Question

An engine pumps water through a pipe. Water passes through the pipe and leaves it with a velocity of 2m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

Answer 1

As we know

$\left|P\right|=Fv$

$=\frac{\Delta p}{\Delta t}v$

$=\frac{m\Delta v}{\Delta t}v$

$=\frac{m{v}^{\frac{2}{}}}{t}$

$now,massperunitlength\left(\frac{m}{l}\right)=density\times area;\therefore density=\frac{mass}{volume}\frac{kg}{m^3}$

$power=\left\{\frac{(density\times area\times length)\left(v^2\right)}{t}\right\};\therefore \frac{l}{t}=v$

$power=\frac{mass}{length}\times v^3$

$power=\left(100\right)\left(8\right)=800W$