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A non-viscous fluid of constant density of 1000 kg/m³ flows in a stream line motion along a tube of variable cross-section.
The area of cross-section at two points P and Q of length 5m are 40cm² and 20cm² respectively. If velocity of fluid at P is 3 m/s then find velocity of fluid at Q.

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3 m/s

4 m/s

5 m/s

6 m/s

answer is D.

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Detailed Solution

Explanation

We use the continuity equation for fluid flow:

A_P · v_P = A_Q · v_Q

Given:

A_P = 40 cm² = 0.004 m²
A_Q = 20 cm² = 0.002 m²
v_P = 3 m/s

Using the continuity equation:

0.004 × 3 = 0.002 × v_Q

Simplify:

v_Q = (0.004 × 3) / 0.002

v_Q = 6 m/s

Final Answer:

The velocity of the fluid at Q is 6 m/s.

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