Water flows from a 6.0cm diameter pipe into 8.0cm diameter pipe. The speed in the 6.0cm pipe is 5.0m/s. the speed in the 8cm pipe is:
Correct answer: A. 2.8m/s
- A. 2.8m/s
- B. 3.7m/s
- C. 6.6m/s
- D. 8.8m/s
Explanation
The problem can be solved using the continuity equation, which states that A1V1 = A2V2, where A is the cross-sectional area of the pipe. For circular pipes, A = πr2, so:For the 6.0 cm diameter pipe, r1 = 3 cm, and for the 8.0 cm diameter pipe, r2 = 4 cm.Substituting these into the equation:π(3)2 × 5.0 = π(4)2 × V245 = 16V2V2 = 45/16 = 2.8 m/sThe correct answer is 2.8 m/s. The other options are incorrect as they do not satisfy this calculation based on the continuity equation.
This question appeared on the ETEA MDCAT 2016 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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