A pump, taking water from a large reservoir, is used to spray a jet of water with speed 20 ms^1 and radius 0.05 metres, from a nozzle level with the surface of the reservoir. Calculate the power of the pump.
Alright I'll admit I'm pretty lost here and haven't been able to mount a very convincing attempt at a solution. I'm used to force-work-power problems based on the motion of an object so I'm not sure how to model this exercise. Even the wording is unclear; should I take initial speed 20 ms^-1, ending speed 0, distance 0.05? Where is the jet directed, horizontally or vertically?
Any suggestions would be appreciated.
Excuse me for using US Eng units
Velocity of jet = 20mps*3.281=65.6fps
Jet dia =.05m * 39.37 = 1.97 in (.164 ft)
Cross-section of jet (,164)^2*pi/4=.0211 ft^2
Q gpm = 1.38*7.5*60 =623 gpm
Velocity head of jet =(65.6)^2/64.4 =66.8 ft
Hydraulic Hp = gpm *8.33* 66.8/33000 =10.5Hp 7.84 KW
No pipe friction loss and no potential head loss and no pump eff loss