23.5 Unit Conversions & Using the Supplied Formula/Conversion Table

23.5 Unit Conversions & Using the Supplied Formula/Conversion Table

ADEQ states plainly that formula and conversion sheets are supplied at the testing site and that non-programmable calculators are permitted. That single fact should reshape how you prepare: the exam is not testing whether you memorized the pounds formula. It is testing whether you can select the right formula and set the problem up correctly.

Download the WPI formula and conversion table from gowpi.org and practice with it until you know where each item sits on the page. An operator who has never seen the sheet before exam day loses time hunting for entries.

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Dimensional Analysis: The Setup Check

The most common calculation error is not arithmetic — it is setting the problem up upside down. Dimensional analysis catches this by tracking units through the calculation.

Write each quantity with its units, arrange the conversion factors so that unwanted units cancel, and confirm that what remains is what the question asked for.

Example. Convert 850 gpm to MGD.

$850\ \frac{\text{gal}}{\text{min}} \times 1{,}440\ \frac{\text{min}}{\text{day}} \times \frac{1\text{ MG}}{1{,}000{,}000\text{ gal}} = 1.224\text{ MGD}$

The minutes cancel, the gallons cancel, and million gallons per day remains. If you had divided by 1,440 instead, the units would not have resolved and the error would be visible before you finished.

[!IMPORTANT] If the units do not cancel to the answer's units, the setup is wrong. This check costs seconds and catches the majority of calculation errors on an exam where every item is multiple choice and a wrong setup usually lands exactly on one of the distractors.

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The Conversions Used Most

Volume

Flow

Weight and Pressure

Power

[!NOTE] The 8.34 factor is the weight of a gallon of water in pounds, and it is what converts a concentration into a mass. Understanding why it appears rather than memorizing where it goes prevents most pounds-formula errors: milligrams per liter is a ratio, millions of gallons per day is a volume rate, and 8.34 pounds per gallon converts that volume into weight.

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Geometry

Worked example — tank volume in gallons. A cylindrical tank 40 ft in diameter with 22 ft of water.

$V = 0.785 \times 40^2 \times 22 = 0.785 \times 1{,}600 \times 22 = 27{,}632\text{ ft}^3$ $27{,}632 \times 7.48 = 206{,}687\text{ gallons}$

Worked example — pipe volume. 1,500 ft of 10-inch main. Convert diameter to feet: 10/12 = 0.833 ft.

$V = 0.785 \times 0.833^2 \times 1{,}500 = 0.785 \times 0.694 \times 1{,}500 = 817\text{ ft}^3$ $817 \times 7.48 = 6{,}111\text{ gallons}$

[!WARNING] Converting diameter from inches to feet is the single most common error in volume problems. A 10-inch pipe has a diameter of 0.833 ft, not 10 ft and not 0.10 ft. Every dimension in a formula using 7.48 gallons per cubic foot must be in feet.

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A Systematic Approach to Word Problems

1. Read the question last line first. Know what is being asked before absorbing the data.
2. List the given values with their units.
3. Identify what is irrelevant. WPI deliberately includes unused data — recall the published example where a tank's 12-ft diameter is given but static pressure depends only on the 21-ft water level.
4. Select the formula from the supplied sheet.
5. Convert units so everything is consistent before substituting.
6. Substitute and solve.
7. Check the answer for reasonableness. A chlorine dose of 4,000 mg/L, a detention time of 0.02 minutes, or a pump efficiency of 340 percent are all signals of a setup error.
8. Confirm the units of the answer match what was requested.

Dual Units

WPI presents each calculation item in US Standard units first with metric in parentheses, and each is independently solvable.

[!IMPORTANT] Pick one unit system and stay in it for the entire problem. Mixing feet with kilopascals or gallons with cubic meters partway through is the most self-inflicted error available on the exam. Read the whole problem in one system, ignore the parenthetical values entirely, and select the answer in the same system you worked in.

Rounding

Carry intermediate values to at least one more significant figure than the answer requires and round only at the end. Rounding at each step accumulates error and can move a result past the nearest answer choice. Where answer choices are close together, that accumulated error is exactly what separates the correct choice from the distractor placed next to it.