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Re: Viscosity demo.?



At 12:43 AM 4/1/00 -0800, Bernard G. Cleyet & Nancy Ann Seese wrote:

>A few years ago some one at UCSC showed me a demo that
>was supposed to demonstrate the
>increased (yes) viscosity of a gas with temperature.
...
>What is it? Any of you heard of this demo.,
>and what does it "really" demonstrate?

It depends on what one means by "viscosity". Choices include
* dynamic viscosity (eta or mu, measured in poise):
http://www.treasure-troves.com/physics/DynamicViscosity.html
* kinematic viscosity (nu = eta / rho, measured in Stokes)
http://www.treasure-troves.com/physics/KinematicViscosity.html

To calculate the viscous force in a bearing (where you have controlled
geometry and you don't much care what happens to the lubricant) then
dynamic viscosity shows up in the formulas. OTOH if you are trying to pump
fluid through a pipe (i.e. you care how many moles of fluid get moved), or
if you are trying to swim through a fluid and drag a viscous boundary layer
with you (i.e. uncontrolled geometry), then kinematic viscosity shows up in
the formulas.

At 04:42 AM 4/1/00 -0500, John Cooper wrote:
>To a first approximation, the viscosity of an 'ideal' gas,
>is independent of its density

That is correct if viscosity means _dynamic viscosity_ and if you consider
change of density at constant temperature (as opposed to, say, change in
density at constant pressure).

>.. simple kinetic molecular 'theory': the
>longer mean free path and the reduced collison rate approximately cancel
>each other in the rate of momentum transport transverse to the
>streamlines.

That's the correct physics.

> The increase in viscosity with temperature, roughly proportional to
>T^1/2, reflects the increased speed, hence rate of momentum transport,
>with temperature.

Hmmm. The momentum per particle is increasing like sqrt(T), but don't we
also need to account for the fact that each particle is being transported
more expeditiously? Rayleigh's formula says:

eta_2 / eta_1 = (T_2 / T_1) ^ 0.75

=====================

Meanwhile, the kinematic viscosity is going up even faster, because of the
extra factor of 1/rho. The brightness of the flame in the demo in question
will depend on kinematic viscosity, because it depends on transport of mass
not transport of volume.