The water that powers the generators enters and leaves the system at a low speed (thus we can neglect its change of kinetic energy) and loses 160 m of altitude during the process. What is the water flow required, in cubic meters per second, to produce this power, assuming 83.5 % efficiency?

Question

Abdullah Walter

Physics

27 June, 08:52

The water that powers the generators enters and leaves the system at a low speed (thus we can neglect its change of kinetic energy) and loses 160 m of altitude during the process. What is the water flow required, in cubic meters per second, to produce this power, assuming 83.5 % efficiency?

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Hodges · Answer 1

Let density of water be ρ.

During flow, volume of water flowing per second is constant

loss of P. E per unit volume = ρ gh, 83.5 % is lost

Gain of K E per unit volume = 1/2 ρ v²

83.5 % of mgh = ρ 1/2 ρ v²

1/2 ρ v² =.835 x 9.8

v² = 2 x. 835 x 9.8

= 16.366

v = 4.04 m / s