Water flows in a streamline manner through a capillary tube of radius a. The pressure difference being P and the rate of flow is Q ….

Q: Water flows in a streamline manner through a capillary tube of radius a. The pressure difference being P and the rate of flow is Q . If the radius is reduced to a/2 and the pressure difference is increased to 2P, then find the rate of flow

Sol: Rate of flow $\large Q = \frac{P \pi r^4}{8 \eta l} $

$\large Q \propto P r^4 $

$\large \frac{Q_1}{Q_2} = \frac{P_1}{P_2} \times (\frac{r_1}{r_2})^4 $

$\large \frac{Q_1}{Q_2} = \frac{P}{2P} (\frac{a}{a/2})^4 $

$\large Q_2 = \frac{Q}{8} $

Rate of flow will become 1/8 times.