Question

A volume $V$ of viscous liquid flows per unit time due to a pressure head $\Delta P$ along a pipe of diameter $D$ and length $L$. Instead of this pipe a set of $4$ pipes each of diameter $\frac{D}{2}$ and length $2L$ is connected to the same pressure head $\Delta P$. Now, the volume of the liquid flowing per unit time is:

• A. V
• B. $\frac{V}{4}$
• C. $\frac{V}{8}$
• D. $\frac{V}{16}$

Answer 1

The correct option is C $\frac{V}{8}$

Given,
v=$\frac{\pi \Delta P{\left(\frac{D}{2}\right)}^4}{8\eta L}=\frac{\pi \Delta P{D}^4}{16\times 8\eta L}$ ---------(1)
Now,
Total flow through smaller pipelines = $\frac{\pi \Delta P{\left(\frac{D}{4}\right)}^4\times 4}{8\times \eta \times 2L}$
=$\frac{\pi \Delta P{D}^4}{4^3\times 16\times \eta L}$--------(2)
So, from (1) and (2),
flow through smaller pipes = $\frac{V}{8}$