Texas Commission on Environmental Quality (TCEQ). Class C Water License Exam

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By how many times does the carrying capacity of a pipe increase when the diameter is doubled, disregarding friction?

2 times
3 times
4 times
5 times

The correct answer is: 4 times

The carrying capacity of a pipe is related to its cross-sectional area, which is determined by the diameter of the pipe. When the diameter is doubled, the cross-sectional area increases based on the formula for the area of a circle, A = πr², where r is the radius. When the diameter is doubled, the radius also doubles. Therefore, the new area becomes: - Original radius = r - New radius = 2r Calculating the areas: - Original area = π(r)² = πr² - New area = π(2r)² = π(4r²) = 4πr² As a result, the new area is four times larger than the original area. This means that the carrying capacity of the pipe increases by a factor of four when the diameter is doubled, assuming friction is disregarded. Hence, the correct answer is indeed that the carrying capacity increases by 4 times.