1. What is the Linear Velocity Profile Formula?

Definition: This formula calculates the velocity at a given point in Couette flow, where the velocity profile is linear.

Purpose: It helps in fluid mechanics to determine velocity distribution between parallel plates or surfaces in relative motion.

2. How Does the Formula Work?

The formula is:

Where:

• \( u \) — Velocity at distance y (m/s)
• \( \frac{du}{dy} \) — Velocity gradient (1/s)
• \( y \) — Distance from the stationary surface (m)

Explanation: The velocity increases linearly with distance from the stationary surface, with the slope determined by the velocity gradient.

3. Importance of the Linear Velocity Profile

Details: This profile is fundamental in analyzing simple shear flows, lubrication problems, and understanding viscous fluid behavior between moving surfaces.

4. Using the Calculator

Tips: Enter the velocity gradient (shear rate) in 1/s and the distance from the stationary surface in meters. Distance must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is Couette flow?
A: Couette flow is the flow of viscous fluid between two parallel plates, where one plate is stationary and the other moves parallel to it.

Q2: When is the linear velocity profile valid?
A: It's valid for steady, laminar flow of Newtonian fluids with no pressure gradient in the flow direction.

Q3: What affects the velocity gradient (du/dy)?
A: It depends on the relative velocity between surfaces and the gap distance: du/dy = U/h, where U is plate velocity and h is gap height.

Q4: Can this be used for non-Newtonian fluids?
A: No, this linear profile is specific to Newtonian fluids. Non-Newtonian fluids may have nonlinear profiles.

Q5: How does this relate to shear stress?
A: For Newtonian fluids, shear stress τ = μ(du/dy), where μ is dynamic viscosity.