Shear Stress Given Friction Factor And Density Calculator

Shear Stress Formula:

\[ \text{Shear Stress} = \frac{\rho_{\text{Fluid}} \times f \times V_{\text{mean}} \times V_{\text{mean}}}{8} \]

Density of Fluid (ρFluid):

kg/m³

Darcy Friction Factor (f):

(dimensionless)

Mean Velocity (Vmean):

m/s

Shear Stress (τ):

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1. What is Shear Stress?

Shear Stress refers to the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. In fluid dynamics, it represents the internal friction between fluid layers moving at different velocities.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \text{Shear Stress} = \frac{\rho_{\text{Fluid}} \times f \times V_{\text{mean}} \times V_{\text{mean}}}{8} \]

Where:

\( \rho_{\text{Fluid}} \) — Density of Fluid (kg/m³)
\( f \) — Darcy Friction Factor (dimensionless)
\( V_{\text{mean}} \) — Mean Velocity (m/s)

Explanation: This formula calculates the shear stress at the wall in pipe flow, which is proportional to the fluid density, friction factor, and the square of the mean velocity.

3. Importance of Shear Stress Calculation

Details: Shear stress calculation is crucial in fluid mechanics for determining flow resistance, pressure drop calculations, pipe sizing, and understanding fluid behavior in various engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the Darcy friction factor?
A: The Darcy friction factor is a dimensionless quantity used in the Darcy-Weisbach equation to calculate pressure loss due to friction in pipes. Its value depends on the flow's Reynolds number and the pipe's relative roughness.

Q2: How is mean velocity determined?
A: Mean velocity is the average velocity of fluid flow through a cross-section, calculated as the volumetric flow rate divided by the cross-sectional area.

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

Q4: When is this formula applicable?
A: This formula is specifically for calculating wall shear stress in fully developed turbulent flow in circular pipes.

Q5: How does fluid density affect shear stress?
A: Shear stress is directly proportional to fluid density - higher density fluids will experience greater shear stress for the same flow conditions.