1. What is Shear Stress in Turbulent Flow?

Shear stress in turbulent flow refers to the force per unit area acting parallel to the flow direction due to fluid viscosity and turbulent momentum transfer. It plays a crucial role in determining flow resistance and energy losses in pipe systems.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

Where:

• \( \rho_f \) — Density of fluid (kg/m³)
• \( V' \) — Shear velocity, also called friction velocity (m/s)

Explanation: The formula calculates the shear stress at the pipe wall for turbulent flow conditions, where shear velocity represents the characteristic velocity scale for turbulent momentum transfer.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is essential for designing pipe systems, predicting pressure drops, determining pumping requirements, and analyzing flow characteristics in various engineering applications.

4. Using the Calculator

Tips: Enter fluid density in kg/m³ and shear velocity in m/s. Both values must be positive numbers. Common fluid densities: water ≈ 1000 kg/m³, air ≈ 1.225 kg/m³ at sea level.

5. Frequently Asked Questions (FAQ)

Q1: What is shear velocity?
A: Shear velocity, also called friction velocity, is a velocity scale that characterizes the shear stress at the boundary. It's defined as the square root of the wall shear stress divided by fluid density.

Q2: How does turbulent flow differ from laminar flow in terms of shear stress?
A: In turbulent flow, shear stress is significantly higher due to additional momentum transfer caused by turbulent eddies, unlike laminar flow where shear stress is solely due to viscous effects.

Q3: What are typical shear stress values in pipe flow?
A: Shear stress values vary widely depending on flow conditions, ranging from fractions of Pascal for low-velocity flows to hundreds of Pascal for high-velocity flows in large pipes.

Q4: How is shear velocity measured or determined?
A: Shear velocity can be determined from velocity profile measurements, pressure drop data, or through direct measurement of wall shear stress using specialized instruments.

Q5: Does this formula apply to all turbulent flow conditions?
A: This formula provides the wall shear stress for fully developed turbulent flow in pipes. It may need modifications for complex geometries or transitional flow regimes.