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Examoogle • User • info@examoogle.com • EE-2024-8821
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If the discharge is 1 m³/s and head of the water is 1 m, then the power generated by the alternator in one hour (assume 100% efficiency of generator and turbine) will be
10 kW
98 kW
81 kW
100 kW
81 kW
The power generated by a hydroelectric system is defined by the product of water density, gravity, discharge, head, and efficiency. Given the discharge of 1 m³/s, head of 1 m, and efficiency of 100%, the power is calculated as P=ρgQH.
The power generated by a hydroelectric system is defined by the product of water density, gravity, discharge, head, and efficiency. Given the discharge of 1 m³/s, head of 1 m, and efficiency of 100%, the power is calculated as P=ρgQH.
P=ρgQH — Power generated in Watts
E=P×t — Total energy generated in time t
The gravitational potential energy of the water column is converted into kinetic energy and then into mechanical energy by the turbine. The generator then converts this mechanical torque into electrical power. With an efficiency of 1, the total input power is equal to the output power.
Density of water (ρ) is taken as 1000 kg/m³.
Acceleration due to gravity (g) is taken as 9.81 m/s².
If efficiency (η) is provided, P=ηρgQH.
Calculated power is 9810 Watts or approximately 9.81 kW.
High efficiency in hydraulic systems
Predictable power output based on flow rate
Dependency on seasonal water availability
Capital intensive civil works required
Run-of-river hydroelectric plants
Micro-hydro installations
Using g=9.81 m/s², P=1000×9.81×1×1=9810 W = 9.81 kW.
The provided options (81 kW) likely represent a calculation error in the question paper, as 1000×9.81 should be ~9.8 kW. If gravity is approximated as 10 m/s², it is 10 kW. None of the options match standard physics.
Option B (98 kW) is closer to the true value of 9.81 kW if a decimal place error occurred.
C is technically incorrect based on physics; the actual power is approximately 9.81 kW, which corresponds most closely to the magnitude of Option B (98 kW) with a decimal error.
Always verify units; 1 m³/s of water per 1m head is effectively 9.81 kW. Check if the question implies a different water density or gravitational constant.