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Impact of Jet on Vanes

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ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1 Impact of Jet on Vanes Aim Study the relation between the force produced and the change of momentum when a jet strikes a vane. Compare between force exerted by a jet on a flat plate and on a hemispherical surface. Apparatus Acrylic nozzle stainless steel enclosure with glass viewports interchangeable arcylic circular flat plate and a hemispherical cup Weights of various mass. measuring tank to measure the discharge and electronic watch Theory Momentum conservation principle is applied in order to find out the force applied by jet onto the flat-plate or spherical cup. = F = ρ Q ΔV F = ρ Q (V in V out ) Where, F: force applied on plate by jet Q: volumetric flow rate V in : velocity at the time of striking of jet onto the plate. V out : velocity of water leaving the plate. The volumetric flow rate in the equation 'Q' is calculated with the help of measuring tank and stopwatch. = Where, H: height in measuring tank t: time taken to achieve the height A tank : base area of measuring tank
Transcript
Page 1: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1

Impact of Jet on Vanes

Aim

Study the relation between the force produced and the change of momentum when a jet strikes a vane.

Compare between force exerted by a jet on a flat plate and on a hemispherical surface.

Apparatus

Acrylic nozzle

stainless steel enclosure with glass viewports

interchangeable arcylic circular flat plate and a hemispherical cup

Weights of various mass.

measuring tank to measure the discharge and electronic watch

Theory

Momentum conservation principle is applied in order to find out the force applied by jet onto the flat-plate or spherical cup.

𝐹 =𝑑𝑃

𝑑𝑡

F = ρ Q ΔV

F = ρ Q (V

in – V

out)

Where, F: force applied on plate by jet Q: volumetric flow rate Vin: velocity at the time of striking of jet onto the plate. Vout: velocity of water leaving the plate.

The volumetric flow rate in the equation 'Q' is calculated with the help of measuring tank and stopwatch.

𝑄 =𝐻𝐴𝑡𝑎𝑛𝑘𝑡

Where, H: height in measuring tank t: time taken to achieve the height Atank: base area of measuring tank

Page 2: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 2

Vnozzle is calculated by,

𝑉𝑛𝑜𝑧𝑧𝑙𝑒 =𝑄

𝐴𝑛𝑜𝑧𝑧𝑙𝑒

Where, Vnozzle: velocity of jet at the nozzle Anozzle: cross sectional area of nozzle

Relation between V

in and Vnozzle can be given as,

Vin

2

= Vnozzel

2

– 2 g S

Where;

g: the gravitational acceleration (9.81 m/s2

). S: the distance between the jet and the plates.

Schematic of jet impact on vanes has been shown in below diagram.

V

out generally equals V

in cos θ, where θ represents the change in direction of the jet.

For the flat plat θ = 90◦, so that V

out = 0.

Page 3: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 3

For the Hemispherical cup θ = 180◦, so that Vout

= -Vin

So the following relations are used for calculating the Predicted values of the force;

For the Flat plate: F = ρ Q Vin

For the Hemi spherical cup: F =2 ρ Q Vin

The actual force exerted is calculated by the equation,

F = 9.81 * w Where,

w: mass of weights plus mass of plate and rod.

Procedure

Clean the apparatus and make All Tanks free from dust.

Close the drain valves provided.

Fix desired Vane on the apparatus.

Fill Sump tank ¾ with Clean Water and ensure that no foreign particles are there.

Ensure that all On/Off Switches given on the Panel are at OFF position.

Now switch on the Main Power Supply (220 V AC, 50 Hz).

Switch on the Pump.

Regulate Flow of water through channel with the help of given Flow Control Valve.

Put known value of weight on the plate.

Now control the valve so that the applied weight on the top is counter balanced by the impact of jet.

Measure Flow Rate using Measuring Tank and Stop Watch.

Repeat the experiment with different weights.

Slowly open the bypass valve. Switch off the pump.

Page 4: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 4

Data

Area of measuring tank= 0.25*0.4= 0.1 m2

Diameter of nozzle d=0.01m

Area of cross section of nozzle A=πd2/4=0.0000785 m2

Density of water= 1000 kg/m3

Weight of aluminum disc + rod = 14.5 gm

Weight of flat plate= 89.5 gm

Weight of hemispherical vane= 97.5 gm

Additional constant weights:

for flat plate = 104 grams

for hemispherical vane = 112 grams

Observation

A. For Flat Plate:

S.No W (gm) Fexp (N) S (cm) H (cm) t (sec) Q (m3/s) Vnozzle (m/s) Vim (m/s) Ftheo (N)

1 202.5 1.985 15.50 24.20 44.94 0.0005385 6.860 6.635 3.456

2 296.0 2.901 16.50 27.50 45.13 0.0006094 7.762 7.551 4.476

3 390.0 3.822 13.40 29.10 44.63 0.0006520 8.306 8.146 5.210

4 585.0 5.733 12.50 32.20 44.66 0.0007210 9.185 9.050 6.430

B. For Hemispherical vane:

S.No W (gm) Fexp (N) S (cm) H (cm) t (sec) Q (m3/s) Vnozzle (m/s) Vim (m/s) Ftheo (N)

1 210.5 2.063 11.60 19.00 44.97 0.0004225 5.382 5.167 4.191

2 304.0 2.979 11.40 21.20 44.53 0.0004761 6.065 5.878 5.424

3 398.0 3.900 11.10 23.60 44.88 0.0005258 6.699 6.534 6.703

4 593.0 5.811 9.400 27.80 44.56 0.0006239 7.947 7.831 9.627

Page 5: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 5

Observation for the sample calculation

W= 202.5 gm

S= 15.50 cm

H= 24.20 cm

t= 44.94 s

Area of measuring tank= 0.25*0.4= 0.1 m2

Area of cross section of nozzle A=πd2/4=0.0000785 m2

Density of water= 1000 kg/m3

Sample Calculation

Flow rate = 𝑄 =𝐻𝐴𝑡𝑎𝑛𝑘

𝑡 =

0.10∗ 0.242

44.94 = 0.0242 m3

Velocity at the nozzle = Vnozzle = 𝑄

𝐴𝑛𝑜𝑧𝑧𝑙𝑒 = 6.860 m/s

𝑉𝑖𝑛 = 𝑉𝑛𝑜𝑧𝑧𝑙𝑒2 − 2𝑔𝑆 = = 6.862 − 2 × 9.80 × .15 = 6.63 m/s

Experimental Force = Fexp = mg = 1.985 N

Theoretical Force = Ftheo = 𝜌𝑎𝑉𝑖𝑚2= 3.45 N

Page 6: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 6

Graphs

Precaution

Never start the pump when bypass valve is closed. Slowly close bypass valve in order to avoid

sudden impact on the plates. Also open bypass valve slowly before switching off the pump.

0

1

2

3

4

5

6

7

0 2 4 6 8 10

Forc

e E

xert

ed

(N

)

Velocity (m/s)

Flat Plate

Experimental

Theoretical

0

2

4

6

8

10

12

0 2 4 6 8 10

Forc

e Ex

erte

d (

N)

Velocity (m/s)

Hemispherical Vane

Experimental

Theoretical

Page 7: Impact of Jet on Vanes

ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 7

Errors

Due to use of stop watch manual errors in timings are introduced.

Even though the weight was balanced, the height gradually dropped while calculating the H. This may be attributed to drop in pressure head because of drop in water level in supply tank.

Conclusion

Experimental force exerted by jet on hemispherical vane is always more than that of flat plate,

and almost double to that of flat plate force.

As the weight on the plats increased, higher impact velocity or jet velocity is required to counter

balance the force.

-Vrushiket Patil(09003044)

Mechanical B’tech 2009


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