Question

Hoover Dam on the Colorado River is the highest dam in the United States at 221 m, with an output of 1300 MW. The dam generates electricity with water taken from a depth of 108 m and an average flow rate of 655 m3/s.(a) Calculate the power in this flow in watts.(b) What is the ratio of this power to the facility's average 680 MW?

Answer 1

a) 6.93 ×10^8 W

b) 1.01

Step-by-step explanation:

height of the dam h= 221 m

power output= 1300 MW

power:

P=Fv

also, Q= 655
`m^3/s`

depth d = 108 m

also, pressure p=F/A= ρdg

ρ= density of fluid, g= acceleration due to gravity

ρdg= 1000×108×9.81=1059400 N/m^2

Power flow= p×Q

now, Power flow= 1059400×655 =693,907000 W = 6.93 ×10^8 W

b) Ratio of this power to the facility = Power flow / average power

=
`(693*10^6)/(680*10^6)`

Ratio of this power to the facility= 1.01