Question

The reading of pressure metre attached with a closed pipe is \( 4.5 \times 10^4 \, N/m^2 \). On opening the valve, water starts flowing and the reading of pressure metre falls to \( 2.0 \times 10^4 \, N/m^2 \). The velocity of water is found to be \( \sqrt{V} \, m/s \). The value of \( V \) is \_\_\_\_\_\_\_.

Answer 1

Correct Answer: 50

Using Bernoulli’s theorem for the flow of an ideal fluid:

\(P_1 + \frac{1}{2} \rho v^2 = P_2\)

Given:
- \(P_1 = 4.5 \times 10^4 \, \text{N/m}^2\),
- \(P_2 = 2.0 \times 10^4 \, \text{N/m}^2\),
- \(\rho = 1000 \, \text{kg/m}^3\).

Substituting values:

\(4.5 \times 10^4 + \frac{1}{2} \cdot 1000 \cdot v^2 = 2.0 \times 10^4\)

Rearranging:

\(\frac{1}{2} \cdot 1000 \cdot v^2 = 4.5 \times 10^4 - 2.0 \times 10^4\)

\(500v^2 = 2.5 \times 10^4\)

\(v^2 = 50 \implies v = \sqrt{50} \, \text{m/s}.\)

Therefore: \(v = 50 \, \text{m/s}.\)

The Correct answer is: 50 m/s