1. What Is A Velocity Profile?

Definition: The velocity profile describes how fluid velocity varies across the cross-section of a pipe during laminar flow.

Purpose: Understanding velocity profiles is essential for fluid dynamics calculations, pipe design, and flow rate analysis.

2. How Does the Calculator Work?

The calculator uses the laminar flow velocity profile 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 formula shows a parabolic velocity distribution with maximum velocity at the center (r=0) and zero velocity at the pipe wall (r=R).

3. Importance of Velocity Profile Calculation

Details: Accurate velocity profiles help determine flow rates, shear stresses, pressure drops, and energy requirements in piping systems.

4. Using the Calculator

Tips: Enter the maximum velocity (centerline velocity), radial position from center (must be ≤ pipe radius), and pipe radius. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow?
A: Laminar flow occurs when fluid moves in parallel layers with no disruption between them, typically at low Reynolds numbers (Re < 2100).

Q2: How does this differ from turbulent flow?
A: Turbulent flow has a flatter velocity profile and requires different equations. This calculator is only valid for laminar flow.

Q3: What's the average velocity in laminar flow?
A: The average velocity is exactly half of the maximum velocity (u_avg = u_max/2) for laminar flow.

Q4: Can r be greater than R?
A: No, the radial position cannot exceed the pipe radius. The calculator will not compute results for r > R.

Q5: How do I find u_max?
A: Maximum velocity can be calculated from pressure drop or measured experimentally. It's twice the average velocity in laminar flow.