Question

Q12. Show that for the flow in the stokes law region, the terminal falling velocity of a spherical particle in a fluid medium may be given by vt = [4𝐷(𝜌𝑠−𝜌)𝑔3𝐶𝐷𝜌]1/2

Answer 1

Answer

According to physics concept the

Terminal velocity: It is maximum constant velocity acquired by the body while falling freely in a viscous medium.

Now we can say

When a small spherical body falls freely through a viscous medium, three forces act on it.

(i) Weight of the body acting vertically downwards.

(ii) Upward thrust due to buoyancy equal to weight of liquid displaced.

So

$F_T+F_v=W$

$\frac{4\pi r^3 \rho_s g}{3}+6\pi\eta v_t=\frac{4\pi r^3 \rho g}{3}$

We get

$v_t=\frac{2D^2(\rho-\rho_s)g }{9\eta}$

Now putting above conditions

We get

$v_t=[4D(\rho_s-\rho) g3CD\rho]^\frac{1}{2}$