Question
A cylindrical vessel of area of crosssection A and filled with liquid to a height of h_{1} has a capillary tube of length 1 and radius r protruding horizontally at its bottom. If the viscosity of liquid is , density and g = 9.8 m/s^{2}, find the time in which the level of water in vessel falls to h_{2}.




None of these
easy
Solution
Lat 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 capillary tube,
Further the rate of flow as given by Poiseuille formula,
From eq. (i) and (ii),
Required time is obtained by integrating,
.
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