1. What is Shear Stress?

Shear Stress of Fluid can be defined as a unit area amount of force acting on the fluid parallel to a very small element of the surface. It represents the internal friction within the fluid when layers move at different velocities.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

Where:

• \( \sigma \) — Shear Stress (Pascal)
• \( \mu \) — Dynamic Viscosity (Pascal Second)
• \( \frac{du}{dy} \) — Velocity Gradient (s⁻¹)

Explanation: The formula calculates the shear stress by multiplying the fluid's dynamic viscosity by the velocity gradient perpendicular to the flow direction.

3. Importance of Shear Stress Calculation

Details: Shear stress calculation is crucial in fluid mechanics for understanding flow behavior, designing piping systems, predicting drag forces, and analyzing fluid-structure interactions in various engineering applications.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s and velocity gradient in s⁻¹. Both values must be valid positive numbers for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between dynamic and kinematic viscosity?
A: Dynamic viscosity (μ) measures a fluid's resistance to flow under an applied force, while kinematic viscosity (ν) is the ratio of dynamic viscosity to fluid density (ν = μ/ρ).

Q2: How does temperature affect viscosity and shear stress?
A: For liquids, viscosity decreases with increasing temperature, reducing shear stress. For gases, viscosity increases with temperature, potentially increasing shear stress.

Q3: What are typical units for shear stress?
A: The SI unit is Pascal (Pa), which equals N/m². Other common units include pounds per square inch (psi) and dynes per square centimeter.

Q4: Where is shear stress important in practical applications?
A: Important in pipe flow design, lubrication systems, blood flow analysis, aerodynamics, and any application involving fluid movement past surfaces.

Q5: How does shear stress relate to Newtonian and non-Newtonian fluids?
A: For Newtonian fluids, shear stress is directly proportional to velocity gradient. For non-Newtonian fluids, the relationship is more complex and may not follow this linear formula.