Question

A capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by 10% then the rate of flow of liquid will change nearly by

• A. (a) + 10%
• A. (b) + 46%
• A. (c) – 10%
• A. (d) – 40%

Answer 1

(b)

$V = \frac{P\pi r^{4}}{8\eta l}$

⇒ $\frac{V_{2}}{V_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{4}$

⇒ $\mathbf{V}_{\mathbf{2}}\mathbf{=}\mathbf{V}_{\mathbf{1}}\left( \frac{\mathbf{110}}{\mathbf{100}} \right)^{\mathbf{4}}\mathbf{=}\mathbf{V}_{\mathbf{1}}\mathbf{(1.1}\mathbf{)}^{\mathbf{4}}\mathbf{= 1.4641V}$

$\frac{\Delta V}{V} = \frac{V_{2} - V_{1}}{V} = \frac{1.4641V - V}{V} = 0.46\mspace{6mu}\mspace{6mu}\mspace{6mu}\text{or}\mspace{6mu}\mspace{6mu}\mspace{6mu} 46\%$.