## Newtonian Fluid and Shear Stress

Viscosity – For a*Newtonian Fluid*, the shear stress, τ, and the rate of shear deformation d

**u**/dz are linearly related:

- τ = μ d

**u**/dz

**u**/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”).

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