Re: High viscosity and Navier-Stokes

> ... Can this equation be used ...

When these oils can be regarded as Newtonian - yes. The Navier-Stokes are
derived from the continuous form of F = ma, which is called Cauchy's
equation of motion. It is given by:

\rho Du_i/Dt = /rho f_i + d/dx_j \tau_ji

with u_i the velocity, f_i the body forces and tau_ij the stress tensor and
summation over repeating indices. This equation holds for any continuum no
matter how the stress tensor is connected to the rate of strain. When we
take a linear relation between stress and strain (which is called a
Newtonian fluid) and substitute that into Cauchy's equation, we end up with
the Navier-Stokes equations.

> 
> And BTW...what is the definition of a Newtonian fliud?

In a Newtonian fluid the viscous stresses are proportional to the element
strain rates and the coefficient of viscosity. It's one of the simplest
stress-strain relation, a linear relation. You could see it as an 
equivalent of Hook's law for solids. In 3D the stress tensor for a
newtonian fluid is given by:

\tau_ij = -P \delta_ij + mu(du_i/dx_j + du_j/dx_i)

Which is a 3x3 matrix with the pressure on the diagonals.

Hope this helps.

Maarten
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Maarten van Reeuwijk                        Heat and Fluid Sciences
Phd student                             dept. of Multiscale Physics
www.ws.tn.tudelft.nl                 Delft University of Technology