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)

10.3 m/s

Answer 2

Bernoullis equation for flowing liquid be written as
$p+\frac{1}{2} \rho v^{2}+\rho g h=$ constant ...(i)
Here, $p=$ pressure energy per unit volume of liquid
$\rho=$ density of liquid (water)
$h=$ height of liquid column
$v=$ velocity of liquid and
$g=$ acceleration due to gravity
Dividing the E (i) by $\rho g$, we have
$\frac{p}{\rho g}+\frac{v^{2}}{2 g}+h=$ constant
In this expression, $\frac{v^{2}}{2 g}$ is velocity head and $\frac{p}{\rho g}$ is pressure head.
It is given that,
Velocity head $=$ pressure head
ie, $\frac{v^{2}}{2 g}=\frac{p}{\rho g}$
or $v^{2}=\frac{2 P}{\rho}$
or $=\frac{2 \times 13.6 \times 10^{3} \times 40 \times 10^{-2} \times 9.8}{10^{3}}$
$\therefore v=10.32 \,m / s$