Local Shear Stress Calculator

Wall Shear Stress Formula:

\[ \tau_w = \frac{0.0296 \times \rho_{fluid} \times (u_{\infty})^2}{(Re_l)^{0.2}} \]

Wall Shear Stress:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Wall Shear Stress?

Wall shear stress is defined as the shear stress in the layer of fluid next to the wall of a pipe or surface. It represents the force per unit area exerted by the fluid on the wall in the direction parallel to the wall.

2. How Does the Calculator Work?

The calculator uses the Wall Shear Stress formula:

\[ \tau_w = \frac{0.0296 \times \rho_{fluid} \times (u_{\infty})^2}{(Re_l)^{0.2}} \]

Where:

\( \tau_w \) — Wall shear stress (Pa)
\( \rho_{fluid} \) — Density of fluid (kg/m³)
\( u_{\infty} \) — Free stream velocity (m/s)
\( Re_l \) — Local Reynolds number

Explanation: This formula calculates the shear stress at the wall based on fluid properties and flow characteristics, using the local Reynolds number to account for flow regime effects.

3. Importance of Wall Shear Stress Calculation

Details: Wall shear stress is crucial in fluid dynamics for understanding boundary layer behavior, predicting flow separation, designing efficient piping systems, and analyzing forces on submerged structures.

4. Using the Calculator

Tips: Enter fluid density in kg/m³, free stream velocity in m/s, and local Reynolds number. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 0.2 exponent in the formula?
A: The 0.2 exponent comes from empirical correlations for turbulent boundary layers and represents the relationship between Reynolds number and shear stress.

Q2: How does wall shear stress affect fluid flow?
A: Wall shear stress directly influences boundary layer development, flow separation, and energy losses in fluid systems.

Q3: What are typical values of wall shear stress?
A: Values vary widely depending on fluid properties and flow conditions, ranging from fractions of Pa in laminar flows to tens of Pa in high-speed turbulent flows.

Q4: Are there limitations to this formula?
A: This formula is specifically for turbulent boundary layers and may not be accurate for laminar flows or complex geometries.

Q5: How is local Reynolds number different from global Reynolds number?
A: Local Reynolds number is calculated using local flow properties at a specific point, while global Reynolds number uses characteristic length and average flow properties.