A liquid is flowing in a horizontal uniform capillary tube under … - Vidyadip

MCQ

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference $P$. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

A
$P$
B
$\frac{3 P}{4}$
C
$\frac{P}{2}$
✓
$\frac{P}{4}$

✓

Answer

Correct option: D.

$\frac{P}{4}$

(d)From $ V=\frac{P \pi r^4}{8 \eta l} $
$\Rightarrow P=\frac{V 8 \eta l}{\pi r^4}$
$\Rightarrow \frac{P_2}{P_1}=\frac{V_2}{V_1}\times\frac{l_2}{l_1}\times\left(\frac{r_1}{r_2}\right)^4=2 \times 2 \times\left(\frac{1}{2}\right)^4=\frac{1}{4} $
$\Rightarrow P_2=\frac{P_1}{4}=\frac{P}{4} .$

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