Calculate velocity of an oobject falling trhough a medium

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SUMMARY

The discussion focuses on calculating the velocity of an object falling through a medium while considering buoyancy and viscous drag. The governing equation derived from Newton's second law is m(dv/dt) = Fg - Fd - Fb, where Fg is the gravitational force, Fd is the viscous drag force, and Fb is the buoyant force. The acceleration can be expressed as a = (Fg - Fd - Fb)/m, leading to the velocity equation v = [(Fg - Fd - Fb)/m]*t + Vo, where Vo is the initial velocity. The discussion emphasizes that the drag force may be velocity-dependent, potentially leading to terminal velocity.

PREREQUISITES
  • Newton's Second Law of Motion
  • Understanding of forces: gravitational, buoyant, and viscous drag
  • Basic calculus for integration
  • Familiarity with terminal velocity concepts
NEXT STEPS
  • Study the derivation of terminal velocity in fluid dynamics
  • Learn about Stokes' law for viscous drag in low Reynolds number flows
  • Explore turbulent drag forces and their impact on falling objects
  • Investigate dimensional analysis and its applications in physics problems
USEFUL FOR

Physics students, engineers, and anyone interested in fluid dynamics and motion analysis will benefit from this discussion.

SFB
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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
 
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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!
 
If the drag force Fd 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
 
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