled nut to counterbalance the

weight of the lever arm and the weight hanger (i.e. set the pointer mid way between theupper and lower stop).d) Place a 50 g mass on the hanger. This will deflect the pointer downwards on to the lower

stop. Unclamp the quadrant arm (knob at left hand side) and rotate it slowly clockwise(upwards) until the pointer lifts off the lower stop pin and reaches a central position between the stop pins.

e) In this position the torque applied to the lever by the weight at 100mm radius iscounteracted by the tension in the spring. Read off the angular position of the pointerrelative to the scale.

f) Add further mass in increment of 20g (10g as appropriate) and read off and record theangular deflection in the spring.

g) Plot a graph of scale reading against mass at 100mm. The resulting graph should bestraight line from which the calibration factors for the dynamometer, Kg/deg. can bedetermined.

h) Mass (g) Scale Reading



Test Procedure

a) When no mass on the hanger, and the pivot of the lever arm is lowered, reassembled thefriction cord around the aluminum drum.

b) Connect the supply. Start up the pump and with the valve on the pelton wheel nozzle set position „4‟ say, turn the supply valve to the fully open position. This setting will giveapp. Maximum flow.

c) Turn the loading (at the top) clockwise to raise the pivot of the lever arm and supply aresisting torque to the pelton wheel. The friction cord will move the pointer to the lowerstop pin.

d) Unclamp the quadrant (by unscrewing the knob at the left hand end of the lever arm) androtate it clockwise (upwards) to lift the pointer off the lower stop pin. The friction cord isthen counteracted by the tension in the spring. Read off and record the angular deflectionof the quadrant scale relative to the pointer.

e) Using the stroboscope check and record the rotational speed of the pelton wheel rotor.f) Repeat for other values of the resisting torque (as given by different setting of the loading

knob) until the rotor stalls (is at standstill).g) Calculate power in watts at each speed.

Power = .

Where = torque in Nm , and = angular velocity in rad/s

rpm

= --------x 2

60

h) Plot torque (Nm) and power (watts) against rotational speed (rev/min)Results of a typical test

Scale reading Mass at 100mmradius(from calibrationgraph)

Torque(nm)

Speed(rev/min)

Power(watts)



EXPERIMENT # 8: Laminar, turbulent flow and Reynold’s no

Friction Loss Along a Pipe

Objectives:

1. To demonstrate the existence of laminar and turbulent flow and to establish the value ofReynolds number for transition from laminar to turbulent flow.2. For the laminar flow regime, to use Poiseuille‟s equation to calculate the coefficient of

viscosity .3. To determine the variation of friction factor „f‟ in the laminar and turbulent flow regimes.

Apparatus

Fig No: 3

Method

1. Connect the bench supply hose to the inlet of the apparatus and direct the outlet flexibleoutlet pipe into the bench drain.

2. Open the needle valve (N) on the right of the apparatus.3. Start the bench pump and slowly open the bench supply valve so that water flows through

the apparatus.4. Open the bleed screws (B) at the top of the mercury U-tube, and then slowly closes the

needle valve so that the air is expelled from the piezometer tubes. Open the air valve (V)to release the air from the water manometer. When all air bubbles have been driven out,

close the bleed screws and air valve.5. With the needle valve (N) closed, check that the mercury levels in the U–tube are in

balance. If not repeat the process of expelling air. For the first part of the experimentobtain readings of head loss h along the pipe using the mercury U-tube as follows.

6. Close the water manometer isolating tap (T) and fully open the needle valve.7. Collect the flow from the outlet pipe into a measuring cylinder and measure the time t for

collection of a known quantity Q.8. Read the heights of the two columns of mercury in the U-tube.



9. Reduce the flow rate by partially closing the needle valve to produce approximately 10%reduction in differential U-tube reading, and then repeat the measuring process.

10. Repeat this procedure until you have about 10 sets of readings over the whole flow range.11. Measure the water temperature from time to time during the experiment. Now obtain a

similar set of readings over a smaller range of flow, using the constant head tank and thewater manometer for measurement of head loss. To do this, proceed as follows;

12. Switch on the bench pump and adjust the bench supply valve until you obtain a steadytrickle of water down the overflow pipe.

13. Open the isolating tap (T), and then pump some air into the top of the manometer to

depress the water surfaces to a convenient level in the two limbs.14. Check that the two sides balance at zero flow; If they do not, repeat the process of

bleeding air from the top of the manometer.15. Starting with a differential manometer reading of about 450mm of water again take

readings of head loss and flow rate until you have about10 sets of readings over thewhole range.

16. Measure the water temperature from time to time during the experiment.17. Record the length L and diameter D of the test pipe.



Results

Length of pipe between piezometer taping, L = mm = m

Diameter of pipe D = mm = m

Cross-section area A = m

2

Result with Mercury U-tube

Mean temperature of water = oCCoefficient of viscosity = Ns/m2 (from graph)Hydraulic gradient, i = (h1 – h2)/LVelocity, V = Qty/ t x AReynold‟s number, Re = VD/Where; = 1000 Kg/m3

Plot i against V and add a scale of Re along the top of the graph. Obtained values of log i and logV and plot a graph.

Qty

t h1 h2 ioC

V Re Log i Log V

Determination of critical Reynolds number

As the flow rate reduced, laminar flow first becomes established and when V has the value,V = m/sRe =

Calculation of viscosity from experimental results

Poiseuille‟s equation i = 32 V/ gD2

= gD2/ 32 x i / VFrom fig 1. the standard value of viscosity at the mean temperature is

= --------------------Ns/m2

Calculation of index n in turbulent regime

For the turbulent regime the slope of the line is

n =i V



Calculation of „f‟ as a function of Re

The relationship between friction factor f and hydraulic gradient i is given by the equation;i = 4f/D V2/2gf = i/4 D2g/V2

The relationship between Reynolds number Re and velocity V has been established previously inthese results for the particular temperature of the tests.Read off values of i at few values of Vin each of the laminar and turbulent region. Calculatevalues of f and Re from the expressions. Then plot a graph between friction f and Re with thefollowing standard equations.

Laminar: f = 16/ ReTurbulent: 1/ f = 4log (Re f) – 0.4

Conclusions

In your laboratory, write a summary what you have learned from the experiment and answer thefollowing questions.

1. At what value of Re does turbulent flow change to laminar flow? How does this valuecompare with the accepted value of 2000?

2. What accuracy have you achieved in measuring the coefficient of viscosity?

3. What difference in friction factor you expect if the inside surface of the pipe is veryrough?



EXPERIMENT # 9: Pressure losses in bends and pipes

Objectives

1. To determine the relationship between total head loss and flow rate for pipe bends andother common fittings.

2. To determine the loss coefficient K for each fitting and to compare the results withstandard data.

Apparatus

Fig No:4

Methods

1. Close the globe valve K and open the gate valve D. Switch on the bench pump and openthe bench supply valve to admit water to the dark blue circuit. Allow water to flow for 2to 3 minutes.

2. Close the gate valve D and bleed all the air into the top of the manometer tubes. Checkthat all the manometers show zero pressure difference.

3. Open the gate valve and then, by carefully open the bleed screws at the top of themercury U-tube, fill each limb with water. Make sure that all air bubbles have beenexpelled, and then close the bleed screws.

4. Close the gate valve, open the globe valve, and repeat the procedure for the light bluecircuit.

Dark Blue Circuit

5. Open fully the bench supply valve. Then close the globe valve and open fully the gatevalve to obtain the maximum flow rate through the dark blue circuit.

6. If necessary, adjust the water level in the manometers by pumping air into, or releasingair from the bleed valves at the tops of the manometers.

7. Record the readings of the manometers in the dark blue circuit. Note the referencenumber of each manometer and also record the type of fitting next to each pair of results.Also read the levels in the mercury U-tube connected between the inlet and out let of thegate valve D.

8. Measure the flow rate by timing the collection of water in bench weighing tank.9. Measure the water temperature.10. Close the gate valve to reduce the differential manometer readings by about 10%. Again

read the manometer and U-tube, and then measure the flow rate.11. Repeat this procedure until you have about 10 sets of readings over the whole range of

flow.



Result for dark blue circuit

Water temperatures:-------------- oC Mean temperatures: ---------------------oCSr.

NoMKg

ts

Vm/s

V2/2gmm

Manometer readings and differential heads (mmof water)

U-tube(mm of Hg)

Elbow Bend Straight pipe Mitre bend Gate valve1 2 h‟ 3 4 hf 5 6 h‟ h1 h2 H

123

45678910



Light Blue Circuit

Close the gate valve and open the globe valve. Then repeat (6) and (11) to obtain the sets ofreadings for the light blue circuit.

Results for light blue circuit

Water temperature:-------------- o

C Mean temperature: ---------------------o

C

Sr.

No

MKg

ts

Vm/s

V2

/2gmm

Manometer readings and differential heads (mm of water) U-tube(mm of

Hg)Expansion Contraction Bend J Bend H Bend G Globe

Valve7 8 h

‟9 10 h‟ 1

112

h‟

13

14

h‟

15

16

h‟

h1

h2 H



EXPERIMENT # 10: To visualize the difference between Laminar &

Turbulent Flow

INTRODUCTION

The Osborne Reynolds demonstration apparatus has been designed for students experiment onthe laminar, transition and turbulent flow. It consists of a transparent header tank and flow

visualization pipe. The header tank is provided with a diffuser and stilling materials at the bottomto provide a constant head of water to be discharged through a bell mouth entry to the flowvisualization pipe. Flow through this pipe is regulated using a control valve at the discharge end.The water flow rate through the pipe can be measured using the volumetric tank (or volumetriccylinder). Velocity of the water can therefore be determined to allow the calculation of theReynolds number. A dye injection system installed on top of the header tank so that flow patternin the pipe can be visualized.



GENERAL DESCRIPTION

Unit Assembly

1. Dye reservoir 2.Dye injector3. Stilling tank 4. Observation tube4. Water inlet valve 5. Bell mouth6. Water outlet valve 7. Overflow tube

The Osborne Reynolds Demonstration apparatus is equipped with a visualization tube forstudents to observe the flow condition. The rocks inside the stilling tank are to calm the inflowwater so that there will not be any turbulence to interfere with the experiment. The waterinlet/outlet valve and dye injector are utilized to generate the required flow.



INSTALLATION AND COMMISSIONING

1. Assemble the Osborne Reynolds as shown in the picture.2. Place the Osborne Reynolds apparatus on a level ground. Use a level spirit to level the

apparatus.3. Connect hose to the apparatus outflow, inflow and overflow.4. Fill up the dye reservoir with ink.5. Establish water supply by connecting the inlet hose to a water source and open the inlet

valve.6. Fill the stilling tank with stones that are being provided and proceed to fill up the stilling

tank with water.7. Open the outflow valve to test the unit. Check for any leaking of water and proceed to

inject the ink.8. The unit is now ready to use.



THEORY

The Reynolds number is widely used dimensionless parameters in fluid mechanics.Reynolds number formula . R = VL

v

R = Reynolds numberV = Fluid velocity, (m/s)L = Characteristic length or diameter (m)v = Kinematic viscosity (m

2/s)

Reynolds number R is independent of pressure

Pipe Flow ConditionsFor water flowing in pipe or circular conduits, L is the diameter of the pipe. For Reynolds numberless than 2300, the pipe flow will be laminar. For Reynolds number = 2300 the pipe flow will beconsidered a transitional flow. Turbulent occur when Reynolds number is above 2300. Theviscosity of the fluid also determines the characteristic of the flow becoming laminar or turbulent.Fluid with higher viscosity is easier to achieve a turbulent flow condition. The viscosity of fluid isalso dependant on the temperature.

Laminar FlowLaminar flow denoted a steady flow condition where all streamlines follow parallel paths, there

being no interaction (mixing) between shear planes. Under this condition the dye observed willremain as a solid, straight and easily identifiable component of flow.

Transitional FlowTransitional flow is a mixture of laminar and turbulent flow with turbulence in the center of thepipe, and laminar flow near the edges. Each of these flows behaves in different manners in termsof their frictional energy loss while flowing, and have different equations that predict theirbehavior.

Turbulent FlowTurbulent flow denotes and unsteady flow condition where streamlines interact causing shearplane collapse and mixing of the fluid. In this condition the dye observed will become disperse inthe water and mix with the water. The observed dye will not be identifiable at this points.



EXPERIMENT

Aim:- To compute Reynolds number (R).- To observe the Laminar, Transitional and Turbulent flow.

Procedure

1. Lower the dye injector until it is seen in the glass tube.2. Open the inlet valve and allow water to enter stilling tank.3. Ensure a small overflow spillage through the over flow tube to maintain a constant level.4. Allow water to settle for a few minutes.5. Open the flow control valve fractionally to let water flow through the visualizing tube.6. Slowly adjust the dye control needle valve until a slow flow with dye injection is achieved.7. Regulate the water inlet and outlet valve until an identifiable dye line is achieved.8. Measure the flow rate using volumetric method i-e collect the water from the outlet having

die in it in a volumetric tank and calculate the time with a stop watch.9. Repeat the experiment by regulating water inlet and outlet valve to produce different

flows.

Table

Sr. # Discharge

(Liter)

Time (sec) Flow rate Q

(LPS)

Flow Rate Q

(m3 /sec)

Reynolds

Number



EXPERIMENT # 11: Stability of Floating Body

Objectives

1. To determine how the stability of a rectangular pontoon is affected by altering the vertical position of its center of gravity.

2. To demonstrate how the metacentric height can be used as a measure of the stability.

3. To determine the height of the metacenter and compare this with the theoretical value.

Theory:-

Whenever a body is placed over a liquid, either it sinks down or float on the liquid. If weanalyze the phenomenon of floatation, we find that the body, placed over a liquid , is subjected tothe following two forces:-

1. Gravitational Force 2. Upthrust of the liquid.Since the two forces are opposite to each other, therefore we have to study the the comparativeeffect of these forces. A little consideration will show, that if the gravitational force is more thanthe upthrust of the liquid, the body will sink down. But if the gravitational force is less than theupthrust of the liquid, the body will float. This may be best understood by the Archimedecs‟s

principle as discussed below.a). Achimedecs‟s Principle:-Whenever a body is immersed wholly or partially in a fluid, it is buoyed

up (i.e lifted up) by a force equal to the weight of the liquid displaced by the body.

b). Buoyancy: - The tendency of a fluid to uplift a submerged body, because of the upward thrustof the fluid, is known as the force of buoyancy or simply buoyancy. It is always equal to theweight of the fluid displaced by the body.

c). Centre of Buoyancy: - It is the point through which the force of buoyancy is supposed to act. It is always the centre of gravity of the volume of the liquid displaced.

d). Metacentre:-Whenever a body, floating in a liquid, is given a small angular displacement, itstarts oscillating about some point. This point, about which the body starts oscillating, is calledmetacentre.

e). Metacentric Height:-The distance between the centre of gravity of a floating body and

metacentre is called metacentric height.

As a matter of fact, the metacentric height of the floating body is a direct measure of its stability.Or in other words, more the metacentric height of a floating body, more it will be stable. In themodern design offices, the metacentric height of a floating body or a ship accurately calculated to

check its stability. Some values of metacentric height are given below:Merchant Ships = up to 1 mSailing ships = up to 1.5 mBattle ships = up to 2.0 mRiver Craft = up to 3.5 m

Conditions of equilibrium of Floating Body:A body is said to be in equilibrium, when it remains in a steady state,

while floating in a liquid. Following are the three conditions of equilibrium of a floating body.



Stable equilibriumUnstable equilibrium Neutral equilibrium

Stable Equilibrium:-A body is said to be in stable equilibrium, if it returns back to its original

position, when given a small angular displacement. This happens when metacentre ( M ) is higherthan the centre of gravity ( G ).

Unstable Equilibrium:-A body is said to be in an unstable equilibrium , if it does not return back

to its original position and heels farther away, when given a small angular displacement. Thishappens when the metacentre (M) is lower than the centre of gravity (G).

Neutral Equilibrium:-A body is said to be in a neutral equilibrium, if it occupies a new position

and remains at rest in the new position, when given a small angular displacement. This happenswhen metacentre (M) coincides with the centre of gravity (G).



Method

1. Record the weights, W of the complete pontoon, w of the jockey and Wy of theadjustable weight on the mast.

2. Measure the over all length L and width D of the pontoon.3. Set the adjustable weight about half way up the mast and measure its height Y 1 from the

base of the pontoon.4. Determine the height y of the center of the gravity from the base of pontoon by “up-

ending” it and balancing the mast on the edge of a steel rule. Loop the plumb the plumb

line over the scale so that the plumb bob is kept approximately in its normal position.When the pontoon is hanging vertically, mark the balance point with pencil.

5. Measure the height of the balance point from the base of pontoon. This represents theheight y of the center of gravity.

6. Fill the plastic container with water to a depth of about 70mm and float the pontoon in it.Set the jockey weight exactly half way across the pontoon and check the reading of the plumb line on the scale. If necessary, set the reading to zero by adjusting the pin at thetop of the mast.

7. Set the adjustable weight to its lowest position on the mast and record its height from the base of the pontoon.

8. Set the jockey weight to 5 different position on each side of the pontoon, for each position, record the distance X1 from the center of the pontoon and measure the angle of

tilt9. Repeat the reading for three or four other height of the adjustable weight, raising it each

time by about 50mm. The pontoon will become decreasingly stable as you move theadjustable weight up the mast, so the number the tilt angle reading you can take will belimited by the width of the scale.



Results and calculations

Weight of total floating assembly W = KgfJockey weight w = KgfAdjustable weight Wy = KgfLength of pontoon L = mm = mBreadth of pontoon D = mm = mEnter your other results in table.

Calculations

Second moment of water plain area,1

I = --------- LD3

121

12I = m4

Volume of water displaced,

Weight WV = --------------------Specific weight of water

Theoretical value of BM,BM = I / V

Depth of immersion (2X Y b) = V/ LDHeight of center of buoyancy B above base, Y b = mm

Determination of height of G

Height of adjustable weight of above base Y1 = mmMeasured height of G above base Y = mm

The ratio of the adjustable weigh Wy to the total weight W is 1:Y = Y1 + AWhere A is a constant. Substituting for Y and Y1

= ------------- + AA = ---------------- mm

Hence calculate values of Y in table



GRAPHICS OF TILT ANGLE AGAINST JOCKEY WEIGHT POSITION



BG=Y- Y B

W X1GM = ------- X --------- (mm)

W Ø



Table: measured angles of tilt

Height of

AdjustableWeight Y1

(mm)

Height

Of GY

(mm)

Position of jockey weight X1 (mm)-75 -60 -45 -30 -15 0 15 30 45 60 75 Angle

OfTilt

Table: calculated values of GM and BM from experimental results

Height of GY

(mm)

X1/ GM=w/W.X1/

(mm)

BG=Y-Y b (mm)

BM=BG+GM

(mm)(mm/degree) (mm/radian)



EXPERIMENT # 12: Center of Pressure and Hydrostatic Force on a

submerged body

Objectives:

• To understand the hydrostatic pressure distribution• To verify the location of center of pressure

Apparatus:

The apparatus is designed in a way that only the moment due to hydrostatic pressuredistribution on the vertical end of water vessel should be included. The water vessel isdesigned as a ring segment with constant cross-section. The top and bottom faces areconcentric circular arcs centered on the pivot so that the resultant hydrostatic force atevery point passes through the pivot axis and does not contribute to the moment.



EXPERIMENT # 13: Calibration of a Pressure Gauge

Objectives:

To study dead weight calibration.

INTRODUCTION

A dead weight tester apparatus uses known traceable weights to apply pressure to a fluidfor checking the accuracy of readings from a pressure gauge. A dead weight tester(DWT) is a calibration standard method that uses a piston cylinder on which a load is placed to make an equilibrium with an applied pressure underneath the piston.Deadweight testers are so called primary standards which means that the pressuremeasured by a deadweight tester is defined through other quantities: length, mass and

time. Typically deadweight testers are used in calibration laboratories to calibrate pressure transfer standards like electronic pressure measuring devices.



GENERAL DESCRIPTION

The mechanism of the gauge is shown in the figure below. A tube, having a thin wall ofoval cross section, is bent to a circular arc encompassing about 270 degrees. It is rigidlyheld at one end, where the pressure is admitted to the tube, and is free to move at theother end, which is sealed. When pressure is admitted , the tube tends to straighten, andthe movement at the free end operates a mechanical system which moves a pointer roundthe graduated scale – the movement of the pointer being proportional to the pressureapplied. The sensitivity of the gauge depends on the material and dimensions of theBourden tube; gauges with a very wide selection of pressure ranges are commerciallyavailable.

FORMULA

The formula on which the design of a DWT is based basically is expressed as follows :

p = F / A [Pa]

where :



: reference pressure [Pa] F : force applied on piston [N]

: effective area [m2]

PART IDENTIFICATION

Diameter of piston = 18mm

Mass of piston = 0.5kg



EXPERIMENT

Aim

To find out pressure with a bourdon tube pressure gauge and compare it with theoreticalresults.

Procedure

1. Remove the piston from unit.2. Close valve V1 and open valve V2.3. Fill cylinder with oil.4. Now close valve V2.5. Put piston back in position with V1 and V2 in close position.6. Read out pressure value on gauge and compare it with theoretical results.7. Repeat the experiment by adding weights.

Observations

Sr. # AppliedLoad

(kg)

AppliedLoad

(N)

Area(m

2)

TheoreticalPressure

(N/m2)

PracticalPressure

(N/m2)

1

2

3

4

5

6

7

8

9



EXPERIMENT # 14: FREE AND FORCED VORTEX

Free Vortex

Objectives:

1. To study on surface profile and speed.2. To find a relation between surface profile and speed.

Procedure:

1. Perform the general start-up procedures.2. Select an orifice with diameter 24mm and place it on the base of cylinder tank.3. Close the output valve and adjust the valve to let the water flows into the sink from twopipes with 12.5 mm diameter. The water can flow out through the orifice.4. Switch on the pump and open the valve slowly until the tank limit. Maintain the water levelby controlling the valve.

5. When the water level is stable, collect the vortex profile by measuring the vortex diameterfor several plane.6. Push down the profile measuring gauge until the sharp point touch the water surface.7. Record the measured height, h (from the top of the profile measuring gauge to the bridge.Obtain the value of a (mm) - distance from the bridge to the surface of the water level (bottom levelof the cutout).8. Use the pitot tube to measure the velocity by sinking it into the water at the depth of 5mmfrom the water surface. Measure the depth of the pitot tube in the water and also the heightdifference of the U tube at the side of the tank.9. Repeat Step 3-8 for another two orifice with diameter 16mm and 8mm respectively.10. Plot the coordinates of vortex profile for all diameter of orifice in the same graph and

calculate the gradient of graph as shown below:X =

Which X is the pressure head / depth of the pitot tube.11. Plot the velocity which study from the pitot tube reading, H versus the radius of the profile.

V = (2gH)0.5

Theoretically, the velocity can be calculated by using the following equation:

r

K V

Diameter atCentre, D

(mm)

MeasuredHeight, h

(mm)

Pitot TubeHead

Difference,H (mm)

PressureHead / Depthof the pitot

tube, X (mm)



Forced Vortex

Objectives:1. To study on surface profile and angular velocity.2. To find a relation between surface profile and total head.

Procedures:

1. Perform the general start-up procedures.2. Place a closed pump with two pedals on the foot of the bed.3. Close the output valve and adjust the valve to let the water flows into the sinkfrom two pipes with 9.0 mm diameter. The water can flow out through another two pipes with12.5mm diameter.4. Make sure that the water flow with the siphon effect by raising the hose to astandard before letting the water to the sink.5. Measure the angular speed of the pedals by counting the number of circles ina certain times.

6. Push down the surface probe until the sharp point touch the water surface.7. Record the vertical scale reading.8. Repeat Step 4-7 for another two volumetric flow rate.9. Plot the coordinates of vortex profile for different angular velocity.10. Plot the calculated profile vortex in the same graph as they relate as

h = h0 + r 2

Compare both experimental and calculated profile.

Distance from

Centre (mm)

ho (mm)

1st (___LPM) 2nd (___LPM) 3rd (___LPM)0

30

70

110

No of revolutionsin 60s

Angular Velocity(rad/s)

SUMMARY OF THEORY

1.1

Free Cylindrical Vortex

When a liquid is flowing out of a tank through a hole at the bottom of the tank, free vortexis formed with the number of oscillation depending on the distortion that created the flow.The liquid is moving spirally towards center following current, energy per unit mass isassumed to be constant when energy loss by viscosity is neglected. If, while the mass of



water is rotating, the central exit hole is plugged, the flow of water in the vertical planeceases and the motion becomes one of simple rotation in the horizontal plane. This isknown as free cylindrical vortex.

Bernoulli’s theorem can be used because the movement is along the flow axis,

z g

V

g

p

2

2

constant

For horizontal plane, the relation becomes

g

V

g

p

2

2

constant

Integration of the above relation with r gives

01

dr

dV

g

V

dr

dp

g (1)

Next, consider a pair of stream line being divided with distance r and is in samehorizontal plane and are linked by a fluid tube wide A . The centrifugal force of the tube isbalanced by the pressure difference between both ends, that is

Ar dr

dp

gr

V r A g

2

dr

dp

gr

gV 2 (2)

Combine (1) and (2) to produce

02

dr

dV

g

V

gr

V

0r V

dr dV

Integrate above relation to obtainV r lnln constant

vr (constant)

r

K V (3)

In free cylinder vortex, velocity is inversely proportional to distance from spiral axis.Bernoulli’s theorem is used to determine surface profile as follow:

C z g

V

2

2

(constant) (4)

Substitute (3) into (4)



C z gr

K 2

2

2

2

2

2 gr

K z C (5)

That is, equation for hyperbolic curve A x 2 that is symmetry to axis of rotation and is

horizontal to z = C

1.2

Free Vortex

Movement in free vortex is different with free cylindrical vortex because free vortexcontains radial velocity towards center. Equation for such situation can be generated byconsidering the water passes through round segments towards its diameter, where energypassing any tube and is kept constant until

z g

V

g

p

2

2

constant

If A and V is surface area and velocity of a particular position, and 1 , 1V are surface areaand velocity at distance r from center circle,

11V AV constant

By taking Kr ,

r

V r V 11

If is constant,

C gr

V r

g

p

2

2

1

2

1

2

2

2

1

2

1

2 gr

V r C

g

p (6)

Also,

C g

V

g

p

2

2

11

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p p

2

2

1

2

11 12 r

r

g

V

g

p p (7)

Free vortex can be said as combination of cylinder vortex and radial flow. Velocity isinversely proportional to radius in every case. Angle between flow axis and radius vector atany point is constant and these axis form the spiral pattern.

1.3

Forced Vortex



As we know, angular velocity is constant,

r V

Increase in radial pressure is given by

r r

V

dr

dp 22

2

1

2

1

2 p

p

r

r rdr dp

)(2

1 2

1

2

2

2

12 r r p (8)

By taking 01 p , when 01r , and p2 when r r 2 ,

22

0

2r

g

w

g

p p

Because h g

p , so

22

2r

g hh o

22

02

r g

hh (9)

This is a parabolic equation.

Surface profile for forced vortex can be represented by equation:

g

r z

2

22

Distribution of total head can be represented by equation:

g

r H

22

Where:Z = Surface profile

= Angular velocityr = Radiusg = Gravity

H = Total Head Angular velocity can be calculated by:

Where:Z = Surface profile



Ω = Angular velocityr = Radiusg = Gravity



EXPERIMENT # 15: Wind Tunnel

Objectives

1. To study the operation of the wind tunnel.

2. To find the velocity of air in the test section of the wind tunnel using Pitot tube.

Apparatus:

Wind Tunnel Specifications:

Overall Length = 4.4 meters

Height = 2.0mWidth=0.9mTest section airspeed = 50 m/s (max)Test section dimensions = 230 mm x230 mm x480 mm

AF-81 Wind Tunnel is basically designed for study of aerodynamics in subsonic region.Typically Subsonic (or low-speed) aerodynamics studies fluid motion in flows which aremuch lower than the speed of sound everywhere in the flow.

A purpose built contraction is designed to allow uniform velocities in the test section ofthe wind tunnel and velocities up to 50 m/s are attainable in the wind tunnel. Amechanical damper assembly is installed in the wind tunnel which provides continuousvariable control of the air velocity.

In solving a flow problem, one decision is to be made, whether to incorporate the effectsof compressibility or not. Compressibility is a description of the amount of change ofdensity in the flow. When the effects of compressibility on the flow are small i.e. at lowvelocities, the density is assumed to be constant. The problem is then treated as anincompressible low-speed aerodynamics or a subsonic flow problem. If study of the flowis characterized by large velocities, the density is not constant anymore and varies

according to the velocity, the problem is then called a compressible flow problem andeffects of compressibility on the flow have to be incorporated in the solution. In air,compressibility effects are usually ignored when the Mach number of the flow does notexceed 0.3. Flows involving Mach number greater than 0.3 should be solved byincorporating compressibility effects.

Test Section of the Wind Tunnel:



1. In the test section, the air velocity can be measured by a Pitot Static Tube, and the pressure variation can be measured along various models/aero foils.

2. To prevent unnecessary vibrations in the test section the fan assembly is mountedin its own support and fitted with anti-vibration mounts.

Calculation of Velocity:

Air Velocity in the test section can be calculated from the Bernoulli‟s equation.

Total Pressure = Static Pressure + Dynamic Pressure

Mathematically;

Static pressure is negative because of the air flowing above the Pitot static tube creates anegative pressure on the surface of the Pitot static tube,

Air velocity can be derived from the velocity pressure relation which comes out to be:

Since; and;

Substituting and solving for V in the above mentioned equation yields;

Here;

P1 = atmospheric pressure (mbar)P2 = Pressure difference on the manometer (mbar)R = Specific Gas Constant (287.1 J/Kg 0K)

⇒

⇒

⇒



T = Temperature (Kelvin)

Observations:

S No Temperature(Kelvin)

P1 (mbar) P2 (mbar) Velocity (m/s)

fluid mechanics lab manual

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