1.0 INTRODUCTION

1.1 OBJECTIVES:

1) To determine the reaction force generated by impact of the jet on vanes of various shapes such as conical cup, flat plate and hemispherical cup.2) To compare the experimentally measured force with the theoretical calculated force.

1.2 BACKGROUND:A fundamental phenomenon of fluid mechanics is the production of mechanical work from fluid with high pressure which works in such a degree so that the pressure can be used to accelerate the fluid to a high velocity in a jet. Momentum is carried in moving streams of water and it is essential for a force to be applied with an equal opposite force applied to the object redirected the stream of water to change the direction or velocity of the water flow[1]. As the jet hits the vanes which is directed tangentially on to the vanes, a momentum change or impulse occurs along with a formation of force which generates a torque of the turbine wheel causing it to rotate and develop power. This concept has one of the major application in engineering world known as water turbines which are widely used throughout the world to generate power. Substantial output at high efficiency can be produced by such turbines. With an efficiency of greater than 90% and outputs of the order of 100,00 kW, water turbine have been constructed by applying this impulse principle[2] signifying the essence to understand the phenomenology through the impact of jet experiment.

In this experiment, measurement of force generated by a jet of water as it hits a flat plate, conical plate, and hemispherical cup were performed to answer the question " How does the reaction force generated by impact of the jet differs as vanes of various shapes are used? " using a graph and later comparing with the theoretical value along with the comparison of the momentum flow rate in the cup.

2.0 EXPERIMENTAL DESIGN

2.1 MATERIALS

The experiment consists of:1) A jet impact apparatus H8, consisting a plumbing for revaluating water, a water nozzle, and a spring scale connected to a balance beam and a flow meter.

Figure 1. Diagrammatic Arrangement of Apparatus2) Volumetric Hydraulic Bench/Water H1 to get the water admitted through the bench supply valve

Figure 2. Volumetric Hydraulic Bench3) 3 Different shapes of vanes: Flat Plate, Conical Cup and Hemispherical Cup used to determine the variety of forces it produces when it is directed tangentially by the jet

Flat PlateHemispherical CupConical CupFigure 3. Shapes of Vanes used in the experiment4) Stop watch to measure the time

Figure 4. Stopwatch

2.2 METHODSThe principle of conservation of linear momentum was used throughout the experiment, which states that "In a closed system the total momentum of a system of colliding objects stays the same on condition that there is no resultant external force acts on the system"(Newton's Third Law"[3].

Before the experiment was performed, it was scrutinized to ensure that the unit was in proper operating condition such as ensuring the plate was screwed well enough to hinder the plate from moving otherwise it can give an outcome of consistent wrong result producing systematic errors. The set up was done in such a way so that the nozzle through which jet emerges tangentially to the vane may be observed through the transparent cylinder. A hydraulic bench was used in the experiment to render momentum to the nozzle. As the plate deflector were placed, the lock nut on rod was constricted and the cover was screwed back onto vessel. Cautions were taken to ensure that the indicating pointer has been zeroed which is done by adjusting the pointer position alighting it with the white lines on the plate. The time recorded for level in the volumetric tank to accumulate 5 liters were recorded for later use in the calculation of the mass flow rate leading to the calculation of the rate of change of momentum. After that the flow control valve were turned off and the catchment tank plug was allowed for drainage once the pump was closed. All the results were recorded and tabulated to organize quantitative information into tables and graphs, with appropriate units. For the purpose of comparing the experimental value with the actual value, the information was then used to plot a graph of force against the rate of change of momentum in order to determine the percent error which is a percentage of difference between the measured value and the "true value" that is obtained theoretically[4].

2.3 PROCEDURES1) The apparatus was initally level beginning with the flat plate and the level was set to balanced position by the screw in the jet impact apparatus

2) With the jockey mass of 0.6kg at its zero position the level was set to the balanced position which was indicated by the tally.

3) Water was supplied through the bench supply valve to the jet impact apparatus

4) The rate of was then maximized and the position of the jockey weight which retains the lever to the balanced position was observed, as the discharge was weighed in the weighing tank.

5) With approximately equally spaced positions of the jockey weight a serious of about four readings were taken by decreasing the flow rate from the bench.

6) Weight of water collected was adjusted to ensure discharge over 60 seconds.

7) Stop watch was used to record the time taken for the water completely fill up 5 liters of water.

8) The diameter of the nozzle, the height of the vane above the tip of the nozzle when the lever was balanced, the distance between the centre of the vane and the pivot of the lever and the jockey weight were noted.

9) Steps 1 to 7 were repeated for conical cup and the hemispherical cup plate.

3.0 RESULTS AND DISCUSSIONIt was observed that the time taken for the hydraulic bench to accumulate a volume of water of 5 kg decreased as the distance y(m) from its zero position were increased from 0.015 m to 0.060 with an increment of 0.015 for 4 readings. Each deflectors had a different amount of time, and the recorded time were used to calculate force and rate of delivery of momentum, for Flat Vanes, Hemispherical Vane, Conical Cup as shown in Table 1, Table 2 and Table 3.

3.1 TABLE OF DATATable 1. Flat VanesQuantity(kg)t(s)y(m)(kgs-1)u(ms-1)uo(ms-1)uo(N)F(N)

523.150.0150.2162.7522.6240.5670.5886

518.750.0300.2673.4013.2980.8811.177

515.250.0450.3284.1784.0951.3431.766

512.430.0600.4025.1215.0532.0312.351

Table 2. Hemispherical VaneQuantity(kg)t(s)y(m)(kgs-1)u(ms-1)uo(ms-1)uo(N)F(N)

539.690.0150.1261.6051.3740.1730.5886

527.000.0300.1852.3572.2060.4081.177

520.690.0450.2423.0832.9690.7181.766

517.460.0600.2863.6433.5471.0142.354

Table 3. Conical VaneQuantity(kg)t(s)y(m)(kgs-1)u(ms-1)uo(ms-1)uo(N)F(N)

532.250.0150.1551.9751.7930.2780.5886

520.720.0300.2413.0702.9560.7121.177

516.560.0450.3023.8473.7571.1351.766

514.940.0600.3554.2684.1871.4032.354

3.2 GRAPHICAL REPRESENTATION

Figure 5. Graph of forces of vanes with its rate of delivery of moment3.3 CALCULATION DETAILS

1) Calculation of (kgs-1) which is the volumetric flow rate.For each vanes = Note: Volume of water was kept constant as 5 kg throughout the experiment.

2) Calculation of u(ms-1) which is the velocity of the jet as it leaves the nozzle .

For each Vanes

3) Calculation of uo(ms-1) which is the velocity of the jet when it is deflected by the vane. This velocity is less than the velocity u at exist from the nozzle as gravity takes part to cause deceleration.

For each vanes

or

3.4 INTERPRETATION OF RESULTSThe results obtained from the experiment allowed to determine the properties of forces that acts on the different type of deflector and also aids to calculate the calculated force F(N). From the graph, a comparison can be made with the different types of deflectors used. It can be observed using the best-fit line from the graph that a proportionality relationship exists between the force produces on each of the vanes against the rate of delivery of momentum as it passes in the jet. From the experiment a deduction can be implied that for different deflector with different angles will produce different rate of delivery of momentum and force . The theoretical force for each shape of the vanes and their angle are shown on Table 4.Table 4. The deflection angle, , and the force, F, developed on different shapes of vanes.Shape of the vaneF

Flat Plate 90

Conical Cup 1201.5

Hemispherical Cup 1802

The theoretical force represents the gradient in the graph of forces of vanes against rate of delivery of momentum, which can be used to compare with the experimental resultant force obtained and calculate the percentage error for each vanes.

Referring Figure 5, the gradients can be found for each shape for calculating percentage error. Percentage error for Flat Plate : = 17.51%Percentage error for Conical Cup: = 2.18%Percentage Error for Hemispherical Cup: = 3.52%Systematic experimental errors, such as errors like measuring the value of nozzle diameter could be the cause of such discrepancies[5].

Some kind of systematic errors could be like, the jockey weight having an error by 1 g, then the F, force produced by the vanes will not be the same as F 0.15 = mjockey g y (newtons). Assuming g =9.81 ms-1 and letting F be the force produced from the vanes and the distance from the nozzle to the jockey weight be y, so that the new value will be +1g from what was used before, resulting to F x 0.15 = (0.6+0.001) x g x y (N) which leads to F= 39.31y. In the case of a -1g error the F will be 39.17y.The percentage difference will be (39.31 39.24) / 39.24 x100 = 0.178% between the cases of having an error in jockey weight by 1g and actual value.

In the case of having an error in the distance from centre of vane to pivot of lever by 1mm, the force produced by the vanes will also be altered. Considering case the distance augmenting by 1mm then the force will be : F x (0.15+0.001) = 0.6 x g x y (Newton) F= 38.98y and another case of a decreased in the distance by 1mm then the force will be F x (0.15-0.001) = 0.6 x g x y (newton) F= 39.50y . The percentage difference caused by the differences in distance between the actual value by 1mm will be 1.88%.From the above discussions , a conclusion can be made that whenever the jockey weight is increased or the distance from center of vane to pivot of lever is increased the force will increase proportionally and vice versa.Net momentum transferred is the main dependence on the impact of a fluid jet and the mass flow rate which is related to the average velocity of the jet is depended by the momentum. This implies that when the mass flow rate is same in two jets of the same fluid , it will deliver the same momentum, independent of their velocity distribtuion.Considering a case where the impact of jet that has 10% greater area, the force will be decreased by 0% as as . The impact of a fluid jet depends only on the net momentum transferred. The momentum depends on the mass flow rate which related to the average velocity of the jet. This means two jets of the same fluid with the same mass flow rate will deliver the same momentum, regardless of their velocity distribution.Considering a case where the impact of jet possesses 10% greater area, the force will be decreased by % as .Assuming Ao= 1.1 A (1.0+0.1)Ao=1.1AF=V2AoF=V2(1.1)A0.91F= 2AConsidering a case where the impact of jet has a slower velocity of 10%, the force will be increased by 110% of the original force Assume A1 as 0.9A (1.0-0.1)F= V2A1F= V2(0.9)A1.1F= V2A4.0 Error Analysis

Some kind of systematic errors that could have occurred while doing the experiment are :

1) Discrepancy in velocity due to the difference in height between nozzle and vanes2) The viscosity effects were not included in the calculation of the theoretical value.3) Losses such as frictional losses were not considered..4) The vane cannot be fully in equilibrium as human error is always there which will cause some fluctuation leading to errors.5) Parallax errors could have occurred due the differences in eye level of the experimenter leading to a result that is higher or lower than the ideal results.

5.0 Conclusion

ABSTRACT

LEFT FOR CONCLUSION:The impact of jet experiment helps us to understand how does turbines works under fluid pressure. The mechanical work produced by using pressure of moving fluid at a high velocity jet of water from nozzle produces force when it strikes on the plane of the surface of the plate. The forces exerted on the surface plane will also depend on the density of fluid at specific temperature. The force exerted on the impact will generate the momentum change and also to determine the mass flow rate. This experiment aims at assessing the different forces exerted by the same water jet on a variety of geometrical (flat plate and hemispherical plate ).