Question

Water flows out horizontally from a hole with a velocity of $20m{s}^{-1}$. The area of cross section of the hole is 2.5$\times {10}^{-3}{m}^2$. Density of water is $1000kg{m}^{-3}$. Power needed to generate kinetic energy from water is

• A. $2.5kW$
• B. $20kW$
• C. $1kW$
• D. $10kW$

Answer 1

The correct option is D $10kW$

$Power=\frac{\Delta W}{t}=\frac{\Delta (K.E)}{t}=\frac{\frac{1}{2}m{v}^2}{t}$
$=\frac{1}{2}\times d\times A\times \frac{dx}{dt}\times v^2$

where d is the density of the water, A is the cross sectional area of the hole and $\frac{dx}{dt}=v$ is the speed of the water
$=\frac{1}{2}\times d\times A\times v^3$
$=\frac{1}{2}\times {10}^3\times 2.5\times {10}^{-3}\times {20}^3$
$=10kW$