Impact of a Jet

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Abstract
The objective of this experiment is to measure the force generated by impact of the jet on vanes of various shapes like flat plate, conical cup and hemispherical cup. Besides that, the results from the experiment have to be compared with the theoretical calculations too.

1.0 Introduction
Water turbines are widely used throughout the world to generate power. By allowing fluid under pressure to strike the vanes of a turbine wheel, mechanical work can be produced. Rotational motion is then produced by the force generated as the jet strikes the vanes. One way of producing mechanical work from fluid under pressure is to use the pressure to accelerate the fluid to a high velocity in a jet. The jet is directed on to the vanes of a turbine wheel, which is rotated by the force generated in the vanes due to the momentum change or impulse which takes place as the jet strikes the vanes. Water turbines working on this impulse principle have been constructed with outputs of the order of 100,000 kW and with efficiencies greater than 90%. In this experiment, the force generated by a jet of water as it strikes a flat plate, conical plate and hemispherical cup may be measured and compared with the momentum flow rate in the jet.

2.0 Experimental Design
2.1 Apparatus and Materials
The jet impact apparatus
Volumetric hydraulic bench/water
3 different shapes of vanes :
Flat plate
Conical cup
Hemispherical cup
Stopwatch

Figure 1. Arrangement of apparatus.

Procedure
Starting with the flat plate, the apparatus is firstly leveled and the lever set to the balanced position (as indicated by the tally) with the jockey weight at its zero position.
Water is admitted through the bench supply valve. The rate of flow is then increased to the maximum and the position of the jockey weight which restores the lever to the balanced position is noted, while the discharge is weighed in the weighing tank.

A series of about four readings with roughly equally spaced positions of the jockey weight, are then taken by decreasing the flow rate from the bench. (The weight of water collected is adjusted to ensure discharge over 60 seconds.)

The experiment is repeated by using conical plate and hemispherical cup.
The diameter of the nozzle, the height of the vane above the tip of the nozzle when the lever is balanced, the distance between the centre of the vane and the pivot of the lever and the jockey weight are noted.

3.0 Results and Calculations
Table 1. Results for flat plate
Quantity (kg)t
(s) y
(m)
(kg/s)u
(m/s)uo
(m/s) ṁuo
(N)F
(N)
10.0024.350.100.415.245.172.123.92
10.0028.460.080.354.484.401.543.14
10.0031.290.060.324.083.991.272.35
10.0040.770.040.253.123.010.741.57

Table 2. Results for conical cup
Qty
(kg)
t (s)
t1 t2 t3 tavg
y
(m)
(kg/s)u
(m/s)uo
(m/s) ṁuo
(N)F
(N)
10.0023.90 23.36 23.89 23.72 0.130.425.385.322.255.10 10.0030.41 28.84 28.97 29.410.100.344.344.261.453.92 10.0034.83 34.15 37.47 35.480.070.283.603.500.992.75 10.001.03.48 58.28 59.21 1.00.320.040.172.121.950.321.57

Table 3. Results for hemispherical cup
Quantity (kg)t
(s) y
(m)
(kg/s)u
(m/s)uo
(m/s) ṁuo
(N)F
(N)
10.0023.000.170.445.555.492.396.67
10.0028.350.130.354.504.421.565.10
10.0037.000.090.273.443.340.903.53
10.0057.000.050.182.232.070.361.57

Calculations are obtained by using the following equations : ṁ = Quantity/t
u = 12.75 ṁ
uo = u2 – 0.687
F = 39.24y

Figure 2. Force developed on vanes of different shapes.

4.0 Conclusion
As a conclusion, the calculated force is correlated with the measured force. Both the forces have a directly proportional relation. Theoretically, the calculated force should be the same as the measured force. However,...
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