An Incompressible liquid flow along the pipe with area of cross section A1 and A2 with velocities V1 and V2 respectively. The ratio of the speeds V1 / V2 is:
Correct answer: B. A2/A1
- A. A1/A2
- B. A2/A1
- C. (A1 + A2)/(V1 + V2)
- D. (V1 + V2)/(A1 + A2)
Explanation
According to the continuity equation for incompressible fluids, the flow rate (product of cross-sectional area and velocity) is constant. This means that A1V1 = A2V2. From this relationship, we can derive that V1/V2 = A2/A1, making Option B the correct choice.Options A and C incorrectly suggest relationships that don't comply with the continuity equation, while Option D presents a ratio that doesn't apply to the problem's context.
This question appeared on the ETEA MDCAT 2015 paper, which you can sit online with every answer explained.
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About Equation of Continuity
The equation of continuity expresses conservation of mass in fluid flow. For steady incompressible flow, Av remains constant, so fluid speed increases when the cross-sectional area decreases; for compressible flow, ρAv is constant. This relation describes flow rate and area-speed changes without including pressure effects from Bernoulli’s equation.
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