Derive mathematically the Viscosity law

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Derive mathematically the Viscosity law
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Step 1

The law of viscosity defines a relation between the shear stress and shear rate of a fluid subjected to mechanical stress. The ratio of shear stress to shear rate is constant. For a given temperature and pressure it is defined as the viscosity.

Shear stress is given by,

shearstress=FSshearrate=ΔvΔx

The viscosity is independent of shear rate.

μ=shearstressshearrate=FsΔvΔx

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