Mean Velocity Of Flow Given Shear Stress Calculator

Mean Velocity Formula:

\[ V_{mean} = (\tau + \frac{dp}{dr} \times (0.5 \times D - R)) \times \frac{D}{\mu} \]

Shear Stress (τ):

Pressure Gradient (dp/dr):

N/m³

Distance between plates (D):

Horizontal Distance (R):

Dynamic Viscosity (μ):

Pa·s

Mean Velocity (V_mean):

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1. What is Mean Velocity in Fluid Flow?

Mean velocity represents the average velocity of fluid particles across a cross-section of flow. It's a fundamental parameter in fluid mechanics that helps characterize flow behavior and calculate flow rates in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the mean velocity formula:

\[ V_{mean} = (\tau + \frac{dp}{dr} \times (0.5 \times D - R)) \times \frac{D}{\mu} \]

Where:

\( V_{mean} \) — Mean velocity (m/s)
\( \tau \) — Shear stress (Pa)
\( \frac{dp}{dr} \) — Pressure gradient (N/m³)
\( D \) — Distance between plates (m)
\( R \) — Horizontal distance (m)
\( \mu \) — Dynamic viscosity (Pa·s)

Explanation: This formula calculates the average flow velocity between parallel plates considering shear stress, pressure gradient, geometric parameters, and fluid viscosity.

3. Importance of Mean Velocity Calculation

Details: Accurate mean velocity calculation is essential for designing fluid transport systems, predicting flow behavior, calculating flow rates, and analyzing pressure drops in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure dynamic viscosity and distance between plates are positive values. The calculator handles both positive and negative pressure gradients.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of shear stress in fluid flow?
A: Shear stress represents the force per unit area required to maintain fluid motion and is directly related to the fluid's viscosity and velocity gradient.

Q2: How does pressure gradient affect flow velocity?
A: A positive pressure gradient (decreasing pressure in flow direction) accelerates the flow, while a negative gradient decelerates it.

Q3: What are typical values for dynamic viscosity?
A: Water at 20°C has μ ≈ 0.001 Pa·s, air ≈ 1.8×10⁻⁵ Pa·s, while honey can be around 2-10 Pa·s depending on temperature.

Q4: When is this formula applicable?
A: This formula is specifically designed for laminar flow between parallel plates and may not be accurate for turbulent flow or complex geometries.

Q5: How does horizontal distance affect the calculation?
A: The horizontal distance parameter accounts for the position within the flow field where the velocity is being calculated.