Multiple choice

Two tanks are connected in parallel by two pipes A and B of identical friction factors and lengths. If the size of pipe A is double that of pipe B, then their discharges will be in the ratio of

  1. 2

  2. 4

  3. 5.66

  4. 2.83
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For pipes in parallel, the head loss is the same. Using the Darcy-Weisbach equation, head loss h is proportional to f * L * Q^2 / D^5. Since f and L are identical, Q^2 is proportional to D^5, so Q is proportional to D^2.5. If the diameter of A is double that of B, the ratio of discharges is 2^2.5, which is approximately 5.66.

AI explanation

For pipes with identical friction factors and lengths, the discharge is proportional to the cross-sectional area. Since the size, or diameter, of pipe A is double that of pipe B, the area of pipe A is proportional to the square of 2, which equals 4. The discharge ratio of pipe A to pipe B is calculated as the square root of 5 raised to the power of 3, which is approximately 11.18, but based on standard hydraulic radius rules for pipes, the flow ratio is the square root of the diameter to the fifth power, resulting in 5.66.

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