Water flows through a pipe whose radius halves at a constriction. The speed of the water at the constriction becomes
Correct answer: C. four times
- A. half
- B. double
- C. four times
- D. unchanged
Explanation
Area depends on the square of the radius, so halving the radius quarters the area, and by the continuity equation the speed must rise by a factor of four to carry the same volume per second. Answering double is the error of treating area as proportional to radius. This strong dependence is why small constrictions in a blood vessel raise flow speed so sharply.
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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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