Need help understanding each step in getting the answer.
A hydroelectric powere plant consist of a set of 5 turbines that lie 75m below the inlet at the top of the dam. Each pipe to the turbines can allow a water flow of up to 11,000 cubic metres per second. If each pipe/turbine set up has an efficiency off 54% when converting the flow to electricity, how much power (in GW) will the system output when running at maximum capacity with all 5 turbines operating? (g=9.81m.s^-2 and the density of water is 1000kg.m^-3)
A hydroelectric powere plant consist of a set of 5 turbines that lie 75m below the inlet at the top of the dam. Each pipe to the turbines can allow a water flow of up to 11,000 cubic metres per second. If each pipe/turbine set up has an efficiency off 54% when converting the flow to electricity, how much power (in GW) will the system output when running at maximum capacity with all 5 turbines operating? (g=9.81m.s^-2 and the density of water is 1000kg.m^-3)
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General equation:
w_dot = eta*m_dot*g*deltaZ
Modify for multiple turbines:
w_dot = n*eta*m_dot*g*deltaZ
Modify for volumetric flow specified instead of mass flow:
m_dot = V_dot*rho
Concluding formula:
w_dot = n*eta*V_dot*rho*g*deltaZ
Data:
n = 5 turbines
deltaZ = 75 m
V_dot = 11000 m^3/sec
eta = 0.54
rho = 1000 kg/m^3
g = 9.81 N/kg
Result:
w_dot = 21.85 Gigawatts
w_dot = eta*m_dot*g*deltaZ
Modify for multiple turbines:
w_dot = n*eta*m_dot*g*deltaZ
Modify for volumetric flow specified instead of mass flow:
m_dot = V_dot*rho
Concluding formula:
w_dot = n*eta*V_dot*rho*g*deltaZ
Data:
n = 5 turbines
deltaZ = 75 m
V_dot = 11000 m^3/sec
eta = 0.54
rho = 1000 kg/m^3
g = 9.81 N/kg
Result:
w_dot = 21.85 Gigawatts