Question

A manometer connected to a closed tap reads 3.5 $\times$ ${10}^5$ N/$m^2$. When the valve is opened, the reading of manometer falls to 3.0 $\times$ ${10}^5$ N/$m^2$, then velocity of flow of water is

• A. 100 m/s
• B. 10 m/s
• C. 1 m/s
• D. 10 .10m/s

Answer 1

The correct option is B

10 m/s

Bernoulli's theorem for unit mass of liquid

$\frac{P}{\rho }+\frac{1}{2}{v}^2$ = constant

As the liquid starts flowing, it pressure energy decreases $\frac{1}{2}{v}^2=\frac{P_1-p_2}{\rho }\Rightarrow \frac{1}{2}{v}^2=\frac{3.5\times {10}^5-3\times {10}^5}{{10}^3}$
$\Rightarrow v^2=\frac{2\times 0.5\times {10}^5}{{10}^3}\Rightarrow v^2=100\Rightarrow v=10m/s$