1. What is Pipe Flow Velocity Profile?

Definition: This calculator determines the fluid velocity at a specific radial position in a pipe using the power-law velocity profile equation.

Purpose: It helps engineers and fluid dynamics researchers understand velocity distribution in pipes for laminar and turbulent flows.

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 centerline (m/s)
• \( r \) — Radial position from center (m)
• \( R \) — Pipe radius (m)
• \( n \) — Profile exponent (dimensionless)

Explanation: The equation describes how velocity varies from the pipe wall (where u=0) to the centerline (where u=u_max).

3. Importance of Velocity Profile

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

4. Using the Calculator

Tips:

• Enter u_max (typically 1.2-2× average velocity)
• r must be ≤ R (pipe radius)
• Use n=2 for laminar flow, n=7 for turbulent flow

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between laminar and turbulent profiles?
A: Laminar (n=2) has a parabolic profile, while turbulent (n=7) has a flatter center with steeper wall gradients.

Q2: How do I determine u_max?
A: For turbulent flow, u_max ≈ 1.2×V_avg (Re≈4000) to 2×V_avg (Re>10⁶).

Q3: What if my r value equals R?
A: At the pipe wall (r=R), velocity should be zero (no-slip condition).

Q4: Can I use other n values?
A: Yes, n varies with Reynolds number (4-10 for turbulent). n=7 is typical for smooth pipes at Re≈10⁵.

Q5: Does this work for non-circular pipes?
A: No, this formula is specifically for circular pipes. Other geometries require different approaches.