How Much Water Flow Is Needed to Generate 780 kW from a 27m Dam?

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SUMMARY

The discussion focuses on calculating the required water flow rate to generate 780 kW of electrical energy from a dam with a height of 27 meters and an efficiency of 65%. The key equations involved are the kinetic energy formula and the power equation, specifically P = τ x ω. The participant attempts to determine the mass of water falling and the kinetic energy gained, factoring in the efficiency loss, to find the necessary flow rate in liters per second.

PREREQUISITES
  • Understanding of basic physics concepts such as kinetic energy and gravitational potential energy.
  • Familiarity with power calculations in electrical engineering.
  • Knowledge of efficiency calculations in energy conversion processes.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study the principles of gravitational potential energy and its conversion to kinetic energy.
  • Learn about the efficiency of energy conversion in hydroelectric systems.
  • Explore the relationship between power output and water flow rate in hydroelectric applications.
  • Investigate the impact of height and flow rate on the overall efficiency of a dam.
USEFUL FOR

Students in physics or engineering courses, electrical engineers, and anyone involved in hydroelectric power generation or energy efficiency analysis.

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Homework Statement



A small dam produces electrical power. The water falls a distance of 27m to turn a turbine. If the efficiency to produce electrical energy is 65%, at what rate must water flow over the dam to produce 780 kW of electrical energy?


Homework Equations



v2 = u2 + 2as

P = \tau x \omega

The Attempt at a Solution



I've basically been at this one on and off for a few hours, and have tied myself so completely in knots that I have no idea what I'm doing anymore. Please help someone!
 
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Consider a litre of water going over that dam in one second.
What is its mass?
How much kinetic energy will it pick up by falling 27 metres?
The energy conversion is not totally efficent so reduce that by 35%.
Now how many litres per second do I need?
 

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