RE: non-compressible, laminar flow, newtonain fluid.(adsbygoogle = window.adsbygoogle || []).push({});

Viscosity is often defined by looking at a fluid between two plates with the upper plate moving at a small velocity relative to the lower plate. The plate moves in the x direction and a velocity gradiant is created. Viscosity is then defined as:

Fx/Axz= Sxy = mu dVx/dy.

Fx = force between adjaycent fluid layers in the x direction.

Axz = area between the fluid layers

Sxy = stress in the direction of the force (x) where y is the direction of the normal to the area.

mu = viscosity

dVx/dy = Velocity gradient in the y direction.

This is the standard way texts define viscosity (unless I've messed it up!).

Next this idea is generalized to multiple dimensions and the stress tensor is defined. This is where I need help. It is argued that for non rotating fluids that the stress tensor must be symmetric. In particular Sxy = Syx. I see this in one sense. Usually this idea is arrived at by noting that a small element would develop an infinite torque or moment if it was not symmetric....okay good. BUT:

Finally my problem: In the simple example, how does a force in the Y direction develop. How does a normal force to the direction of fluid flow, Fy, exist. By definition of a fluid, if Fy exists, the fluid must shear....Any help or reference would be most appreciated.

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# Simple Laminar Flow Stress

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