Problem 1.18*
For small particles at low velocities, the first term in Stokes-Oseen drag law, Prob. 1.10, is dominant,
hence
F ≈ KV, where K is a constant.
Suppose a particle of mass m is constrained to move horizontally from the initial position x
=
0
with initial velocity Vo. Show (a) that its velocity will decrease exponentially with time and (b)
that it will stop after travelling a distance x = mV0/K.
Problem 1.10
The Stokes-Oseen formula [33] for drag force F on a sphere of diameter D in a fluid stream low
velocity V, density
, and viscosity
is:
22
9
F 3 DV V D
16
=+
Is this formula dimensionally homogeneous?