Lesson 1 of 8 · 14 minutes
Units First: Build a Calculation That Can Be Checked
Most operator-math errors begin before the arithmetic. A unit-first setup makes the relationship visible, exposes incompatible time or volume bases, and gives you a way to check the answer.
Learning objectives
- Write the requested unit before selecting a formula.
- Use conversion factors that cancel unwanted units.
- Carry units through every line instead of attaching them at the end.
Key relationships
- A conversion factor is a ratio equal to one, such as 7.48 gal/ft³.
- Arrange the ratio so the unit you do not want cancels.
- Do not mix minutes and days, gallons and million gallons, or milligrams and pounds without an explicit conversion.
Formulagiven value × conversion factor(s) = requested value
- 1 ft³ = 7.48 gal
- 1 day = 1,440 min
- 1 MGD = 1,000,000 gal/day
- 1 mg/L = 1 ppm for dilute water-based calculations
Unit-first worked example
Convert 2.50 cubic feet per second (ft³/s) to gallons per minute (gpm).
2.50 ft³/s × 7.48 gal/ft³ × 60 s/min
- Cancel ft³ between the given flow and 7.48 gal/ft³.
- Cancel seconds by multiplying by 60 s/min.
- Calculate: 2.50 × 7.48 × 60 = 1,122.
Answer: 1,122 gpm (about 1,120 gpm to three significant figures).
Reasonableness check: One ft³/s is about 449 gpm, so 2.5 ft³/s should be a little above 1,100 gpm.
Common mistake
Multiplying by 7.48 but forgetting the 60-second-to-one-minute conversion produces gallons per second, not gallons per minute.
Field takeaway
If the units do not cancel to the unit requested, the setup is not finished.
Knowledge check