Question

From a waterfall, water is falling at the rate of $100\mathrm{kg}/\mathrm{s}$ on the blades of a turbine. If the height of fall is $100\mathrm{m}$, the power delivered to the turbine is

Answer 1

Step 1: Given

The flow rate of water is $\frac{m}{t}=100\mathrm{kg}/\mathrm{s}$
Where $m$is the mass and $t$ is the time taken

Height of the waterfall, $h=100\mathrm{m}$

Step 2: Formulas used

We know that power is given as,

$P=\frac{W}{t}$ where $W$ is the work done

We also know that potential energy,
$P.E.=mgh$
where $g$ is the acceleration due to gravity and $h$is the height

Step 3: Calculate power

Work done is the amount of energy transferred when a body does work on another body.
Thus, the work done by bringing the water down is the same as the potential energy stored in it because the work done to move the water up is stored as potential energy.

Thus,

$\begin{array}{cc}& P=\frac{mgh}{t}\\ \Rightarrow & =\frac{m}{t}gh\\ \Rightarrow & =100\times 9.81\times 100\left[\because g=9.81\mathrm{m}/\mathrm{s}\right]\\ \because & P=98.1\mathrm{kW}\end{array}$

Therefore, the power delivered to the turbine is $98.1\mathrm{kW}$.