1. What is Velocity Gradient?

The 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, and is a fundamental concept in fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \frac{du}{dy} \) — Velocity Gradient (s⁻¹)
• \( \sigma \) — Shear Stress of Fluid (Pa)
• \( \mu \) — Dynamic Viscosity (Pa·s)

Explanation: This formula relates the velocity gradient to the shear stress and dynamic viscosity of the fluid, based on Newton's law of viscosity.

3. Importance of Velocity Gradient Calculation

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

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 for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of velocity gradient?
A: Velocity gradient quantifies the rate at which fluid velocity changes across different layers, indicating the intensity of shearing within the fluid.

Q2: How does viscosity affect velocity gradient?
A: Higher viscosity fluids require greater shear stress to achieve the same velocity gradient, meaning they resist deformation more strongly.

Q3: What are typical units for velocity gradient?
A: Velocity gradient is typically measured in reciprocal seconds (s⁻¹), representing the rate of change of velocity with distance.

Q4: Where is this calculation commonly applied?
A: This calculation is used in various fields including chemical engineering, mechanical engineering, petroleum industry, and biomedical applications involving fluid flow.

Q5: How does temperature affect the calculation?
A: Temperature significantly affects dynamic viscosity, with most fluids becoming less viscous as temperature increases, which would affect the velocity gradient for a given shear stress.