InterviewSolution
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InterviewSolution
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A cylindrical vessel of area of cross-section A and filled with liquid to a height of `h_(1)` has a capillary tube of length l and radius r protuding horizontally at its bottom. If the viscosity of liquyid is `eta` and density `rho`. Find the time in which the level of water in the vessel falls to `h_(2)`.A. `(8etalA)/(pirhogr^(4))` ln `(h_(1))/(h_(2))`B. `(8etalA)/(pirhogr^(4))`C. `(etaA)/(g)(sqrt(h_(1))-sqrt(h_(2)))`D. `(8etalA)/(pirhogr^(4))` ln `(h_(2))/(h_(1))` |
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Answer» Correct Answer - A Let `h` be the height of water level in the vessel at instant `t` which decreases by dh in time dt. `:.` rate of flow of water through the capillary tube, `V=-A((dh)/(dt))` ….(1) Further, the rate of flow from poiseuille formula `V=(piPr^(4))/(8etal)` ....(2) The hyddrostatic pressure at depth h is `P=rhogh` from eqns (1) and (2) we have `-A(dh)/(dt)=(pirhohr^(4))/(8etal)` `dt=-(8etalA)/(pirhor^(4))(dh)/(h),t=(-8etalA)/(pirhogr^(4))int_(h_(1))^(h_(2))(dh)/(h)` |
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