1. What is a Velocity Profile Calculator?

Definition: This calculator determines the fluid velocity at a specific radial position in a pipe using the parabolic velocity profile equation.

Purpose: It helps engineers and physicists analyze fluid flow characteristics in pipes and ducts.

2. How Does the Calculator Work?

The calculator uses the formula for laminar flow in a circular pipe:

Where:

• \( u(r) \) — Velocity at radial position r (m/s)
• \( u_{max} \) — Maximum velocity at centerline (m/s)
• \( R \) — Pipe radius (m)
• \( r \) — Radial position from center (m)

Explanation: The velocity profile is parabolic with maximum velocity at the center (r=0) and zero velocity at the wall (r=R).

3. Importance of Velocity Profile Calculation

Details: Understanding velocity profiles is crucial for designing efficient piping systems, calculating flow rates, and analyzing shear stresses.

4. Using the Calculator

Tips: Enter the maximum velocity, pipe radius, and the radial position where you want to know the velocity. The radial position must be between 0 and the pipe radius.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this equation apply to?
A: This equation is valid for fully developed laminar flow in circular pipes (Re < 2300).

Q2: How does the profile change for turbulent flow?
A: Turbulent flow has a flatter velocity profile with a steeper gradient near the walls.

Q3: What's the relationship between u_max and average velocity?
A: For laminar flow, the average velocity is exactly half of the maximum velocity.

Q4: Can this be used for non-circular ducts?
A: No, this specific equation is only for circular pipes. Other geometries have different profiles.

Q5: How does viscosity affect the velocity profile?
A: Viscosity determines the shape of the profile but doesn't appear explicitly in this equation.