The relative velocity of two consecutive layers is 8 cm/s. If the perpendicular distance between the layers is 0.1 cm, then the velocity gradient will be

The correct option is 80sec⁻¹.

Understanding Velocity Gradient:
Velocity gradient is defined as the rate of change of velocity with respect to the perpendicular distance between two fluid layers. Mathematically, it is given by the formula:

$\text{Velocity Gradient}=\frac{\Delta v}{\Delta x}$

where:
• $\Delta v$ is the relative velocity between the two consecutive layers.
• $\Delta x$ is the perpendicular distance between the layers.

Given Data:
• Relative velocity ($\Delta v$) = 8 cm/s
• Perpendicular distance ($\Delta x$) = 0.1 cm

Step-by-Step Calculation:
Substitute the given values into the velocity gradient formula:

$\text{Velocity Gradient}=\frac{8\text{cm/s}}{0.1\text{cm}}$

$\text{Velocity Gradient}=\frac{8}{0.1}{\text{sec}}^{-1}=80{\text{sec}}^{-1}$

Hence, the velocity gradient is 80sec⁻¹.