Numerical problem on Terminal Velocity with solution

Last updated on April 17th, 2021 at 09:38 am

In this post we will solve Numerical problems on Terminal Velocity. Here is the first set.

Numerical problem on Terminal Velocity with solution

1 ) Find the terminal velocity of (a) a steel ball bearing of radius 1 mm and (b) a steel ball bearing of radius 2 mm falling through glycerine in a cylinder.

The viscosity of glycerine 1.5 Pa s. (at 20 degree C)
Density of steel = 7800 kg/m^3
Density of glycerine = 1200 kg/m^3
g = 9.81 m/s^2

Solution:

(a) for 1 mm radius ball bearing:
V_term = [2 r² g (ρ_s – ρ_f )] / [9Ƞ]
= [2(1×10^-3)² x 9.81 X (7800-1200)]/[9×1.5] = 9.6 x 10^-3 ms^-1

(b) for 2 mm radius ball bearing:
V_term = [2 r² g (ρ_s – ρ_f )] / [9Ƞ]
= [2(2×10^-3)² x 9.81 X (7800-1200)]/[9×1.5] = 3.8 x 10^-2 ms^-1

Reference:

Derivation of Terminal Velocity (step by step)

Stokes’ Law | drag force Formula