Answer to Question #194990 in Civil and Environmental Engineering for Zerick

Question

A 1 inch diameter nozzle there is a water flows under 400ft head to operate a turbine. There is 90% efficient of turbine and connected to a 94% efficient generators. Find the power output in kilowatts.

Answer 1

The water flows through a nozzle of 1 inch = 0.0254 m

head loss 400 ft. = 121.92 m

Area = $\pi r^2$ = 3.142 $\times (\frac{0.0254}{2})^2= 5.068 \times 10^{-4} m^2$

Assuming that the flow rate is 3 m/s the mass of water of = 3000 kg/s

Hydropower W = $m \times g \times H_{net} \times \eta$

$\eta =$ $0.90 \times 0.94= 0.846 = 84.6$ %

assuming the that the head loss = 10%

the net head $H_{net}= 0.9\times$ 121.92 = 109.728 m

$\eta = 3000 \times 9.8\times 109.728 \times 0.846= 2.7 Megawatts$