The turbine pits at the Niagara falls are 50m deep. The average horse power developed is 5000, the efficiency being 85%. How much water passes through the turbine per minute?given 1 HP = 746W and g= 10m/s^{2}

h = 50 m

P

_{o}= 5000 HP

g = 10 ms

^{-2}

η = 0.85

Let the input power to run the turbine = P

Output power / Input power = 0.85

P

_{o}/P

_{i}= 0.85

P

_{o}= 5000 HP = 5000×746 W

So

P

_{i}= 5000×746/0.85 W

Now let m be the mass of water must be passed per second to deliver the power P

_{i}

5000×746/0.85 = mgh

=> m = 5000×746/(0.85×10×50)

=> m = 8776.47 kg / s

In 1 min mass flow will be

8776.5 × 60 = 526588 kg

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