How To Calculate Cgs

Calculate dynamic viscosity in CGS units (poise) with precision. Enter your fluid properties below.

Comprehensive Guide: How to Calculate CGS (Centigram-Second) Units for Fluid Dynamics

The CGS (centimeter-gram-second) system provides fundamental units for measuring dynamic viscosity (poise) and kinematic viscosity (stokes) in fluid mechanics. This guide explains the theoretical foundations, practical calculations, and real-world applications of CGS units in viscosity measurements.

1. Understanding Viscosity in CGS Units

Viscosity measures a fluid’s resistance to flow. In the CGS system:

• Dynamic viscosity (μ): Measured in poise (P) where 1 P = 1 g·cm⁻¹·s⁻¹ = 0.1 kg·m⁻¹·s⁻¹
• Kinematic viscosity (ν): Measured in stokes (St) where 1 St = 1 cm²/s = 10⁻⁴ m²/s

The relationship between these quantities is:

ν = μ/ρ
where ρ (rho) is the fluid density in g/cm³

2. Conversion Between SI and CGS Units

Quantity	SI Unit	CGS Unit	Conversion Factor
Dynamic Viscosity	kg·m⁻¹·s⁻¹ (Pa·s)	poise (P)	1 Pa·s = 10 P
Kinematic Viscosity	m²/s	stokes (St)	1 m²/s = 10,000 St
Density	kg/m³	g/cm³	1 g/cm³ = 1000 kg/m³

3. Step-by-Step Calculation Process

1. Determine fluid properties:
   • Measure or reference the fluid’s density (ρ) in kg/m³
   • Obtain kinematic viscosity (ν) in m²/s through experimentation or literature values
2. Calculate dynamic viscosity in SI units:

   μ(SI) = ν × ρ
   (where μ is in kg·m⁻¹·s⁻¹ when ν is in m²/s and ρ in kg/m³)

3. Convert to CGS units:

   μ(CGS) = μ(SI) × 10
   ν(CGS) = ν(SI) × 10,000

4. Apply temperature corrections if needed using:
   • Sutherland’s formula for gases: μ = μ₀ × (T₀ + C)/(T + C) × (T/T₀)^3/2
   • Andrade’s equation for liquids: μ = A × e^B/T

4. Practical Example Calculations

Example 1: Water at 20°C

Given:

• Density (ρ) = 998.2 kg/m³
• Kinematic viscosity (ν) = 1.004 × 10⁻⁶ m²/s

Calculations:

1. Dynamic viscosity (SI): μ = 1.004×10⁻⁶ × 998.2 = 0.001002 kg·m⁻¹·s⁻¹
2. Dynamic viscosity (CGS): μ = 0.001002 × 10 = 0.01002 P (poise)
3. Kinematic viscosity (CGS): ν = 1.004×10⁻⁶ × 10,000 = 0.01004 St (stokes)

Example 2: Air at 15°C (using Sutherland’s formula)

Given:

• Reference viscosity μ₀ = 1.716×10⁻⁵ kg·m⁻¹·s⁻¹ at T₀ = 273.15 K
• Sutherland constant C = 120 K
• Temperature T = 15°C = 288.15 K

Sutherland calculation:

μ = 1.716×10⁻⁵ × (273.15 + 120)/(288.15 + 120) × (288.15/273.15)^3/2
μ ≈ 1.784×10⁻⁵ kg·m⁻¹·s⁻¹
μ(CGS) ≈ 0.0001784 P

5. Temperature Dependence of Viscosity

Viscosity varies significantly with temperature:

Fluid	Temperature (°C)	Dynamic Viscosity (mPa·s)	Dynamic Viscosity (cP)
Water	0	1.792	1.792
	20	1.002	1.002
	50	0.547	0.547
	100	0.282	0.282
Air	-20	0.0168	0.0168
	0	0.0172	0.0172
	20	0.0181	0.0181
	100	0.0217	0.0217

Note: 1 mPa·s (millipascal-second) = 1 cP (centipoise) = 0.01 P (poise)

6. Common Measurement Techniques

• Capillary viscometers: Measure time for fluid to flow through a thin tube (Ostwald, Cannon-Fenske)
• Rotational viscometers: Measure torque required to rotate a spindle in the fluid (Brookfield)
• Falling ball viscometers: Measure time for a ball to fall through the fluid (Höppler)
• Vibrating viscometers: Measure damping of an oscillating probe

7. Industrial Applications of CGS Viscosity

CGS units remain widely used in:

• Petroleum industry: Crude oil and lubricant specifications (e.g., SAE 10W-30 at 0.065-0.093 P at 100°C)
• Pharmaceuticals: Injectables and syrups (typically 1-100 cP)
• Food processing: Chocolate (25-50 P), honey (2,000-10,000 P)
• Paints and coatings: Typically 50-200 P for brush application
• HVAC systems: Refrigerant oil viscosities (3-30 cP at 40°C)

8. Advanced Considerations

For precise calculations, consider:

• Non-Newtonian fluids: Viscosity changes with shear rate (e.g., ketchup, blood)
• Pressure effects: Viscosity of liquids increases ~0.1% per bar; gases are less affected
• Mixture rules: For solutions, use equations like:

  ln(μ_mix) = Σ(x_i·ln(μ_i))
  where x_i is mole fraction of component i

• High-temperature corrections: Above 100°C, use extended Sutherland constants

9. Common Calculation Errors to Avoid

1. Unit mismatches: Ensure all inputs use consistent units (e.g., kg/m³ for density, not g/cm³)
2. Temperature scale confusion: Always convert to Kelvin for gas calculations
3. Ignoring pressure effects: Critical for high-pressure applications (>100 bar)
4. Assuming Newtonian behavior: Many real fluids are non-Newtonian
5. Using outdated reference data: Viscosity databases are periodically updated

10. Software and Calculation Tools

Professional tools for viscosity calculations include:

• NIST REFPROP: Reference fluid thermodynamic and transport properties
• CoolProp: Open-source thermophysical property library
• DIPPR Database: Design Institute for Physical Properties data
• ASPEN Plus: Process simulation software with viscosity models

Authoritative Resources

NIST Standard Reference Data – Fluid properties databases NIST Chemistry WebBook – Viscosity data for pure compounds Purdue University – Fluid properties and viscosity calculations