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velocity of a body fall. th. viscous medium

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Old   September 11, 2001, 06:43
Default velocity of a body fall. th. viscous medium
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sohrab arora
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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?
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Old   September 11, 2001, 07:12
Default Re: velocity of a body fall. th. viscous medium
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Jan Rusås
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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

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Old   September 11, 2001, 07:22
Default Re: velocity of a body fall. th. viscous medium
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Jan Rusås
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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

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Old   September 11, 2001, 22:33
Default Re: velocity of a body fall. th. viscous medium
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Dan Williams
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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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