

SStoke's Law
Name: Wil
Status: educator
Grade: 912
Location: MI
Country: USA
Date: Fall 2013
Question:
I am trying to find a general term for the property of an object that accounts for its tendency to fall at a certain velocity in water. It would be a function of the object's size and mass/density according to Stoke's Law. In everyday speech the "buoyancy" of an object describes the property, however in this context I want to maintain the technical sense of buoyant forces
Replies:
"Buoyancy" is a physical concept that is well defined and fairly easily measurable. The ?buoyancy? is the force that is equal to the ?weight of the volume? of the fluid that is displaced by the object that is displaced.
Thus it depends upon the weight of the object, its volume, and the weight (or on a per unit volume) its density (weight per unit volume). And all depends upon the weight / density of the fluid being displaced. Thus a very ship floats (or sinks) depending upon its ?displacement?. This is all shape dependent.
It is not a function of the speed at which the object sinks. It is an equilibrium process. That is why submarines can rise or sink depending upon the amount of air/water that is pumped from its ballast tanks. The volume remains constant, but the lighter fluid (air) is removed from the vessel, and is replaced by water.
Vince Calder
Hi Wil,
Thanks for the question. Buoyancy is a force that pushes a submerged object upward in a fluid. However, buoyancy does not account for the resistance when an objecet is moved laterally underwater. Stoke's Law accounts for the resistance of motion when moving an object in a fluid.
In a mathematical sense, the fluid's resistance force can be expressed as a polynomial in the speed. For instance, some private planes (e.g., Cessna) have a v^2 dependence, but faster moving planes (e.g., Boeing 747) have a v^4 dependence.
I hope this helps.
Thanks
Jeff Grell
The term is 'terminal velocity'.
You might typically think of terminal velocity in situations where drag is more important than buoyancy, but in fluid dynamics circles, buoyancy is also routinely considered in determining the terminal velocity.
Hope this helps,
Burr Zimmerman
Wil
Does this help?
"In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a continuous viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations:[1]
where Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (in N),ì is the dynamic viscosity (N s/m2),R is the radius of the spherical object (in m), and v is the particle's velocity (in m/s).
Stokes' law makes the following assumptions for the behavior of a particle in a fluid:
Laminar Flow
Spherical particles
Homogeneous (uniform in composition) material
Smooth surfaces
Particles do not interfere with each other."
Terminal velocity of a sphere in a fluid is often called the "settling velocity."
Sincere regards.
Mike Stewart
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Update: November 2011

