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Question

A volume V of viscous liquid flows per unit time due to a pressure head ΔP along a pipe of diameter D and length L. Instead of this pipe a set of 4 pipes each of diameter D2 and length 2L is connected to the same pressure head ΔP. Now, the volume of the liquid flowing per unit time is:

A
V
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B
V4
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C
V8
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D
V16
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Solution

The correct option is C V8
Given,
v=πΔP(D2)48ηL=πΔPD416×8ηL ---------(1)
Now,
Total flow through smaller pipelines = πΔP(D4)4×48×η×2L
=πΔPD443×16×ηL--------(2)
So, from (1) and (2),
flow through smaller pipes = V8

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