The power dissipated due to aerodynamic drag acting on a moving body is empirically…

PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

The power

P

dissipated due to aerodynamic drag acting on a moving body is empirically expressed as

P = k\,C_D\,\rho\,A\,v^{3}

where

k

is a dimensionless numerical constant,

C_D

is the drag coefficient,

\rho

is the density of the surrounding medium,

A

is the frontal area of the body and

v

is its speed. For slow viscous flow around a sphere, the drag coefficient is found to vary as

C_D = \alpha\;\dfrac{\mu}{\rho v L}

with

\alpha

a dimensionless constant,

\mu

the dynamic viscosity of the medium and

L

the diameter of the sphere. (i) Verify, by dimensional analysis, that the first relation gives

P

the correct dimensions of power. (ii) Using the second relation for

C_D

, deduce the dimensional formula of the dynamic viscosity

\mu

. (iii) From your result, write the SI unit of

\mu

. Explain each step clearly.