Velocity gradient is ntg but velocity divided by distance between two layers so the answer may be 80

Velocity Gradient

The velocity gradient is a measure of how the velocity of a fluid changes with respect to a distance. It quantifies the rate at which the velocity of a fluid changes per unit distance.

Given Information

- Relative velocity between two parallel layers of water = 8 cm/s
- Perpendicular distance between the layers = 0.1 cm

Calculating Velocity Gradient

The velocity gradient can be calculated using the formula:

Velocity Gradient = (Change in velocity) / (Change in distance)

In this case, the change in velocity is given by the relative velocity between the layers of water, which is 8 cm/s. The change in distance is the perpendicular distance between the layers, which is 0.1 cm.

Using the formula:
Velocity Gradient = 8 cm/s / 0.1 cm

Simplifying the expression:
Velocity Gradient = 80 cm/s²

Explanation

The velocity gradient of 80 cm/s² means that for every unit distance increase in the perpendicular direction between the layers of water, the velocity increases by 80 cm/s. This indicates a steep change in velocity with respect to distance.

Interpretation

The high velocity gradient suggests that the fluid is undergoing significant deformation or shearing. The layers of water are moving past each other at a relatively fast rate, resulting in a large velocity gradient. This scenario is commonly observed in situations involving viscous fluids or fluids flowing through narrow gaps or channels.

Conclusion

The velocity gradient between the two parallel layers of water is found to be 80 cm/s². This indicates a significant change in velocity with respect to distance, suggesting a deformation or shearing effect within the fluid.