Question

What is the power required by the pump to lift $1000\text{kg}$ of water per minute from a $20\text{m}$ deep well and eject it with the speed of $20\text{m/s}$?

• A. $3666.7\text{W}$
• B. $4666.7\text{W}$
• C. $6666.7\text{W}$
• D. $5666.7\text{W}$

Answer 1

The correct option is C $6666.7\text{W}$

Given:
Depth of well, $h=20\text{m}$
Speed of water, $v=20\text{m/s}$
Mass of water lifted per minute, $m=1000\text{kg}$
We know that, power
$P=\frac{\Delta E}{\Delta t}$ ...............(1)
where $\Delta E$ is change in mechanical energy and $\Delta t$ is time taken
Now, change in mechanical energy,
$\Delta E=mgh+\frac{1}{2}m{v}^2$
$\Rightarrow \Delta E=1000\times 10\times 20+\frac{1}{2}\times 1000\times {20}^2$
$\Rightarrow \Delta E=4\times {10}^5\text{J}$ .............(2)
Also,
Time taken,
$\Delta t=1$ minute [ given ]
$\Rightarrow \Delta t=60\text{s}$ ...........(3)
On putting (2) and (3) in (1)
$P=\frac{4\times {10}^5}{60}=6666.7\text{W}$
Hence option $\left(c\right)$ is correct.