Water from a reservoir passes over a dam through a turbine and discharges from a 70-cm ID pipe at a point 55 m below the reservoir surface. The turbine delivers 0.80 MW. Calculate the required flow rate of water in m3 /min if friction is neglected. (See Example 7.7-3.) If friction were included, would a higher or lower flow rate be required

91.2 m³/min

Explanation:

From the question, we say,

let ΔP = 0

Also, we know that

U₂ = (V/A)²

U₂ = 6.76V²

gΔz = 9.8 * -55

gΔz = -539 m²/s²

W(s)/m = 0.8*10^6/V/1000

W(s)/m = 0.8*10^3/V

W(s)/m = 800/V

6.76V² – 539 + 800/V = 0

When we solve this simultaneously or by using the general formula, we find that V = 1.52 m³/s. In converting to minute, we multiply by 60, so that

V = 1.52 m³/s * 60 = 91.2 m³/min

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