1. What is a Parabolic Velocity Profile?

Definition: This describes the velocity distribution of a fluid flowing through a pipe, where velocity is maximum at the center and zero at the walls.

Purpose: It helps engineers and physicists understand and predict fluid behavior in laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The velocity profile is parabolic because of viscous effects in laminar flow, with maximum velocity at the centerline (r=0).

3. Importance of Velocity Profile Calculation

Details: Understanding the velocity profile is essential for calculating flow rates, pressure drops, and designing efficient fluid transport systems.

4. Using the Calculator

Tips: Enter the maximum velocity, radial position (must be ≤ pipe radius), and pipe radius. All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: When is the parabolic profile valid?
A: For fully developed, steady, laminar flow of Newtonian fluids in circular pipes.

Q2: What's the average velocity in this profile?
A: The average velocity is exactly half of the maximum velocity (u_avg = u_max/2).

Q3: How does this change for turbulent flow?
A: Turbulent flow has a flatter velocity profile due to increased momentum transfer.

Q4: What if my radial position equals the pipe radius?
A: Velocity will be zero at the pipe wall (r=R) due to the no-slip condition.

Q5: How is maximum velocity determined?
A: It can be calculated from pressure gradient, fluid viscosity, and pipe radius.