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Q.

When water flows at a rate Q through a tube of radius r placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference will be:

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a

8 P

b

P

c

P / 8

d

P / 32

answer is D.

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Detailed Solution

Poiseuille’s formula gives the quantity of liquid flowing through a capillary, Q=π8pr4ηli.e. p=8πQ.ηlr4if Q'=Q2,r'=2rp'=8πQ2.ηl2r4=8πQ.ηlr4×132 i.e., pressure p'=p32

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