1. What Is Velocity Gradient?

Velocity Gradient is the difference in velocity between adjacent layers of a fluid. It represents how quickly the fluid velocity changes with respect to distance perpendicular to the flow direction.

2. How Does The Calculator Work?

The calculator uses the velocity gradient formula:

Where:

• Velocity Gradient (dv/dy) — Difference in velocity between fluid layers (Hz)
• Shear Stress (τ) — Force per unit area acting parallel to fluid layers (Pa)
• Dynamic Viscosity (μ) — Resistance to movement between fluid layers (Pa·s)

Explanation: The formula shows that velocity gradient is directly proportional to shear stress and inversely proportional to dynamic viscosity.

3. Importance Of Velocity Gradient Calculation

Details: Calculating velocity gradient is essential in fluid dynamics for understanding flow behavior, designing fluid systems, and analyzing shear rates in various engineering applications.

4. Using The Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units are used for velocity gradient?
A: Velocity gradient is typically measured in Hertz (Hz) or per second (s⁻¹), representing the rate of change of velocity with distance.

Q2: How does viscosity affect velocity gradient?
A: Higher viscosity fluids require greater shear stress to achieve the same velocity gradient, as viscosity resists the relative motion between fluid layers.

Q3: What is the relationship between shear stress and velocity gradient?
A: For Newtonian fluids, shear stress is directly proportional to velocity gradient, with dynamic viscosity as the constant of proportionality.

Q4: Where is velocity gradient calculation important?
A: Important in pipe flow design, lubrication systems, blood flow analysis, and any application involving fluid shear and deformation.

Q5: Can this formula be used for non-Newtonian fluids?
A: No, this formula is specifically for Newtonian fluids where viscosity is constant. Non-Newtonian fluids require more complex relationships.