1. What is the Density Formula?

The density formula calculates the density of a fluid based on wall shear stress, local friction coefficient, and free stream velocity. It is derived from the relationship between these parameters in fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \rho \) — Density (kg/m³)
• \( \tau_w \) — Wall shear stress (Pa)
• \( C_{fx} \) — Local friction coefficient
• \( u_{\infty} \) — Free stream velocity (m/s)

Explanation: This formula relates the density of a fluid to the wall shear stress, local friction coefficient, and the square of the free stream velocity.

3. Importance of Density Calculation

Details: Accurate density calculation is crucial for various fluid dynamics applications, including pipe flow analysis, aerodynamics, and hydraulic system design.

4. Using the Calculator

Tips: Enter wall shear stress in Pascals, local friction coefficient (dimensionless), and free stream velocity in m/s. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is wall shear stress?
A: Wall shear stress is the shear stress in the fluid layer adjacent to a solid boundary, such as a pipe wall.

Q2: How is local friction coefficient determined?
A: The local friction coefficient is typically determined experimentally or through computational fluid dynamics simulations.

Q3: What is free stream velocity?
A: Free stream velocity is the velocity of the fluid undisturbed by any obstacles or boundaries.

Q4: What are typical density values for common fluids?
A: Water has a density of about 1000 kg/m³, air at sea level about 1.225 kg/m³, and mercury about 13500 kg/m³.

Q5: Are there limitations to this formula?
A: This formula is specific to certain flow conditions and may not be applicable to all fluid flow scenarios.