Fluid Property Calculator

Validity Range: 0-100°C at atmospheric pressure Typical Accuracy: ±1-2% for most properties

Air Properties (Standard Atmosphere)

Calculate temperature-dependent properties of air at atmospheric pressure:

• Density (kg/m³) - Ideal gas law
• Dynamic viscosity (Pa·s) - Sutherland's formula
• Kinematic viscosity (m²/s) - Derived from dynamic viscosity
• Thermal conductivity (W/m·K) - Polynomial correlation
• Specific heat capacity (J/kg·K) - Temperature-dependent correlation
• Prandtl number - Dimensionless heat transfer parameter

Validity Range: -50 to 200°C at 101.325 kPa Typical Accuracy: ±1-3% for most properties

Viscosity Correlations

Sutherland's Formula (Gases)

Temperature-dependent viscosity for gases:

μ = μ₀ × (T/T₀)^(3/2) × (T₀ + S)/(T + S)

Available for:

• Air (S = 110.4 K)
• Nitrogen (S = 111 K)
• Oxygen (S = 127 K)
• Carbon dioxide (S = 240 K)

Andrade Equation (Liquids)

Temperature-dependent viscosity for liquids:

μ = A × exp(B/T)

Provides empirical correlation for various liquids with custom parameters.

Vapor Pressure (Antoine Equation)

Calculate saturation vapor pressure:

log₁₀(P) = A - B/(C + T)

Available for:

• Water
• Ethanol
• Methanol
• Acetone
• Benzene
• Toluene

Units: Temperature in °C, Pressure in mmHg or Pa (depending on constants)

Dimensionless Numbers

Reynolds Number

Calculate flow regime indicator:

Re = ρ × V × L / μ = V × L / ν

Where:

• ρ = density (kg/m³)
• V = velocity (m/s)
• L = characteristic length (m)
• μ = dynamic viscosity (Pa·s)
• ν = kinematic viscosity (m²/s)

Interpretation:

• Re < 2300: Laminar flow (pipe)
• 2300 < Re < 4000: Transition
• Re > 4000: Turbulent flow (pipe)

Friction Factor Calculator

Laminar Flow (Re < 2300):

f = 64 / Re

Turbulent Flow - Smooth Pipes (Blasius): Valid for Re < 100,000:

f = 0.316 / Re^0.25

Turbulent Flow - Rough Pipes (Colebrook-White): Iterative solution for:

1/√f = -2 log₁₀(ε/3.7D + 2.51/(Re√f))

Where:

• ε = absolute roughness (m)
• D = pipe diameter (m)

Swamee-Jain Approximation (non-iterative):

f = 0.25 / [log₁₀(ε/3.7D + 5.74/Re^0.9)]²

Ideal Gas Properties

Calculate properties using ideal gas law and kinetic theory:

• Density: ρ = P/(R×T)
• Specific heat ratio: γ (for common gases)
• Speed of sound: a = √(γ×R×T)
• Molar mass: M (for common gases)

Usage Examples

Example 1: Water Properties at 20°C

from calc import water_properties

props = water_properties(20)
print(f"Density: {props['density']:.2f} kg/m³")
print(f"Viscosity: {props['dynamic_viscosity']:.6f} Pa·s")
print(f"Thermal conductivity: {props['thermal_conductivity']:.4f} W/m·K")

Example 2: Reynolds Number for Pipe Flow

from calc import reynolds_number, water_properties

T = 25  # °C
V = 1.5  # m/s
D = 0.05  # m

props = water_properties(T)
Re = reynolds_number(V, D, props['kinematic_viscosity'])
print(f"Reynolds number: {Re:.0f}")

Example 3: Friction Factor Calculation

from calc import friction_factor

Re = 50000
roughness = 0.045e-3  # 0.045 mm for commercial steel
diameter = 0.1  # m

f = friction_factor(Re, roughness, diameter)
print(f"Friction factor: {f:.5f}")

Example 4: Vapor Pressure of Water

from calc import antoine_vapor_pressure

T = 80  # °C
P_vap = antoine_vapor_pressure('water', T)
print(f"Vapor pressure at {T}°C: {P_vap/1000:.2f} kPa")

Example 5: Air Viscosity using Sutherland's Formula

from calc import sutherland_viscosity

T = 100  # °C
mu = sutherland_viscosity('air', T + 273.15)  # Convert to Kelvin
print(f"Air viscosity at {T}°C: {mu:.6f} Pa·s")

Quick Reference

Common Water Properties

Common Air Properties (at 101.325 kPa)

Limitations

1. Temperature Ranges: Correlations are only valid within specified ranges
2. Pressure Effects: Most correlations assume atmospheric pressure
3. Pure Substances: Mixtures require different approaches
4. Accuracy: Empirical formulas provide estimates (±1-5% typical)
5. Phase Changes: Properties near phase transitions may be less accurate

When to Use This Helper

Good for:

• Quick engineering calculations
• Preliminary design work
• Educational purposes
• When databases are unavailable
• Rapid prototyping

Not suitable for:

• High-precision scientific work
• Properties outside validity ranges
• Non-standard conditions (high pressure, etc.)
• Complex mixtures
• When accuracy better than ±1% is required

Best Practices

1. Check validity ranges before using any correlation
2. Verify units - most functions use SI units (K for temperature in Sutherland, °C elsewhere)
3. Compare results with reference data when possible
4. Use appropriate significant figures based on correlation accuracy
5. Document assumptions in your calculations

Additional Resources

See reference.md for:

• Complete correlation equations
• Literature sources
• Validation data
• Accuracy comparisons
• Alternative formulations