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Q.

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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a

6 m/s

b

3 m/s

c

5 m/s

d

4 m/s

answer is D.

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Detailed Solution

Explanation

We use the continuity equation for fluid flow:

AP · vP = AQ · vQ

Given:

  • AP = 40 cm2 = 0.004 m2
  • AQ = 20 cm2 = 0.002 m2
  • vP = 3 m/s

Using the continuity equation:

0.004 × 3 = 0.002 × vQ

Simplify:

vQ = (0.004 × 3) / 0.002

vQ = 6 m/s

Final Answer:

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

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