Units & Dimensional Analysis

Master the unit systems and conversion techniques that underlie every chemical engineering calculation.

Material & Energy BalancesChemical Engineering Year 1Free preview
⏱️ About 14 min

If a pump spec sheet lists flow in gallons per minute but your equations need kg/s, how do you bridge the gap without losing a decimal?

💡
The big idea: Every engineering quantity has units; converting them reliably means multiplying by ratios equal to one while keeping dimensions homogeneous.
🎯 By the end, you'll be able to
  • Identify the seven SI base quantities and common derived units
  • Distinguish SI, CGS, and American Engineering unit systems
  • Apply dimensional homogeneity to validate equations
  • Convert quantities using conversion factors written as ratios equal to one

Unit Systems & Base Quantities

Chemical engineers communicate quantities using standardized unit systems. The SI system (Système International) is built from seven base quantities — mass (kg), length (m), time (s), temperature (K), amount of substance (mol), electric current (A), and luminous intensity (cd). All other units (N, Pa, J, W) are derived from these.

Two older systems still appear in industry and textbooks: the CGS system (cm, g, s) and the American Engineering (English) system (lbm, ft, s, °F, with lbf as a derived force unit through the conversion constant gc). Recognizing which system a quantity is reported in is the first step in any calculation.

\[ \dot{m} = \rho\, v\, A \]
Dimensional check: [kg/m³] [m/s] [m²] = [kg/s]. A dimensionally homogeneous equation yields the same units on both sides.

Unit Conversion & Significant Figures

To convert units, multiply by conversion factors written as ratios equal to one: since 1 in = 2.54 cm exactly, both (1 in / 2.54 cm) and (2.54 cm / 1 in) equal 1. Choose the orientation that cancels the unit you have and leaves the unit you want.

Report results with the correct number of significant figures: a result is no more precise than its least-precise input. Multiplication and division keep the fewest sig figs; addition and subtraction keep the fewest decimal places.

🔑 Conversion factors equal 1

Multiplying by (2.54 cm / 1 in) does not change a quantity's value — only its units. Chain as many such factors as needed; every intermediate unit should cancel except the target.

📝 Worked example: A pump truck travels at 55 miles per hour. Express this speed in SI base units (m/s).
  1. Write the starting quantity and target units: 55 mi/h → m/s
  2. List exact conversions: 1 mi = 5280 ft, 1 ft = 0.3048 m, 1 h = 3600 s
  3. Set up the chain: 55 mi/h × (5280 ft / 1 mi) × (0.3048 m / 1 ft) × (1 h / 3600 s)
  4. Numerator: 55 × 5280 × 0.3048 = 55 × 1609.344 = 88 513.92 m
  5. Divide by 3600 s: 88 513.92 / 3600 = 24.5872 m/s
  6. Round to 3 sig figs: 24.6 m/s
✓ 24.6 m/s
✏️ Practice: Convert a pressure of 30 psi to kPa. (1 psi = 6894.76 Pa)
kPa
Solution
  1. 1 psi = 6894.76 Pa = 6.89476 kPa
  2. 30 psi × 6.89476 kPa/psi = 206.8 kPa

Check your understanding

1. Which of the following is a base SI quantity?
Mass (kilogram) is one of the seven SI base quantities; force, pressure, and density are all derived from them.
2. Convert 2.0 km to centimeters.
2.0 km × (1000 m / 1 km) × (100 cm / 1 m) = 2.0 × 10⁵ cm.
🔎 Related lessons
Process Flow Diagrams & Composition Variables
✅ Key takeaways
  • SI uses seven base quantities; CGS and American Engineering systems also appear in industry
  • Dimensionally homogeneous equations have matching units on both sides
  • Convert units by chaining factors equal to 1, canceling unwanted units
  • Report results with significant figures matching the least-precise input
➡️ Now that units and conversions are second nature, we'll put them to work reading and labeling process flow diagrams and stream compositions.
Want to test yourself on this? Try the Chemical Aptitude test →