The equation for the fall velocity (terminal velocity) of a particle of a materi

Question

The equation for the fall velocity (terminal velocity) of a particle of a material in a viscous medium has been derived from theory as:

Vt = gd^2(Pp - Pm) / 18 u

Where: Vt is the terminal velocity in m/s; g is the acceleration due to gravity; d is particle diameter in m; Pp and Pm are the densities of the particle and the medium (respectively) in kg/m^3; u is the viscocity of the medium in kg/m/s (kg.m^-1.s^-1)

Demonstrate if this equation is dimensionally homogeneous or not. Show your working.


Could someone show me how you work this out with the cancelling of units.

My final answer I'm getting - m/s = m/s x m

I don't think I'm correct.

Explanation / Answer

Units of g - m/(s^2)

Units of d - m

Units of Pp and Pm - kg/(m^3)

Units of u - kg/(m-s)

So, units of gd^2(Pp - Pm) / 18 u is m/(s^2) *m^2 *kg/(m^3) /[kg/(m-s)]

= m/s

Units of Vt is also m/s.

Hence, the units on Left and right sides of the equation are consistent.

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