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. 1m/s
• D. $10\sqrt{10}$ m/s

Answer 1

Answer: (B)

Bernoullis theorem for unit mass of liquid
$\frac{p}{\rho }+\frac{1}{2}{v}^2=$ constant
As the liquid starts flowing, it pressure energy decreases
$\frac{1}{2}{v}^2=\frac{p_1-p_2}{\rho }\Rightarrow \frac{1}{2}{v}^2=\frac{3.5\times {10}^5-3\times {10}^5}{{10}^3}$
$\Rightarrow v^2=\frac{2\times 0.5\times {10}^5}{{10}^3}\Rightarrow v^2=100$
$\Rightarrow v=10m/s$