First slide

Viscous flow/Laminar flow

Question

The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)

Moderate

A

$\frac{V}{16}$
B

$\frac{V}{17}$
C

$\frac{16 V}{17}$
D

$\frac{17 V}{16}$

Solution

Rate of flow of liquid $V = \frac{P}{R}$
where liquid resistance $R = \frac{8 ηl}{{πr}^{4}}$
For another tube liquid resistance
$R' = \frac{8 ηl}{π {(\frac{r}{2})}^{4}} = \frac{8 ηl}{{πr}^{4}} . 16 = 16 R$
For the series combination
$V_{New} = \frac{P}{R + R'} = \frac{P}{R + 16 R} = \frac{P}{17 R} = \frac{V}{17}$ .

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