Power Inlet
What is the Turbine Power Output given the specifications below?
A hydroelectric power plant operates under the following conditions:
Water flow rate: 1.25 m3/s
River inlet: 1 atm., 4.7°C
Discharge: 1 atm., 5.1°C, 254 m below intake.
Assuming that water intlet and discharge ducts have the same areas, and that no heat is transferred to or absorbed from the surroundings, calculate the power output of the turbine in kilowatts.
Given: acceleration of gravity = 9.81m/s2
Heat Capacity of Water = 4.17 kJ/(kg.K)
Answer must be provided with 3 significant numbers only.
I thought I already answered this….
Take one second. 1.25 m³ of water flows.
density of water = 0.998 g/cm³ = 998 kg/m³
1.25m³ x 998 kg/m³ = 1248 kg
PE of the water is 1248 kg x 9.81 x 254 = 3.108e6 joules
E lost due to heating is
E = 4.17 kJ/(kg.K) x 1248 kg x 0.4K = 2082 kJ
Subtracting
E gained = 3108 kJ – 2082 kJ = 1026 kJ
this occurs every second, so the power out is
1026 kW
.
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