Shear Stress Given Velocity Calculator

Shear Stress Formula:

\[ \text{Shear Stress} = \left( \frac{\mu \cdot V_{\text{mean}}}{D} \right) - \frac{dp}{dr} \cdot \left( 0.5 \cdot D - R \right) \]

Dynamic Viscosity (μ):

Pa·s

Mean Velocity (Vmean):

m/s

Distance between plates (D):

Pressure Gradient (dp/dr):

N/m³

Horizontal Distance (R):

Shear Stress (τ):

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1. What is Shear Stress?

Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. In fluid mechanics, it represents the internal resistance of a fluid to flow when a force is applied.

2. How Does the Calculator Work?

The calculator uses the Shear Stress formula:

\[ \text{Shear Stress} = \left( \frac{\mu \cdot V_{\text{mean}}}{D} \right) - \frac{dp}{dr} \cdot \left( 0.5 \cdot D - R \right) \]

Where:

\( \mu \) — Dynamic Viscosity (Pa·s)
\( V_{\text{mean}} \) — Mean Velocity (m/s)
\( D \) — Distance between plates (m)
\( \frac{dp}{dr} \) — Pressure Gradient (N/m³)
\( R \) — Horizontal Distance (m)

Explanation: The equation calculates shear stress in fluid flow between parallel plates, accounting for both viscous effects and pressure gradient influences.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for understanding fluid behavior, designing piping systems, predicting erosion rates, and analyzing blood flow in medical applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Dynamic viscosity, mean velocity, and distance between plates must be positive values. The calculator provides results in Pascals (Pa).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between shear stress and normal stress?
A: Shear stress acts parallel to the surface, causing deformation, while normal stress acts perpendicular to the surface, causing compression or tension.

Q2: How does viscosity affect shear stress?
A: Higher viscosity fluids generate greater shear stress for the same velocity gradient, as they offer more resistance to flow.

Q3: What are typical shear stress values in engineering applications?
A: Shear stress values vary widely depending on the application, from fractions of a Pascal in low-viscosity flows to thousands of Pascals in high-pressure systems.

Q4: When is the pressure gradient term significant?
A: The pressure gradient term becomes significant in pressure-driven flows where there's a substantial pressure difference along the flow direction.

Q5: Can this formula be used for non-Newtonian fluids?
A: This specific formula is designed for Newtonian fluids. Non-Newtonian fluids require different models that account for their variable viscosity behavior.