Answered: 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,

$shearstress = \frac{F}{S} shearrate = \frac{Δ v}{Δ x}$

The viscosity is independent of shear rate.

$\begin{array}{rcl} μ & = & \frac{shearstress}{shear rate} \\ = & \frac{(\frac{F}{s})}{(\frac{Δ v}{Δ x})} \end{array}$

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