Water flows through a capillary tube of radius r and length l at a rate of 40 ml per second, when connected to a pressure

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Water flows through a capillary tube of radius r and length l at a rate of 40 ml per second, when connected to a pressure difference of h cm of water. Another tube of the same length but radius (r/2) is connected in series with this tube and the combination in connected to the same pressure head. Calculate the pressure difference across each tube and rate of flow of water through the combination.

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The volume of water flowing per second through a tube of length l and radius r under a pressure difference P is given by

v = πpr4/8ηl,

Where η = coefficient of viscosity.

Given that the pressure difference is equal to height of water i.e.,

p = egλ

and volume flowing per second is 40 ml. Hence.

When another tube of same length but radius (r/2) is connected in series with this tube, let P1 and P2 be the pressure difference across these tube respectively. They are connected to the same pressure head.

Dividing equation (i) in equation (ii), we get