How do I use the formula P (in) = #pQgh#?

Question

I'm using it for a hydropower unit of a course I'm taking, and it's confusing to decipher. An example would be greatly appreciated. Thank you.

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Answer 1 · 2017-10-10T16:01:18

You use the formula to calculate the theoretical power available from falling water.

The following is summarized from the following webpage:
Hydropower from www.engineeringtoolbox.com

The theoretical power available from falling water can be calculated from the following equation:

#P_(th) =\rho qgh#

where

#P_(th)# = power theoretically available (#W#)

#\rho# = density = approximately #1000 kg//m^3# for water

#q# = water flow (#m^3//s#)

#g# = acceleration due to gravity (#9.81 m//s^2#)

#h# = falling height, head (#m#)

Note that I'm assuming that the equation in the question is using these same quantities, but had been written with different letters, specifically:

#P("in")=>P_(th)#
#p => \rho#
#Q =>q#

Example

Calculate the power theoretically available from water flowing at a rate of #1 m^3//s# with a fall of #100 m#:

#P_(th)=(1000kg//m^3) * (1m^3//s) * (9.81m//s^2) * (100m)#

#P_(th) = 981000 W#

#P_(th) = 981 kW#