Rate of flow of volume of a viscous liquid through a capillary tube of radius r and length l is Q. Now another capillary tube of radius 2r and length 2l is joined end-to-end with the given tube so as to make a composite tube of length 3l under the same pressure difference between the ends of the composite tube rate of flow of the same liquid through it is
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a
15Q16
b
16Q9
c
8Q9
d
9Q8
answer is C.
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Detailed Solution
By poiseuille's equation, Q=π x ∆p x r48ηlNow, viscous resistance of the given tube, R=8ηlπr4Viscous resistance of the tube of radius 2r, R'=8η2lπ2r4=ηlπr4∴Re=Viscous resistance of the composite tube =R+R'=8ηlπr4+ηlπr4=9ηlπr4∴Q'=Rate of flow through the composite tube=∆pRe=∆p9ηl/πr4=89∆p x πr4 8ηl8Q9