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InterviewSolution
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If two capillary tubes of radii `r_1 and r_2` and having length `l_1 and l_2` respectively are connected in series across a heaed of pressure p, find the rate of flow of the liqid through the tubes, if `eta` is the coefficient of viscosity of the liquid. |
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Answer» Correct Answer - `(pi P)/(8 eta(l_1//r_1^4 + l_2//r_2^4))` Let `P_(1)` and `P_(2)` be the pressure difference across the first and second capillary tube respectively. Let `R_(1), R_(2)` be the second capiliary tube respectively. Then `R_(1)=(8 etal_(1))/(pi r_(1)^(4))` and `R_(2)=(8 etal_(2))/(pir_(2)^(4))` As the two capillary tubes are connected in series total liquid resistance, `R=R_(1)+R_(2)=(8 eta l_(2))/(pi r_(1)^(4))=(8 eta)/(pi)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]` Rate of flow loquid through the tubes is `V=(P)/(R)=(P)/(8 eta)/(pi)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]=(pi P)/(8 eta[(l_(1))/(r_(1)^(4))+(i_(2))/(r_(2)^(4))]` |
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