Re: Units of viscosity
From: Bruce Scott TOK (Use-Author-Supplied-Address-Header_at_[127.1)
Date: 08/30/04
- Next message: Bruce Scott TOK: "Re: From whence the vector?"
- Previous message: johnlawrencereed: "johnreed take 1.1"
- In reply to: Edward Green: "Units of viscosity"
- Messages sorted by: [ date ] [ thread ]
Date: Mon, 30 Aug 2004 19:54:10 +0200 (MEST)
Edward Green wrote:
|> If in a fluid in laminar flow we investigate the ratio of shear stress
|> [N/m^2] to the cross-flow velocity gradient [(m/s)/m], then we are
|> investigating the fluid's viscosity: [Ns/m^2] being a unit of the
|> same. Besides "shear stress/velocity gradient", we may also read this
|> unit as "momentum/area".
|>
|> Is there an aha! interpretation of viscosity in terms of
|> momentum/area, or is this parsing virtually a meaningless coincidence?
Think of it as a dissipative momentum flux; that will give you the
units. For a fluid
(p/pt) (rho v) + div (rho v v) + div (Pi) = 0
where (p/pt) is the partial time derivative, rho v is the momentum
density, rho v v is the advective part of the momentum flux, and Pi is
the general stress tensor. The diagonal part of Pi is the pressure
times the metric tensor, and the off-diagonal part does the dissipation.
Bulk viscosity comes from the traceless part of the diagonal
corrections. Generally, the strain tensor is
W = (grad v) + (grad v)^T - (2/3) div v
where T denotes transpose, and then the dissipative part of Pi is
(minus) the viscosity coefficient (eta) times W. Eta will have units of
diffusivity times rho.
If the shear and bulk viscosities are different, eta itself becomes a
tensor (shear viscosity would be the perp perp component, relative to
the velocity vector).
Geophysical fluid texts tend to be pretty good in explaining this in a
lot of pictorial detail. One example is
Adrian Gill, _Atmosphere-Ocean Dynamics_ (Academic Press, 1982)
If you can't find that, try Pedlosky, _Geophysical Fluid Dynamics_
-- cu, Bruce drift wave turbulence: http://www.rzg.mpg.de/~bds/
- Next message: Bruce Scott TOK: "Re: From whence the vector?"
- Previous message: johnlawrencereed: "johnreed take 1.1"
- In reply to: Edward Green: "Units of viscosity"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
