P15_041 - is the density of water and A is the area of the...

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41. Suppose that a mass ∆ m of water is pumped in time ∆ t . The pump increases the potential energy of the water by ∆ mgh ,where h is the vertical distance through which it is lifted, and increases its kinetic energy by 1 2 mv 2 ,where v is its Fnal speed. The work it does is ∆ W =∆ mgh + 1 2 mv 2 and its power is P = W t = m t µ gh + 1 2 v 2 . Now the rate of mass flow is ∆ m/ t = ρ w Av ,where ρ w
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Unformatted text preview: is the density of water and A is the area of the hose. The area of the hose is A = πr 2 = π (0 . 010 m) 2 = 3 . 14 × 10 − 4 m 2 and ρ w Av = (1000 kg / m 3 )(3 . 14 × 10 − 4 m 2 )(5 . 0 m / s) = 1 . 57 kg / s. Thus, P = ρAv µ gh + 1 2 v 2 ¶ = (1 . 57 kg / s) µ (9 . 8 m / s 2 )(3 . 0 m) + (5 . 0 m / s) 2 2 ¶ = 66 W ....
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