Exploring Exciting Fluid Dynamics

What is the relationship between velocity and pipe diameter in a fluid flowing in a pipe?

Choose the correct option:

1. Velocity increases with pipe diameter
2. Velocity is inversely proportional to the square of the pipe diameter
3. Velocity remains constant regardless of pipe diameter

Answer:

The velocity of a fluid in a pipe is inversely proportional to the square of the pipe diameter for a given mass flow rate.

When a fluid of constant density flows in a pipe, the relationship between velocity and pipe diameter is crucial to understand the dynamics of the flow. In this scenario, the velocity of the fluid does not increase with the pipe diameter, as one might intuitively think. Instead, the velocity is inversely proportional to the square of the pipe diameter.

For a given mass flow rate, the diameter of the pipe plays a significant role in determining the velocity of the fluid. As highlighted in the answer, velocity increases as the pipe diameter decreases, and vice versa. This phenomenon is essential in ensuring that the mass flow rate remains constant throughout the pipe.

The formula to express this relationship mathematically is v ∝ 1 / (d^2), where v represents the velocity of the fluid and d is the diameter of the pipe. This inverse proportionality showcases the unique characteristics of fluid flow in pipes and emphasizes the interplay between velocity and pipe diameter.