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Solved: A hydroelectric dam holds back a lake of surface
Chapter 7, Problem 79P(choose chapter or problem)
Problem 79P
A hydroelectric dam holds back a lake of surface area 3.0 × 106 m2 that has vertical sides below the water level. The water level in the lake is 150 m above the base of the dam. When the water passes through turbines at the base of the dam, its mechanical energy is converted to electrical energy with 90% efficiency. (a) lf gravitational potential energy is taken to be zero at the base of the dam, how much energy is stored in the top meter of the water in the lake? The density of water is 1000 kg/m3. (b) What volume of water must pass through the dam to produce 1000 kilowatt-hours of electrical energy? What distance does the level of water in the lake fall when this much water passes through the dam?
Questions & Answers
QUESTION:
Problem 79P
A hydroelectric dam holds back a lake of surface area 3.0 × 106 m2 that has vertical sides below the water level. The water level in the lake is 150 m above the base of the dam. When the water passes through turbines at the base of the dam, its mechanical energy is converted to electrical energy with 90% efficiency. (a) lf gravitational potential energy is taken to be zero at the base of the dam, how much energy is stored in the top meter of the water in the lake? The density of water is 1000 kg/m3. (b) What volume of water must pass through the dam to produce 1000 kilowatt-hours of electrical energy? What distance does the level of water in the lake fall when this much water passes through the dam?
ANSWER:
Solution 79P
Data given
Area
Height
Efficiency
Density
Step 1:
We need yo energy stored at the top of the water
Mass of the water is
Substituting values we get
We know
Here the energy at the top the tank is same the mass of the water
Hence we have energy as
‘
Thus we have energy stored as