Question

A certain waterfall is 118.7 m high and has water flow rate of 30.2 m3 /s. The acceleration of gravity is 9.8 m/s 2 . Find the maximum electric power that can be generated by these falls assuming 100% conversion of mechanical energy to electric energy. (Take the density of water to be 1.00 × 103 kg/m 3 )

Answer 1

Step-by-step explanation:

Relation between velocity, mass and acceleration due to gravity is as follows.

v = mgh

Also, we know that

`Density (\rho) = (mass)/(volume)`

or, mass =
`\rho * volume`

=
`(10)^(3) * v`

And,
`(dm)/(dt) = (10)^(3) * (dV)/(dt)`

=
`10^(3) * 30.2 m^(3)/s`

=
`3.02 * 10^(4) kg/s`

Formula to calculate power is as follows.

Power =
`(dv)/(dt)` =
`gh((dm)/(dt))`

=
`9.8 * 118.7 m * 3.02 * 10^(4) kg/s`

=
`3.51 * 10^(7) W`

Thus, we can conclude that the maximum electric power that can be generated by these falls assuming 100% conversion of mechanical energy to electric energy is
`3.51 * 10^(7) W`.