Calculate velocity of an oobject falling trhough a medium

[SFB]

How do I calculate for velocity of a falling object through any medium at any given time if I have to consider both buoyancy and viscous drag.


If I consider Newtons law , I assume that it would be something like

m(dv/dt)=Fnet =mg-Drag-Buoyant force


Am I supposed to get a dimensionless quantity while doing dimensional analysis for such a problem.Whats the name of that number.



Thanks

 

[danman5000]

Since you are looking for a velocity, you wouldn't end with a dimensionless number. It would need to be in meters/second (or whatever distance/time measure you are using).

To do problems like this, consider all the different forces and the directions they are acting in. Then, use the sum of the forces equals mass*acceleration to get acceleration, and from there you can derive velocity.

For your problem, gravity is the only force acting to pull the object downward. Both viscous drag and buoyancy are acting upward, against gravity. So, your equation is correct (assuming down as the positive direction).

ma = Fg - Fd - Fb

Fg = force of gravity = mg
Fd = viscous drag force
Fb = buoyant force

From that, solve for acceleration (a) and integrate to get an equation for velocity.

a = (Fg - Fd - Fb)/m
v = [(Fg - Fd - Fb)/m]*t + Vo

where t = time and Vo = initial velocity.

Hope that helps!

 

[Bob S]

If the drag force F_d is velocity dependent (Stokes or turbulent drag), the falling velocity will reach a terminal velocity. See

http://en.wikipedia.org/wiki/Drag_(physics )

Bob S