how can we compute velocity of a body falling through viscous medium at any time before it attains terminal velocity while the viscous drag is itself velocity dependent?

Hi'

You will have to do some iterations to find the solution for the equation of motion for your body,i.e. Predictor-Corrector methods, Newton Raphson, etc.

If you assume a constant drag, which in your case will be a crude or erroneous aassumption, it is straight ahead to find the velocity at any time.

Jan

Hi' again,

I forgot to mention,

It is possible to do an integration of the equation of motion, if some assumptions are allowed.

You would end up with a equation similiar to this

Up = Ug + (Up,0 - Ug)*exp(-dt/tau) + tau*g*(1-exp(-dt/tau))

p - particle g - gas 0 - previous time step tau - response time -depends on the drag You better look in a textbook or paper.

Regards and best of luck, Jan

This is simply a terminal velocity calculation. For a vertically falling object you can get a closed form solution for the velocity by just doing F=ma and solving:

m*dv/dt = mg - 0.5*rho*Cd*pi*r^2*v^2

I've used postive downwards. Just use separation of variables to solve the ODE.

Dan.