4 - Consider the Hoover Dam hydro-electric plant located in Arizona and Nevada.

Question

4 - Consider the Hoover Dam hydro-electric plant located in Arizona and Nevada. If the average lake level is 160 m above the turbine outlet, determine the minimum mass flow rate of water through the 17 turbines if the total power produced from all four turbines is 2080 MW. What is the mass flow rate if the turbines are 88% efficient.?

5 - What is the possible power (kW) production from a 32 m radius wind turbine if the average wind speed is 12 m/s? Assume an ambient air density of 1.20 kg/m3.

6 - How many wind turbines from Problem 5 would need to be installed to replace the Hoover Dam hydro-electric plant power generating capacity discussed in Problem 4? Provide a commentary to actual number of wind turbines needed.

Explanation / Answer

4.

Power = m*g*H where m = Mass flow rate of water, g = gravitational constant = 9.8 m/s^2, H = Head available

For each turbine, 2080*10^6 / 4 = m*9.8*160

m = 331632 kg/s

If turbines are 88 % efficient then mass flow rate reqd will be 331632 / 0.88 = 376855 kg/s

5.

Wind power = 1/2*rho*A*v^3

Wind power = 1/2*1.2*(3.14*32^2)*12^3

Wind power = 3333.7 kW

6.

2080*10^6 = n*3333.7*10^3

n = 623.9 (almost 624)

Actual number of wind turbines needed = 2080*10^6 / 0.88 = n*3333.7*10^3

n = 709

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