1. What is Laminar Flow Velocity Profile?

Definition: This calculator determines the velocity at a specific radial position in a pipe for fully developed laminar flow.

Purpose: It helps engineers and fluid dynamics students understand and calculate the parabolic velocity distribution in laminar pipe flow.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Velocity Profile Calculation

Details: Understanding the velocity profile is crucial for calculating flow rates, shear stresses, and pressure drops in piping systems.

4. Using the Calculator

Tips: Enter the average velocity, radial position (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 is smooth, orderly fluid motion where fluid flows in parallel layers with no disruption between them (Re < 2100).

Q2: What's the maximum velocity in laminar flow?
A: The maximum velocity occurs at the center (r=0) and is exactly twice the average velocity (u_max = 2u_avg).

Q3: What happens if r > R?
A: The calculator will not compute as r must be ≤ R (position can't be outside the pipe).

Q4: Does this apply to turbulent flow?
A: No, turbulent flow has a different velocity profile that's more flattened in the center region.

Q5: How do I calculate average velocity?
A: Average velocity is volumetric flow rate divided by cross-sectional area (u_avg = Q/A).