1. What is Velocity Gradient?

The velocity gradient (du/dy) represents the rate of velocity change perpendicular to flow direction in fluid mechanics. It quantifies how quickly fluid velocity changes across different layers, which is fundamental to understanding fluid behavior and shear flow phenomena.

2. How Does the Calculator Work?

The calculator uses the velocity gradient formula:

Where:

• \( \frac{du}{dy} \) — Velocity gradient (s⁻¹)
• \( \text{Shear Stress} \) — Shear stress acting on the fluid (Pa)
• \( \text{Viscosity} \) — Dynamic viscosity of the fluid (Pa·s)

Explanation: This formula describes the relationship between shear stress, viscosity, and the resulting velocity gradient in Newtonian fluids, following Newton's law of viscosity.

3. Importance of Velocity Gradient Calculation

Details: Velocity gradient is crucial for analyzing fluid flow behavior, designing piping systems, calculating shear rates in industrial processes, and understanding boundary layer development in aerodynamics and hydrodynamics.

4. Using the Calculator

Tips: Enter shear stress in Pascals (Pa) and viscosity in Pascal-seconds (Pa·s). Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of velocity gradient?
A: Velocity gradient indicates the rate at which adjacent fluid layers slide past each other, directly relating to the internal friction and shear forces within the fluid.

Q2: How does velocity gradient relate to shear rate?
A: In fluid mechanics, velocity gradient is essentially equivalent to shear rate, both describing the rate of deformation of fluid elements under shear stress.

Q3: What are typical velocity gradient values in different applications?
A: Values range from very low (0.1-1 s⁻¹) in slow-moving fluids to very high (10,000+ s⁻¹) in high-shear industrial processes like mixing and coating.

Q4: Does this formula apply to all types of fluids?
A: This formula specifically applies to Newtonian fluids. Non-Newtonian fluids require more complex relationships between shear stress and velocity gradient.

Q5: How is velocity gradient measured experimentally?
A: It can be measured using various techniques including laser Doppler velocimetry, particle image velocimetry, or calculated from pressure drop measurements in known geometries.