Hey, have a question in Physics
From a power magazine released 300,000 gallons of water pr.sekund into a pipeline leading to a turbine plant. Height difference between the magazine and the turbines are 300meter.
The turbines provide 0.7 GW power.
How large is the efficiency of the penstock and turbines?
Thanks for your help
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3 *10^5 gal * 3.785 liters/gallon = 11.4*10^5 liters
11.4*10^5 liters * 1 m^3/10^3 liters = 11.4 * 10^2 m^3
so 1.14 * 10^3 m^3/s flow
pressure = rho g h = 10^3 kg/m^3 * 9.8 m/s^2 * 300 m = 2940 *10^3 N/ m^2
= 2.94*10^6 N/m^2
power = pressure * flow rate
=2.94*10^6 N/m^2 * 1.14 *10^2 m^3/s
= 3.35 * 10^8 N m/s or Joules/s or Watts
eff = 3.35*10^8 /7*10^8 = .48 = 48%