The Relationship Between Velocity and Pipe Diameter in Fluid Flow

Explanation:

The relationship between velocity (v) and pipe diameter (D) for a fluid of constant density flowing in a pipe is inversely proportional to the pipe diameter for a given mass flow. This means that as the pipe diameter decreases, the velocity increases, and vice versa.

This relationship is derived from the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the average velocity. According to this equation, for a given flow rate, a smaller pipe diameter will result in a higher velocity.

For example, if you have a pipe with a small diameter and a given flow rate, the fluid will have to flow through a smaller area, which means it will have to travel faster to maintain the same flow rate. On the other hand, if you have a pipe with a large diameter and the same flow rate, the fluid will have more space to flow through, so it won't need to travel as fast.