How Much Water Flow is Needed to Generate 2010 MW at the Grand Coulee Dam?

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SUMMARY

The Grand Coulee Dam, measuring 1270 m in length and 170 m in height, generates approximately 2010 MW of electrical power. To determine the required water flow rate, one must apply the principle that 91% of the gravitational work done on the water is converted into electrical energy. Using the equation for gravitational potential energy, E = mgh, and considering the mass of water (1000 kg/m³) and free fall acceleration (9.80 m/s²), the necessary cubic meters of water flowing per second can be calculated to meet the power output requirement.

PREREQUISITES
  • Understanding of gravitational potential energy (E = mgh)
  • Basic knowledge of power calculations (Power = Work/time)
  • Familiarity with units of measurement (MW, m³/s)
  • Concept of energy conversion efficiency (91% in this case)
NEXT STEPS
  • Calculate the flow rate of water needed for 2010 MW using the energy equation.
  • Research the efficiency of energy conversion in hydroelectric systems.
  • Explore the design and operational principles of the Grand Coulee Dam.
  • Investigate the impact of water flow rates on hydroelectric power generation.
USEFUL FOR

Engineers, hydrologists, energy analysts, and students studying renewable energy systems will benefit from this discussion on hydroelectric power generation and the specific calculations involved in determining water flow requirements.

babbagee
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Using work to find The amount of...

The Grand Coulee Dam is 1270 m long and 170 m high. The electrical power output from generators at its base is approximately 2010 MW.

How many cubic meters of water must flow from the top of the dam per second to produce this amount of power if 91.0 % of the work done on the water by gravity is converted to electrical energy? (Each cubic meter of water has a mass of 1000 kg.)
Take the free fall acceleration to be 9.80m/s2

I need some help on this problem, I don't know where to even start. Can some one give me some hints to start this problem.

Thanks
 
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You know 91% of the work done by gravity is converted to electric energy. simply equate the Power defition to 2010 MW and find the relation Volume/time.
 
Mechanical energy

Think of energy equations:
E=mgh
 

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