Question

Force from a Jet of Water A jet of fluid striking a vane exerts a force on the vane it is equal and opposite to the vane. It is the equal and opposite force of the fluid momentum change that accompanies such a flow. For different weights, the water flow rate is adjusted so the platform stays at the zero reading. These values are given below Q, ftA3/s 0045 0069 0011 0107 0116 0041 0076 0113 0146 Weight Angle, deg 90 Time, s 29.8 18.2 05 Balance spring 15 90 90 180 180 180 180 12.6 10.1 25 21 13.2 11.1 25 02 07 12 17 Vane Tasks: 1) Assume the diameter d is given as 0.4 in. Use the experimental data to construct a graph of the force of the water vs the exit velocity from the nozzle at both 180 and 90 degrees. On the same figure, use the momentum equation to plot the theoretical weight that can be supported by the water jet as a function of V 2.) Assume the exit velocity of the nozzle is now fixed at a constant 10 m/s how would you expect the changes in angle to affect the force of the water, use your theoretical equation to graph the force of the water vs angle (between 90 to 180 degrees)

Answer 1

Water Jet exit from nozzle at V m/sed. Weint Balance springQ is the discharge m /sec. d is the diameter of nozzle W is the weight. 0 is the angle made by exit flow with the direction of inlet flow Force exerted by jet is given by Vane (Mass per sec) * (inlet veloity - Final velocity) (Mass persec) * (Velocity before strike - Velocity after strike) 1809 Force exerted in the direction of inlet jet Y component of the Force, and this component is responsible for lifting the weight Force exerted in the direction of Y-pAV(V-(-Vcos(1809)) where ρ is density of fluid (ie water)-1000kg/ml 3 A is the crosssectional area-πγ2 where r-d/2 Force exerted in X direction pAV(0 (Vsin (180-6))

1) Assume d = 0.4 in = 0.01016 m implies r = 0.00508 implies A: 8.107319 x 10-5 m2 Discharge Q-AV 8.107319x 10-5 * v. 8.107319 x 10-5 Force of the water F Vwhere Fx- pAV(O-(Vsin (180-0) F- PAVIV -(-Vcos(180-e)

The exit velocity and inlet velocity are considered same because, for a situation where the weight balances the vane, the relative velocity of flow is same as the absolute flow velocity by neglecting any hydraulic losses.

Angle Time m (kgt3/sec Qm3 /sec Vel m/sec density AV Vsin(180-angle) Vcos(180-angle) Fx 29.8 18.2 10.1 12.6 10.1 25 21 13.2 11.1 0.050.0045 0.00012743 0.1 0.0069 0.00019539 0.0011 3.1149E-05 1.571737953 0.12742581 1.57 2.4099981940.19538624 2.409998194 0.384202611 0.03114853 3.73724357б| 0.30299026| 3. 4.0515911670.328475424.051 1.432027912 0.11609907 2.654490764 0.21520803 3.946808637 0.31998037 5.0994164690.41342596 1.571737953 0-0.20028 0.20028 0.283239 0-0.47088 0.470880.665926 01-0.01197| 0.0119671 0.016924 0 -1.13235 1.1323481.601382 01-1.33085 1.3308481 1.882103 01 0.332514 0.332514 0 1.142535 1.142535 0 2.525803 2.525803 0 4.2164б2 4.216462 90 90 90 180 180 180 180 0.15 0.2 0.25 0.02 3 0.384202611 0.00030299 3.737243576 0.0116 0.00032848 0.0041 0.0001161 0.070.0076 0.00021521 0.12 0.0113 0.00031998 0.0146 0.00041343 1.432027912 01 2.654490764 이 3.946808637 5.099416469 0.1 4.5 Brown colour indicates the 180 degree graph and Blue color indicates the 90 degree graph the graph is drawn between velocity at the exit of nozzle on x -axis and Force on y axis 3.5 2.5 Series1 Series2 1.5 0.5 velocity

In the above table the force is in newtons. The theoritical weight that the jet can support, so that reading remains zero is the vertical component of force(F) Fy

Angle Timem (k)o ) FN Q ftA3/sec Qm3/sec Velocity (V) m/sec Fy(N Theo.Weight (N) theo.weight (Kg) 0.020415902 0.048 0.001219878 0.115427931 0.135662385 0.033895413 0.116466361 0.257472273 0.42981264 90 90 90 90 90 180 180 180 180 29.8 18.2 10.1 12.6 10.1 25 21 13.2 11.1 0.05 0.1 0.15 0.2 0.25 0.02 0.07 0.12 0.17 0.0045 0.00012743 0.0069 0.00019539 0.0011 3.1149E-05 0.0107 0.00030299 0.0116 0.00032848 0.0041 0.0001161 0.0076 0.00021521 0.0113 0.00031998 0.0146 0.00041343 1.5717379530.20028 0.283239 2.409998194 0.47088 0.665926 0.384202611| 0.011967| 0.016924 3.737243576 1.132348 1.601382 4.051591167 1.330848 1.882103 1.432027912 0.332514 0.332514 2.654490764 1.1425351.142535 3.946808637 2.525803 2.525803 5.099416469 4.216462 4.216462 0.20028 0.47088 0.011967 1.132348 1.330848 0.332514 1.142535 2.525803 4.216462 theo.weight (Kg) Theo Weig 0.5 0.45 0.35 0.3 0.25 0.2 0.15 0.1 0.05 theo.weight (Kg) velocit

2)

The table shows the values for various angles when velocity is constant and equal to 10m/sec. AngleVelocity(m/sec) Cos(180-Angle) Sin(180-Angle density *AV Fx (N) Fy(N) F (N 0.810732-8.10732 8.10732 11.46548 0.810732-7.98415 9.51514 12.42114 0.810732-7.61839 10.88019 13.28226 0.810732-7.02114 12.16098 14.04229 0.810732-6.21056 13.31861 14.69546 0.810732-5.21129 14.31788 15.23678 0.810732 -4.05366 15.12846 15.66214 0.810732-2.77287 15.72571 15.96831 0.810732-1.40782 16.09147 16.15294 0.810732 0 0.173648 0.34202 0.5 0.642788 0.766044 0.866025 0.939693 0.984808 10 10 10 10 10 10 10 10 10 10 90 100 110 120 130 140 150 160 170 180 0.984808 0.939693 0.866025 0.766044 0.642788 0.5 0.34202 0.173648 0 이 16.21464 16.21464

Force Vs Angle 18 16 14 12 10 for constant velocity Force of water jets Force Vs Angle 50 100 150 200 Angle of vane