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

Explanation:

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

               v = mgh

Also, we know that

           $Density (\rho) = \frac{mass}{volume}$

or,               mass = $\rho \times volume$

                            = $(10)^{3} \times v$

And,    $\frac{dm}{dt} = (10)^{3} \times \frac{dV}{dt}$

                       = $10^{3} \times 30.2 m^{3}/s$

                       = $3.02 \times 10^{4} kg/s$

Formula to calculate power is as follows.

       Power = $\frac{dv}{dt}$ = $gh(\frac{dm}{dt})$

                   = $9.8 \times 118.7 m \times 3.02 \times 10^{4} kg/s$                

                   = $3.51 \times 10^{7} W$

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 $3.51 \times 10^{7} W$.