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Homework Statement
19. A 1,500 Watt motor is used to pump water a vertical height of 2.0 meters out of a flooded basement through a
cylindrical pipe. The water is ejected though the end of the pipe at a speed of 2.5 m/s. Ignoring friction and
assuming that all of the energy of the motor goes to the water, which of the following is the closest to the radius
of the pipe? The density of water is ρ = 1000 kg/m3
.
(A) 1/3 cm
(B) 1 cm
(C) 3 cm
(D) 10 cm ← CORRECT
(E) 30 cm
Homework Equations
Pressure = ρgh
Bernoulli's Eq: p + ρgh + 1/2ρv^2 = Constant
Power = F dot v, Power = Work / t = dW/dT
Flow Rate Continuity:
A_0v_0 = Av
The Attempt at a Solution
First, I said that:
A_0v_0 = pir^2*2.5
Thus, v_0 = pir^2*2.5 / A_0
Then, I used Bernoulli's Eq, but I'm confused as to how I make use of the power? I need some guidance on how to use the power in the problem or how to turn one of these equations into
one I can handle.