Density Of Liquid Given Shear Stress And Darcy Friction Factor Calculator

Formula Used:

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

Density of Fluid (ρ_Fluid):

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1. What is Density of Liquid Given Shear Stress and Darcy Friction Factor?

This calculator determines the density of a fluid based on shear stress, Darcy friction factor, and mean velocity parameters. It's particularly useful in fluid mechanics and pipe flow analysis where these parameters are known or measured.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula relates fluid density to shear stress and flow characteristics through the Darcy friction factor relationship.

3. Importance of Density Calculation

Details: Accurate fluid density calculation is essential for various engineering applications including pipe flow design, pump selection, pressure drop calculations, and fluid system analysis.

4. Using the Calculator

Tips: Enter shear stress in Pascal, Darcy friction factor (dimensionless), and mean velocity in m/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is shear stress in fluid mechanics?
A: Shear stress is the force per unit area acting tangentially to a surface, causing fluid deformation. In pipe flow, it's related to the pressure drop and friction.

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

Q3: What is mean velocity in pipe flow?
A: Mean velocity is the average velocity across the pipe cross-section, calculated as volumetric flow rate divided by cross-sectional area.

Q4: When is this calculation particularly useful?
A: This approach is useful when direct density measurement is difficult, but shear stress and flow parameters can be measured or estimated.

Q5: What are typical density values for common fluids?
A: Water at 4°C has density of 1000 kg/m³, air at sea level about 1.2 kg/m³, while oils range from 800-900 kg/m³ and mercury is around 13500 kg/m³.