1. What is Turbulent Flow Velocity Profile?

Definition: This calculator computes the velocity at a given radial position in a pipe for turbulent flow using the 1/7th power law approximation.

Purpose: It helps engineers and fluid dynamicists analyze velocity distributions in turbulent pipe 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)

Explanation: The 1/7th power law is an empirical approximation for fully developed turbulent flow in smooth pipes.

3. Importance of Velocity Profile Calculation

Details: Understanding velocity profiles is crucial for pipe system design, pressure drop calculations, and flow rate estimations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this approximation?
A: The 1/7th power law works well for Reynolds numbers between 10⁴ and 10⁵ in smooth pipes.

Q2: How does this differ from laminar flow profile?
A: Laminar flow has a parabolic profile (u = u_max[1-(r/R)²]), while turbulent flow is flatter in the center.

Q3: What happens when r = R (at pipe wall)?
A: The formula predicts u = 0, though in reality there's a viscous sublayer very close to the wall.

Q4: Can this be used for non-circular ducts?
A: No, this formula is specifically for circular pipes. Different approaches are needed for other geometries.

Q5: How accurate is this approximation?
A: It's reasonably accurate for engineering purposes but may deviate ±5% from actual measurements.