Viscosity

Newtonian Fluid and Shear Stress

Viscosity – For a Newtonian Fluid, the shear stress, τ, and the rate of shear deformation du/dz are linearly related:

τ = μ du/dz

Where du/dz is the velocity gradient in the z-direction (which is perpendicular to the direction of the flow) This is called the shear stress because, if the velocity of the fluid changes in the z-direction, a volume of fluid that is initially cubic will be sheared into a rhomboid. μ is the dynamic viscosity. All real fluids have a viscosity greater than zero (treating μ=0 is called the “inviscid approximation”).