1. What is Laminar Velocity Profile?

Definition: The laminar velocity profile describes how fluid velocity varies radially in a pipe under laminar flow conditions.

Purpose: It helps engineers and scientists understand and predict fluid behavior in pipes and channels.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Laminar Velocity Profile

Details: Understanding velocity profiles is crucial for designing piping systems, calculating flow rates, and predicting pressure drops.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow?
A: Laminar flow is smooth, orderly fluid motion where layers slide past each other without mixing (Re < 2000 for pipes).

Q2: How does this differ from turbulent flow?
A: Turbulent flow has a flatter velocity profile due to random mixing, while laminar flow has a perfect parabolic profile.

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

Q4: Can r be greater than R?
A: No, r must be ≤ R as it represents a position within the pipe.

Q5: What units should I use?
A: Use consistent units (meters for length, m/s for velocity) for accurate results.