Water flows in a streamlined manner through a capillary tube of r… - Vidyadip

MCQ

Water flows in a streamlined manner through a capillary tube of radius $a$, the pressure difference being $P$ and the rate of flow $Q$. If the radius is reduced to $a / 2$ and the pressure increased to $2 P$, the rate of flow becomes

A
$4 Q$
B
$Q$
C
$\frac{Q}{4}$
✓
$\frac{Q}{8}$

✓

Answer

Correct option: D.

$\frac{Q}{8}$

(d)$V=\frac{\pi p r^2}{8 \eta l} \therefore V \propto P r^4 \quad(\eta \text { and } l \text { are constants }) $
$\therefore \frac{V_2}{V_1}=\left(\frac{P_2}{P_1}\right)\left(\frac{r_2}{r_1}\right)^4$
$=2 \times\left(\frac{1}{2}\right)^4=\frac{1}{8}$
$\therefore V_2=\frac{Q}{8}$

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