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Two capillary tubes, one of length L and radius R and the other of length 2L and radius 2R, are joined one after the other in series. If the flow rate through a single capillary is X = πPR⁴ / 8ηL, then the combined flow rate through the series arrangement is:

1. 8/9 X
2. 9/8 X
3. 5/7 X
4. 7/5 X

Correct answer: 8/9 X

Solution

Flow resistance ~ L/R^4. First tube: 8*eta*L/(pi*R^4). Second (2L, 2R): 8*eta*2L/(pi*16R^4) = eta*L/(pi*R^4) = (1/8) of first. Total = 9 times the unit. Flow = X/9 *8... combined = (8/9)X.

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