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:

QuantityUnitSymbol
Lengthmeterm
Masskilogramkg
Timeseconds
Electric CurrentampereA
TemperaturekelvinK
Amount of Substancemolemol
Luminous Intensitycandelacd

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

CategoryConversion
Pressure1 atm = 101.325 kPa = 14.696 psi
Pressure1 bar = 100 kPa = 14.504 psi
Energy1 BTU = 1.055 kJ = 252 cal
Power1 hp = 745.7 W = 2545 BTU/h
Flow1 GPM = 3.785 L/min = 0.227 m³/h
Viscosity1 cP = 1 mPa·s = 0.001 Pa·s
Length1 inch = 25.4 mm = 0.0254 m
Mass1 lb = 0.4536 kg = 453.6 g

Best Practices

1.Always convert to SI units before calculations, then convert results back if needed.
2.Track units through calculations - units must be consistent in equations.
3.Use dimensional analysis to verify equation validity.
4.Be careful with gc (gravitational constant) in imperial unit systems.
5.Document unit assumptions clearly in engineering calculations.

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"