Question

The difference in velocity between two planes of liquids separated/infinitesimal distance is called

• A. Rate of shear
• B. Rate of flow
• C. Rate of force
• D. Shearing stress

Answer 1

The Correct Option is A

To solve the question about the difference in velocity between two planes of liquids separated by an infinitesimal distance, we need to understand the basic concepts of fluid mechanics and how they relate to the options provided. 

In fluid mechanics, when a fluid flows over a surface, the velocity of the fluid varies from zero at the surface to a maximum at some distance from the surface. This velocity change over an infinitesimal distance leads to the concept of shear within the fluid.

The rate of shear or shear rate is defined as the differential change in velocity of two adjacent layers in the fluid divided by the perpendicular distance separating them. Mathematically, it can be expressed as:

\(\frac{dv}{dy}\)

where:

• \(dv\)is the change in velocity
• \(dy\)is the change in perpendicular distance between layers

Shearing stress, not to be confused with shear rate, refers to the force per unit area exerted by the fluid as a result of this velocity change, characterized by viscosity.

Analyzing the options given:

• Rate of flow: This refers to the volume of fluid passing a point in a given time, often denoted by the symbol \(Q\).
• Rate of force: This is not a standard term in fluid dynamics related to the concepts of shear.
• Shearing stress: This is related to the force originated by shear, but not the rate of velocity change itself.

Therefore, the correct answer that defines the difference in velocity between two planes of liquids separated by an infinitesimal distance is the Rate of shear.