impact of jet

1.0 ABSTRACT
The objective for this experiment is to verify the momentum equation experimentally through the impact of jet against deflectors. There are four deflectors used in this experiment. The four deflectors are plate, hemisphere, slope and cone. The loading weights to be used are 0.8 N, 1.0 N, 1.5 N and 2.0 N. In this experiment, the time taken for the water level in the volumetric tank to raise from 10 to 20 L is determined by using a stop watch. The flow rate, calculated force and the error percentage will be calculated in this experiment. The theoretical and measured force will be compared in this experiment.

2.0 INTRODUCTION
The aim of this experiment is to verify the momentum equation experimentally through the impact of jet against deflectors. This experiment use different forces exerted by the water jet on different geometrical plates. The exerted forces will generate the momentum change and also determine the flow rate of water in the volumetric tank to raise from 10 to 20 L. This helps us to understand how forces can affect the change of momentum flow in the jet. The theoretical jet force can be calculated from the principle of linear momentum. The density of water is 1kg/L. The results obtained are to be compared with the theoretical values. To produce mechanical work from fluid under pressure, we use the pressure to accelerate the fluid to a high velocity in a jet. The application of this principle can be seen surrounding us. For example, water turbines are used to generate power in our country. Another example is that the kinetic energy stored in a jet is used by the firemen to deliver water above the level in the nozzle to extinguish fires in tall buildings. And also, the pelton on wheel is used to make flour.

3.0 APPARATUS
i. HM150 impact of jet
a) Loading weights
b) Lever mechanism
c) Deflector
d) Nozzle
e) Perspex vessel
f) Drain connection
g) Base plate
h) Inlet connection ii. Various deflector
Plate
Hemisphere
Slope
Cone iii. A set of weights iv. Stop watch

3.1 PROCEDURES
1) A quick inspection is performed to ensure that the units is in proper operating condition.
2) A hose connection made and the unit is connected to the nearest power supply.
3) The discharge pipe is opened.
4) One of the deflectors (plate, hemisphere, slope or cone) is assembled. The three screws (3) on the cover (4) is loosen. The cover is removed together with the lever mechanism.
5) An appropriate deflector is fitted. The lock nut (2) on the rod is tightened. The cover is screwed back onto the vessel.
6) Adjusting screw (5) is used to set pointer to zero (7). Any loading weights are not placed on measurement system when doing so.
7) The desired loading weight :0.2N, 0.3N, 1N, 2N, and 5N is applied.
8) The main clock is closed.
9) The pump is switched and the main cock is opened carefully until pointer is on zero again.
10) The drain cock is closed and the volumetric flow rate is determined by using stopwatch to establish time required for raising the level in the volumetric tank from 20 to 30 liters.
11) The pump is switched off and the drain is opened.
4.0 RESULTS AND DATA ANALYSIS
Table 1.1 Results of Measurement for 90º deflection
Deflector
Plate (90º deflection)
Force F in N
Measuring time in second
Flow rate in liter per second
0.8
46.34
0.22
1.0
42.59
0.23
1.5
30.18
0.33
2.0
25.35
0.39
Measured volume: 10 L

Table 1.2 Results of Measurement for 180º deflection
Deflector
Hemisphere (180º deflection)
Force F in N
Measuring time in second
Flow rate in liter per second
0.8
82.38
0.12
1.0
52.66
0.19
1.5
47.83
0.21
2.0
39.07
0.26
Measured volume: 10 L

Table 1.3 Results of Measurement for 45º and 135º deflection
Deflector
Slope (45º and 135º deflection)
Force F in N
Measuring time in second
Flow rate in liter per second
0.8
24.52
0.41
1.0
15.05
0.66
1.5
14.58
0.69
2.0
12.95
0.77
Measured volume: 10 L

Table 1.4 Results of Measurement for 45º deflection
Deflector
Cone (45º deflection)
Force F in N
Measuring time in second
Flow rate in liter per second
0.8
39.96
0.25
1.0
39.75
0.25
1.5
33.96
0.29
2.0
27.11
0.37
Measured volume: 10 L

Table 2.1 Results of Force Calculation for 90º deflection
Deflector
Plate (90º deflection)
Flow rate V in liter per second
Velocity w1 in m/s
Calculated force Fth in N
Measured force F in N
0.22
2.80
0.62
0.8
0.23
2.93
0.67
1.0
0.33
4.20
1.38
1.5
0.39
4.97
1.94
2.0

Table 2.2 Results of Force Calculation for 180º deflection
Deflector
Hemisphere (180º deflection)
Flow rate V in liter per second
Velocity w1 in m/s
Calculated force Fth in N
Measured force F in N
0.12
1.53
0.37
0.8
0.19
2.42
0.92
1.0
0.21
2.67
1.12
1.5
0.26
3.31
1.72
2.0

Table 2.3 Results of Force Calculation for 45º and 135º deflection
Deflector
Slope (45º and 135º deflection)
Flow rate V in liter per second
Velocity w1 in m/s
Calculated force Fth in N
Measured force F in N
0.41
5.22
1.07
0.8
0.66
8.40
2.77
1.0
0.69
8.79
3.03
1.5
0.77
9.80
3.77
2.0

Table 2.4 Results of Force Calculation for 45º deflection
Deflector
Cone (45º deflection)
Flow rate V in liter per second
Velocity w1 in m/s
Calculated force Fth in N
Measured force F in N
0.25
3.18
1.19
0.8
0.25
3.18
1.19
1.0
0.29
3.69
1.61
1.5
0.37
4.71
2.61
2.0

4.1 CALCULATION
For plate,
Fth = V × ρ (W1 – W2)
If W2 = 0 then,
Fth = V ρ W1 0.8 N,
Fth
Percentage of error=
1.0 N,
Fth
Percentage of error=
1.5 N,
Fth
Percentage of error=
2.0 N,
Fth
Percentage of error=

For hemisphere,
Fth = V × ρ (W1 – W2)
If W2 = -W1 then,
Fth = 2 V ρ W1

0.8 N,
Fth
Percentage of error=
1.0 N,
Fth
Percentage of error=
1.5 N,
Fth
Percentage of error=
2.0 N,
Fth
Percentage of error=

For slope,
Fth = V × ρ × W1 cos α
If α = 45° then,
Fth = Fx cos α = V × ρ × W1 cos2 α
0.8 N,
Fth
Percentage of error=
1.0 N,
Fth
Percentage of error=
1.5 N,
Fth
Percentage of error=
2.0 N,
Fth
Percentage of error=

For cone,
Fth = V × ρ × (W1 – W2x)
If α = 45° then,
W2 = - W1 cos α
W2x = W2 cos α
Fth = V ρ W1 (1+ cos2 α)

0.8 N,
Fth
Percentage of error=
1.0 N,
Fth
Percentage of error=
1.5 N,
Fth
Percentage of error=
2.0 N,
Fth
Percentage of error=

5.0 DISCUSSION :
In this experiment, 10 L of water and 10 mm diameter nozzle are used. To calculate the calculated force, Fth in N and the percentage of error, we used the time taken. The density of the water used is 1kg/L. To calculate the calculated force Fth , we used the formula below:
For plate :
Fth = V × ρ (W1 – W2)
If W2 = 0 then,
Fth = V ρ W1

For hemisphere :
Fth = V × ρ (W1 – W2)
If W2 = -W1 then,
Fth = 2 V ρ W1

For slope :
Fth = V × ρ × W1 cos α
If α = 45° then,
Fth = Fx cos α = V × ρ × W1 cos2 α

For cone :
Fth = V × ρ × (W1 – W2x)
If α = 45° then,
W2 = - W1 cos α
W2x = W2 cos α
Fth = V ρ W1 (1+ cos2 α)
The time taken for the water in the volumetric tank to raise from 10 L to 20 L decreased as the measured force increased. As a result, the flow rate decreased. In this experiment, hemisphere deflector has the lowest flow rate among the deflectors used. This indicates that hemisphere deflectors are the most efficient to be used in water turbines. The calculated forces for each deflector are different from the measured forces. The comparison between calculated force and measured force for each deflectors is stated in the table below :
Example value :1 N
Calculated force, Fth in N
Measured force, F in N
Plate
0.67
1.0
Hemisphere
0.92
1.0
Slope
2.77
1.0
Cone
1.19
1.0

To calculate the percentage of error:
Percentage of error =

Theoretically, the calculated force is supposed to be the same as the measured force. The percentage of error in this experiment ranged from 3% to 177%. The difference between the calculated force and measured force is due to some errors made throughout the experiment. For example, when setting the pointer, due to parallax error, the pointer may not be set to zero precisely. Next, when adjusting the main cock, error might be made. The main cock may not properly open thus causing the pointer not exactly at zero. Another possibility is that when measuring the water level raise from 10 L to 20 L, parallax error might occured. To improve the accuracy of this experiment,we may repeat the steps to get consistent values. In order to improve the errors, when setting the pointer, make sure the eye level is at the same level with the pointer to ensure it is set to zero accurately. Next, make sure the main cock is properly open by double checking it. Reading on volumetric tank should be on the water meniscus to avoid parallax error. We also must make sure the control valve is completely close before the pump is switched on in order to avoid intrusion of air into the pump. Entrapped air may reduce the exerted force of the jet.

6.0 Conclusion
In conclusion, the momentum equation is verified experimentally through this experiment. The calculated force is supposed to be the same as measured force. But in this experiment, the difference between the calculated force and the measured force may due to some errors made during the experiment. In this experiment, the hemisphere deflector has the lowest flow rate and takes longer time for the volumetric tank to rise from 10 L to 20 L compared to the other deflectors. Therefore hemisphere deflector is the most efficient to be used in water turbine.

7.0 REFERENCES
1) David M. Smiadak. (2008). Impact of jet. [Online]. 24th June 2008. Available from: http://claymore.engineer.gvsu.edu/~smiadakd/EGR365-Lab7.pdf 2) Kisan Bidkar.(2011). Impact of jet. [Online Video]. 10th January 2011. Available from: http://www.youtube.com/watch?v=tXLI-IeAynI 3) Matthew Mitchell.(2013). Final Impact jet. [Online Video].18th February 2013. Available from: http://www.youtube.com/watch?v=ja8N-aZnbF0 4) R.K. Bansal 1983, A Textbook of Fluid Mechanics and Hydraulic Machines, 1st Edition, Laxmi Publications (P) Ltd, India.
5) Rama Durgaiah, 2002, Fluid Mechanics and Machinery, 1st Edition, New Age International (P) Ltd, India.

References: 1) David M. Smiadak. (2008). Impact of jet. [Online]. 24th June 2008. Available from: http://claymore.engineer.gvsu.edu/~smiadakd/EGR365-Lab7.pdf 2) Kisan Bidkar.(2011). Impact of jet. [Online Video]. 10th January 2011. Available from: http://www.youtube.com/watch?v=tXLI-IeAynI 3) Matthew Mitchell.(2013). Final Impact jet. [Online Video].18th February 2013. Available from: http://www.youtube.com/watch?v=ja8N-aZnbF0 4) R.K. Bansal 1983, A Textbook of Fluid Mechanics and Hydraulic Machines, 1st Edition, Laxmi Publications (P) Ltd, India. 5) Rama Durgaiah, 2002, Fluid Mechanics and Machinery, 1st Edition, New Age International (P) Ltd, India.