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name: fluid-property-calculator description: "Quick fluid property calculations using empirical formulas without database queries" category: helpers domain: fluids complexity: basic dependencies: []

Fluid Property Calculator

Quick fluid property calculations using empirical correlations and analytical formulas. Provides instant property estimates without requiring external databases or data files.

Overview

This helper provides fast, practical calculations for common fluids using well-established empirical correlations. All formulas include validity ranges and are verified against reference data.

Available Calculations

Water Properties (0-100°C)

Calculate temperature-dependent properties of liquid water:

• Density (kg/m³) - Polynomial correlation
• Dynamic viscosity (Pa·s) - Vogel equation
• Kinematic viscosity (m²/s) - Derived from dynamic viscosity
• Thermal conductivity (W/m·K) - Polynomial correlation
• Specific heat capacity (J/kg·K) - Polynomial correlation
• Vapor pressure (Pa) - Antoine equation
• Prandtl number - Dimensionless heat transfer parameter

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

T (°C)	ρ (kg/m³)	μ (mPa·s)	ν (mm²/s)	k (W/m·K)	Pr
0	999.8	1.787	1.787	0.561	13.5
20	998.2	1.002	1.004	0.598	7.0
40	992.2	0.653	0.658	0.631	4.3
60	983.2	0.467	0.475	0.654	3.0
80	971.8	0.355	0.365	0.670	2.2
100	958.4	0.282	0.294	0.680	1.8

Common Air Properties (at 101.325 kPa)

T (°C)	ρ (kg/m³)	μ (μPa·s)	ν (mm²/s)	k (W/m·K)	Pr
0	1.293	17.16	13.27	0.0243	0.71
20	1.205	18.24	15.14	0.0257	0.71
50	1.093	19.57	17.90	0.0279	0.71
100	0.946	21.67	22.90	0.0314	0.71

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