Question

A 75 mm diameter pipe of 500 m length operates under a head of 60 m at its inlet. If a nozzle is fitted at its outlet, then for most efficient conditions, the velocity of flow from the nozzle (with \( C_v = 1 \)) is .........

• A. 19.8 m/s
• B. 28 m/s
• C. 10 m/s
• D. 40 m/s

Hint:

For maximum efficiency, the frictional head loss in a pipe-nozzle system is one-third of the total head.

Answer 1

The Correct Option is B

Given:
Diameter of pipe, \( D = 75 \, \text{mm} = 0.075 \, \text{m} \)
Length of pipe, \( L = 500 \, \text{m} \)
Head at inlet, \( H = 60 \, \text{m} \)
Coefficient of velocity, \( C_v = 1 \)
The most efficient velocity from the nozzle is given by:
\[ V = \sqrt{\frac{2gH}{1 + \frac{4fL}{d}}} \]
For most efficient discharge, the head loss due to friction in the pipe is one-third of the total head. Thus:
\[ h_f = \frac{H}{3} = \frac{60}{3} = 20 \, \text{m} \]
The head available for the nozzle is:
\[ H_n = H - h_f = 60 - 20 = 40 \, \text{m} \]
Now, using the velocity formula for the nozzle:
\[ V = C_v \sqrt{2gH_n} = 1 \cdot \sqrt{2 \times 9.81 \times 40} \]
\[ V = \sqrt{784.8} \approx 28 \, \text{m/s} \]
Therefore, the velocity of flow from the nozzle is \( \boxed{28 \, \text{m/s}} \).