# velocity of a body fall. th. viscous medium

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 September 11, 2001, 06:43 velocity of a body fall. th. viscous medium #1 sohrab arora Guest   Posts: n/a 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?

 September 11, 2001, 07:12 Re: velocity of a body fall. th. viscous medium #2 Jan Rusås Guest   Posts: n/a 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

 September 11, 2001, 07:22 Re: velocity of a body fall. th. viscous medium #3 Jan Rusås Guest   Posts: n/a 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

 September 11, 2001, 22:33 Re: velocity of a body fall. th. viscous medium #4 Dan Williams Guest   Posts: n/a 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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