1. What is the Linear Velocity Profile Equation?

Definition: This equation describes how fluid velocity changes linearly with distance from a wall in laminar flow conditions.

Purpose: It helps engineers and physicists analyze fluid behavior near boundaries in various applications.

2. How Does the Equation Work?

The equation is expressed as:

Where:

• \( u \) — Fluid velocity at distance y (m/s)
• \( u_{wall} \) — Wall velocity (m/s)
• \( \frac{du}{dy} \) — Velocity gradient (1/s)
• \( y \) — Distance from the wall (m)

Explanation: The velocity at any point is the wall velocity plus the product of the velocity gradient and distance from the wall.

3. Importance of Velocity Profile Calculation

Details: Understanding velocity profiles is crucial for designing efficient fluid systems, calculating shear stress, and predicting heat transfer rates.

4. Using the Calculator

Tips: Enter the wall velocity, velocity gradient, and distance from the wall. The calculator will compute the fluid velocity at that position.

5. Frequently Asked Questions (FAQ)

Q1: When is the linear velocity profile valid?
A: It's valid for steady, laminar flow of Newtonian fluids near solid boundaries.

Q2: What does a zero wall velocity mean?
A: It means the wall is stationary (no-slip condition).

Q3: Can this be used for turbulent flow?
A: No, turbulent flows have more complex velocity profiles.

Q4: What are typical units for du/dy?
A: The velocity gradient is typically expressed in 1/s (inverse seconds).

Q5: How does this relate to shear stress?
A: Shear stress is proportional to du/dy via the fluid's viscosity (τ = μ(du/dy)).