Question

Problem: Carbon tetrachloride at 20 0C has a viscosity of 0.000967Pa.s. What shear stress is required to deform this fluid at a strain rate of 5000s˗1?

Answer 1

Answer on Question #53010 - Physics - Mechanics - Kinematics - Dynamics

Carbon tetrachloride at $20{}^{\circ}\mathrm{C}$ has a viscosity of $\mu = 0.000967\mathrm{Pa}\cdot \mathrm{s}$ What shear stress $\tau$ is required to deform this fluid at a strain rate of $\frac{\partial v}{\partial y} = 5000\mathrm{s}^{-1}$?

**Solution:**

The shear stress is given by

$$\tau = \mu \frac {\partial v}{\partial y},$$

where $v$ – is the velocity of the fluid along the boundary, $y$ – is the height above the boundary, and $\mu$ – is the dynamic viscosity of the fluid. Since $\frac{\partial v}{\partial y} = 5000 \, \text{s}^{-1}$ and $\mu = 0.000967 \, \text{Pa} \cdot \text{s}$, we obtain

$$\tau = \mu \frac {\partial v}{\partial y} = 0.000967 \, \mathrm{Pa} \cdot \mathrm{s} \cdot 5000 \, \mathrm{s}^{-1} = 4.835 \, \mathrm{Pa}$$

**Answer:** 4.835 Pa.

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