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.
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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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