Unit Conversion Theory
Introduction
Unit conversion is fundamental to engineering calculations. Consistent units are essential for accurate results. The International System of Units (SI) provides a standardized framework, but engineers must often convert between SI, CGS, and imperial systems.
SI Base Units
The SI system defines seven base units from which all other units are derived:
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
Derived Units in Engineering
Pressure
SI: Pascal (Pa) = N/m² = kg/(m·s²)
Common: bar, atm, psi, mmHg
Energy
SI: Joule (J) = N·m = kg·m²/s²
Common: kWh, BTU, calorie
Viscosity
Dynamic: Pa·s = kg/(m·s)
Common: centipoise (cP) = mPa·s
Flow Rate
Volumetric: m³/s, L/min, GPM
Mass: kg/s, lb/h
Dimensional Analysis
Every physical quantity can be expressed in terms of base dimensions:
- [Length] = L
- [Mass] = M
- [Time] = T
- [Temperature] = Θ
Example: Velocity = Length/Time = [L·T⁻¹]
Example: Force = Mass × Acceleration = [M·L·T⁻²]
Dimensional analysis helps verify equations and derive relationships between quantities.
Temperature Conversions
Temperature requires special handling due to offset scales:
K = °C + 273.15
°F = °C × (9/5) + 32
°R = °F + 459.67
K = °R × (5/9)
Note: For temperature differences (ΔT), only the scale factor matters, not the offset. 1°C difference = 1 K difference = 1.8°F difference.
Common Conversion Factors
| Category | Conversion |
|---|---|
| Pressure | 1 atm = 101.325 kPa = 14.696 psi |
| Pressure | 1 bar = 100 kPa = 14.504 psi |
| Energy | 1 BTU = 1.055 kJ = 252 cal |
| Power | 1 hp = 745.7 W = 2545 BTU/h |
| Flow | 1 GPM = 3.785 L/min = 0.227 m³/h |
| Viscosity | 1 cP = 1 mPa·s = 0.001 Pa·s |
| Length | 1 inch = 25.4 mm = 0.0254 m |
| Mass | 1 lb = 0.4536 kg = 453.6 g |
Best Practices
References
- NIST Guide for the Use of the International System of Units
- Perry's Chemical Engineers' Handbook
- Green, D.W. "Unit Operations of Chemical Engineering"