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-   -   velocity of a body fall. th. viscous medium (http://www.cfd-online.com/Forums/main/3883-velocity-body-fall-th-viscous-medium.html)

sohrab arora September 11, 2001 06:43

velocity of a body fall. th. viscous medium
 
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?

Jan Rusås September 11, 2001 07:12

Re: velocity of a body fall. th. viscous medium
 
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


Jan Rusås September 11, 2001 07:22

Re: velocity of a body fall. th. viscous medium
 
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


Dan Williams September 11, 2001 22:33

Re: velocity of a body fall. th. viscous medium
 
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.


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