Water flows through a pipe whose radius halves at a constriction. The speed of the water at the constriction becomes

  • 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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