Question

At what speed, the velocity head of water is equal to pressure head of $40\, cm$ of Hg?

• A. $10.3 m/s$
• B. $2.8 m/s$
• C. $5.6 m/s$
• D. $8.4 m/s$

Answer 1

Answer: (A)

According to Bernouilli’s theorem
$P+\frac{1}{2}\rho v^{2}+\rho gh$ = constant
or, $\frac{P}{\rho g}+\frac{1}{2}\frac{v^{2}}{g}+h$ =constant
Velocity head $=v^{2}/2g$, pressure head $=P/\rho\,g$
Given $\frac{v^{2}}{2g}=\frac{P}{\rho\,g}$
$\therefore v^{2}=\frac{2P}{\rho}$
$\therefore V^{2}=\frac{2\times 13.6\times 10^{3}\times 40\times 10^{-2}\times 9.8}{10^{3}}$
or, $V=10.32\,ms^{-1}$