A pump is used to fill a tank 5 m in diameter from a river as shown. The water surface in the river is 2 m below the bottom of the tank. The pipe diameter is 5 cm, and the head loss in the pipe is given by h_L = 10 V ²/2g, where V is the mean velocity in the pipe. The flow in the pipe is turbulent, so α = 1. The head provided by the pump varies with discharge through the pump as h_p = 20 ^{– 4} × 10⁴ Q₂, where the discharge is given in cubic meters per second (m³/s) and h_p is in meters. How long will it take to fi ll the tank to a depth of 10 m?

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5 m Pump 5 cm 2 m River