Viscous flow/Laminar flow

Question

Two capillary tubes A and B of equal radii r_{a} = r_{b }= r and equal lengths l_{a} = l_{b} = l are held horizontally. When the same pressure difference P is maintained across each tube, the rate of flow of water in each is Q. If the tubes are connected in series and the same pressure difference P is maintained across the combination, the rate of flow through the combination will be

Moderate

Solution

$volumerate=Q=\frac{{\mathrm{\pi Pr}}^{4}}{8\mathrm{\eta l}}V\propto \frac{1}{l}$

A series combination of two identical capillary tubes, each of length l and radius r, is equivalent to a tube of length 2l and radius r.

Since Q is inversely proportional to l, if l is doubled, Q becomes half. Hence the correct choice is (a).

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