1. What is Velocity Profile in a Pipe?

Definition: This calculator determines the local fluid velocity at any radial position in a pipe for laminar flow conditions.

Purpose: It helps engineers and students understand and predict fluid velocity distribution in circular pipes.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation for laminar flow:

Where:

• \( u \) — Local velocity at 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 velocity distribution is crucial for pipe design, flow measurement, and predicting pressure drops in fluid systems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for turbulent flow?
A: No, this is specifically for laminar flow (Re < 2300). Turbulent flow has a different velocity profile.

Q2: What's the maximum velocity in laminar pipe flow?
A: The centerline velocity is exactly twice the average velocity (when r=0).

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

Q4: How do I find average velocity?
A: Average velocity = volumetric flow rate / cross-sectional area of pipe.

Q5: What are typical units for these values?
A: All units are in meters and seconds (m, m/s) in this calculator.