1.

Two capillaries of radii r_(1) and r_(2) and lengths l_(1) and l_(2) are set in series. A liquid of viscosity eta is flowing through the combination under a pressure difference p. The rate of flow of the liquid is :

Answer»

<P>`(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]`
`(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(-1)`
`(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(2)`
`(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(-2)`

Solution :`V=(pi(p_(1)-p_(2))r_(1)^(4))/(8etal_(1))=(pi(p_(2)-p_(3))r_(2)^(4))/(8etal_(2))`
`p_(1)-p_(2)=(8Vetal_(1))/(pir_(2)^(4))`
`p_(2)-p_(3)=(V8etl_(2))/(pir_(2)^(4))`
Adding `p_(1)-p_(3)=(8Veta)/(pi)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]`
`p=(8Veta)/(pi)((l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4)))`
`V=(pip)/(8eta)((l_(1))/(r_(1)^(4)+(l_(2))/(r_(2)^(4)))`
`THEREFORE` Correct choice is (B).


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