A liquid is having the viscosity of 7.5 \times 10^{-4} Pa s. If the strain rate is 5000 s ^{-1} . Calculate the shear stress required to deform the liquid.
Given,
\text { Viscosity, } \mu=7.5 \times 10^{-4}
\text { Strain rate, }\left\lgroup \frac{d \theta}{d t} \right\rgroup =5000 s ^{-1}
From Newton’s law of viscosity,
\tau=\mu \frac{d u}{d y}
So, we know that the velocity gradient is equal to strain rate.
\begin{aligned} \frac{d u}{d y} & =\frac{d \theta}{d t} \\ \tau & =\mu \frac{d \theta}{d t} \\ & =0.0075 \times 5000 \\ & =3.75 Pas \end{aligned}