First slide

Viscosity

Question

Two capillaries of lengths L and 2L and of radii R and 2R are connected in series. The net rate of flow of fluid through them will be: (given rate of the flow through single capillary $X = {πPR}^{4} / 8 ηL)$ )

Easy

A

(8/9) X
B

(9/8) X
C

(5/7) X
D

(7/5) X

Solution

Fluid resistance $R = \frac{8 ηl}{{πr}^{4}}$
When two capillary tubes connected in series then
$R = R_{1} + R_{2} = \frac{8 ηl}{{πR}^{4}} = \frac{8 η (2 L)}{π {(2 R)}^{4}} = \frac{8 ηL}{{πR}^{4}} \times \frac{9}{8}$
Equivalent resistance becomes $\frac{9}{8}$ times, so rate of flow will be $\frac{8}{9}$ X.

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