Shear Stress At Wall Given Friction Coefficient Calculator

Shear Stress Formula:

\[ \tau_w = \frac{C_f \cdot \rho_{Fluid} \cdot (u_{\infty}^2)}{2} \]

Shear Stress (τw):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Shear Stress at Wall?

Shear stress at the wall is the force per unit area exerted by a fluid on a surface parallel to the flow direction. It represents the frictional resistance between the fluid and the solid boundary.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \tau_w = \frac{C_f \cdot \rho_{Fluid} \cdot (u_{\infty}^2)}{2} \]

Where:

\( \tau_w \) — Shear stress at wall (Pa)
\( C_f \) — Friction coefficient (-)
\( \rho_{Fluid} \) — Density of fluid (kg/m³)
\( u_{\infty} \) — Free stream velocity (m/s)

Explanation: The formula calculates wall shear stress based on fluid properties and flow characteristics, where the friction coefficient represents the ratio of wall shear stress to the dynamic pressure of the flow.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for designing fluid systems, predicting flow behavior, estimating energy losses, and analyzing heat transfer in various engineering applications.

4. Using the Calculator

Tips: Enter friction coefficient (dimensionless), fluid density in kg/m³, and free stream velocity in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of friction coefficients?
A: Friction coefficients typically range from 0.001 to 0.01 for laminar flow and 0.01 to 0.1 for turbulent flow in smooth pipes.

Q2: How does surface roughness affect shear stress?
A: Surface roughness increases both friction coefficient and shear stress due to enhanced momentum transfer between the fluid and the wall.

Q3: What units are used for shear stress?
A: Shear stress is measured in Pascals (Pa) in the SI system, which is equivalent to N/m².

Q4: How does fluid viscosity affect shear stress?
A: Higher viscosity fluids generally produce higher shear stresses at the wall for the same flow conditions due to increased internal friction.

Q5: Can this formula be used for both laminar and turbulent flow?
A: Yes, but the friction coefficient must be appropriate for the flow regime (laminar or turbulent) and surface conditions.