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

Question

Infinity Learn · Accepted Answer

By poiseuille's equation, $$Q=$$π x ∆p x $$r48$$ηlNow, viscous resistance of the given tube, $$R=8$$ηl$$π$$$$r4Viscous$$ resistance of the tube of radius $$2r$$, R'$$=8$$η$$2l$$$$π$$$$2r4=$$ηl$$π$$$$r4$$∴$$Re=Viscous$$ resistance of the composite tube $$=R+R$$'$$=8$$ηl$$π$$$$r4+$$ηl$$π$$$$r4=9$$ηl$$π$$$$r4$$∴Q'$$=Rate$$ of flow through the composite $$tube=$$∆$$pRe=$$∆$$p9$$η$$l/$$π$$r4=89$$∆p x π$$r4$$ $$8$$η$$l8Q9$$

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