Question:
Water flows through a horizontal pipe at a speed \(V\). Internal diameter of the pipe is \(d\). If the water is emerging at a speed \(V_1\), then the diameter of the nozzle is
Water flows through a horizontal pipe at a speed \(V\). Internal diameter of the pipe is \(d\). If the water is emerging at a speed \(V_1\), then the diameter of the nozzle is
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For incompressible fluids, area is inversely proportional to velocity.
Updated On: Jan 30, 2026
- \( \dfrac{V}{V_1} \)
- \( d\sqrt{\dfrac{V_1}{V}} \)
- \( d\sqrt{\dfrac{V}{V_1}} \)
- \( \dfrac{dV_1}{V} \)
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The Correct Option is C
Solution and Explanation
Step 1: Apply equation of continuity.
\[ A_1 V = A_2 V_1 \]
Step 2: Write areas in terms of diameters.
\[ \frac{\pi d^2}{4}V = \frac{\pi d_1^2}{4}V_1 \]
Step 3: Solve for nozzle diameter.
\[ d_1^2 = d^2\frac{V}{V_1} \Rightarrow d_1 = d\sqrt{\frac{V}{V_1}} \]
\[ A_1 V = A_2 V_1 \]
Step 2: Write areas in terms of diameters.
\[ \frac{\pi d^2}{4}V = \frac{\pi d_1^2}{4}V_1 \]
Step 3: Solve for nozzle diameter.
\[ d_1^2 = d^2\frac{V}{V_1} \Rightarrow d_1 = d\sqrt{\frac{V}{V_1}} \]
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