When water is flowing through a pipe, then its velocity changes b…

Question

When water is flowing through a pipe, then its velocity changes by 5%. Find the change in percentage, in the power of water.

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Answer

we know
$\text{Powe}=\frac{\text{work}}{\text{time}}$
also
work = change in KE
let power in 2nd case be P₂
P in 1st case $=\frac{\frac{1}{2}}{\frac{\text{mv}^2}{\text{time}}}$
$\text{P}_2=\frac{1}{2}\text{m}\Big(\frac{105}{100}\Big)\text{v}\Big(\frac{105}{100}\Big)\frac{\text{v}}{\text{time}}$
increase in power in 2nd case $=\frac{1}{2}\text{m}\Big(\frac{5}{100}\Big)\text{v}\Big(\frac{5}{100}\Big)\text{v}$
change in % of power $=\frac{\text{increase}}{\text{initial power}}100\%$
$=0.25\%$
I have considered the change of 5% as increase.

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