Q122 / 160 · AP EAMCET 2021 (23 Aug Shift 2) · Physics

The volume of a liquid is proportional to......, given its density $\rho$, viscosity $\eta$ and $t$ the time of flow through a capillary tube of length $L$ and radius $R$, with a pressure difference $p$ across its ends

  • A
    $\frac{p^2 R^2 t}{\eta L}$
  • B
    $\frac{p R^4}{\eta L t}$
  • Correct answer
    C
    $\frac{p R^4 t}{\eta L}$
  • D
    $\frac{p^2 R^2 t}{\eta L^2}$

Solution

Given, density of liquid $=\rho$ Viscosity $=\eta$ Time of flow $=t$, Length of tube $=L$ Radius of cross-section $=R$ Pressure difference between end $s=p$ According to Poiseuille's formula, the rate of flow of liquid through a horizontal tube $=\frac{\text { Volume of liquid flow }}{\text { Time taken }}$ i.e. $\quad Q=\frac{V}{t}=\frac{\pi}{8} \frac{p R^4}{\eta L}$ $\therefore \quad V=\frac{\pi}{8} \frac{p R^4}{\eta L} t$, (where $\frac{\pi}{8}$ is a constant.) Hence, $\quad V \propto \frac{p R^4 t}{\eta L}$ So, the option (c) is correct, where volume of flow of liquid is proportional to $\frac{p R^4 t}{\eta L}$.

Hence, the correct answer is option: 'C'.

Relevant Questions