Very Low Reynolds Numbers: Stokes' Drag
The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, ). Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:
where:
- is a constant that depends on the properties of the fluid and the dimensions of the object, and
- is the velocity of the object
When an object falls from rest, its velocity will be
which asymptotically approaches the terminal velocity . For a given, heavier objects fall faster.
For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant:
where:
- is the Stokes radius of the particle, and is the fluid viscosity.
The resulting expression for the drag is known as Stokes' drag:
For example, consider a small sphere with radius = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity of 10 µm/s. Using 10−3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.
Read more about this topic: Drag (physics)
Famous quotes containing the words reynolds and/or drag:
“My dear dear Mother,
If you don’t let me come home I die—I am all over ink,
and my fine clothes have been spoilt—I have been tost in a blanket, and seen a ghost.
I remain, my dear dear Mother,
Your dutiful and most unhappy son,
Freddy.
P.S. Remember me to my Father.”
—Frederick Reynolds (18th century)
“Our own theological Church, as we know, has scorned and vilified the body till it has seemed almost a reproach and a shame to have one, yet at the same time has credited it with power to drag the soul to perdition.”
—Eliza Farnham (1815–1864)