Mean Velocity Of Flow Given Shear Stress And Density Calculator

Mean Velocity Formula:

\[ V_{mean} = \sqrt{\frac{8 \times \tau}{\rho_{fluid} \times f}} \]

Mean Velocity (V_mean):

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1. What is Mean Velocity of Flow?

Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time period. It represents the overall flow rate through a cross-sectional area of a pipe or channel.

2. How Does the Calculator Work?

The calculator uses the mean velocity formula:

\[ V_{mean} = \sqrt{\frac{8 \times \tau}{\rho_{fluid} \times f}} \]

Where:

\( V_{mean} \) — Mean velocity (m/s)
\( \tau \) — Shear stress (Pa)
\( \rho_{fluid} \) — Density of fluid (kg/m³)
\( f \) — Darcy friction factor (dimensionless)

Explanation: This formula calculates the average flow velocity based on the shear stress at the wall, fluid density, and the Darcy friction factor which accounts for flow resistance.

3. Importance of Mean Velocity Calculation

Details: Calculating mean velocity is essential for fluid dynamics analysis, pipe system design, flow rate determination, and understanding pressure drops in fluid transport systems.

4. Using the Calculator

Tips: Enter shear stress in pascals (Pa), fluid density in kg/m³, and Darcy friction factor (dimensionless). All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is shear stress in fluid flow?
A: Shear stress refers to the force per unit area acting tangentially to the surface, tending to cause deformation of the fluid layers relative to each other.

Q2: How is Darcy friction factor determined?
A: The Darcy friction factor depends on the flow's Reynolds number and the pipe's relative roughness. It can be obtained from Moody's chart or calculated using empirical formulas.

Q3: What are typical values for Darcy friction factor?
A: For laminar flow, f = 64/Re. For turbulent flow, f typically ranges from 0.008 to 0.08 depending on Reynolds number and pipe roughness.

Q4: When is this formula applicable?
A: This formula is applicable for steady, fully developed flow in pipes and channels where the relationship between shear stress and velocity is well-defined.

Q5: Are there limitations to this equation?
A: This equation assumes constant fluid properties and may have limitations for non-Newtonian fluids, compressible flows, or flows with significant temperature variations.