The StokesOseen formul for drag force F on a sphere of diame

The Stokes-Oseen formul for drag force F on a sphere of diameter D in a fluid stream of low velocity V, density p and viscosity is

F=3 DV+9/16 p V^2d^2

Is this formula dimensionally homogenous?

Solution:

Yes, this formula is dimensionally homogeneous.

The explanation is here below:

Stokes - Oseen formula for drag force :

F = 3 DV+9/16 p V^2d^2

1st term has unit : N-s/m^2, D unit : m and V unit : m/s.

So, combinedly N-s/m^2 x m x m/s = N

2nd term has p unit : kg/m^3, V unit = m/s and d unit: m.

So, combinedly kg/m^3 x (m/s)^2 x (m^2) = kg-m/s^2 = N

On the right hand side of the expression, both the term has unit N, which is the unit of force.

That is why dimensional homogenity is maintained here.