Question

The viscous drag force F, on a sphere of radius r, moving through a fluid with velocity v, can be expressed as F = 6PLrv, where L is the coefficient of viscosity of the fluid and P = pie(22/7). What are the base units of L?

Answer 1

Explanation & Calculations

• Dimensional analysis is the method practiced in these types of questions.
• Therefore,

$\qquad\qquad \begin{aligned} \small [F]&=\small [6\pi Lrv]=[6\pi][L][r][v]\\ \small MLT^{-2}&= \small [L]\times L\times LT^{-1}\\ \small [L]&=\small \frac{MLT^{-2}}{L^2T^{-1}}\\ \small [L]&= \small ML^{-1}T^{-1} \end{aligned}$

• Considering the corresponding units yeild

$\qquad\qquad \begin{aligned} \small \text{Units of L}&= \small \bold{kgm^{-1}s^{-1}} \end{aligned}$