Mass loading and the 8.34 conversion on the PE Civil WRE exam

One conversion runs through several areas of the WRE exam: turning a concentration and a flow into a mass per day. It sets up TMDL allocations and stream mixing in Surface Water and Groundwater Quality, and the same step returns as coagulant and chlorine feed in drinking water, as BOD and solids loading in wastewater, and in every mass balance in Analysis and Design. It is quick once the units are reflexive.

What you actually need to own

• The relation. M (lb/day) = C (mg/L) × Q (MGD) × 8.34. The Handbook prints it as a concentration-to-mass-per-day conversion under Mass Conservation and Continuity in the Water Quality section.
• Where 8.34 comes from. A gallon of water weighs about 8.34 lb, so a million gallons weighs 8.34 million lb. In dilute water, 1 mg/L is one part per million by mass. One part per million of 8.34 million lb is 8.34 lb, so 1 mg/L in 1 MGD is 8.34 lb/day. Seeing it that way keeps you from reaching for 7.48 or 62.4 by mistake.
• The cfs version. With Q in cfs, the constant becomes about 5.39 (8.34 ÷ 1.547, since 1 MGD ≈ 1.547 cfs). Use 5.39 with cfs and 8.34 with MGD.
• Dose vs. feed rate. The dose is the concentration you want in the water (mg/L). The feed rate is how much product you add (lb/day or gal/day). Get the pure-chemical mass first, then divide by purity: 2.5 mg/L at 4 MGD is 83.4 lb/day of chlorine, or about 128 lb/day of a 65%-available product. For chlorine, the dose is demand plus the residual you want to keep.
• Solution strength. A liquid at x% by weight with specific gravity SG carries about 8.34 × SG × (x/100) lb of active chemical per gallon. Divide the required lb/day by that to get gal/day. The same form converts a sludge flow at a given percent solids into lb/day of dry solids.
• Mixing and blending. Flow-weighted: C_mix = ΣQᵢCᵢ / ΣQᵢ. Split treatment, a bypass blend and an outfall-into-stream problem are all this balance. Solve it for the unknown flow or concentration.

Where people lose points

• Flow in the wrong unit. gpm and cfs must become MGD before 8.34 applies (1 MGD ≈ 694 gpm). A problem that gives gal/day needs dividing by 10⁶ first.
• Multiplying by purity instead of dividing. Less-pure product means more product. If your feed rate got smaller, the step is upside down.
• Dropping the specific gravity on a strong solution or a thick sludge. There, 8.34 alone undercounts the weight of a gallon.
• mg/L vs. ppm. They are interchangeable for dilute water, but not for dense solutions or sludges, and 1% is 10,000 ppm by mass.
• "As" units. A concentration reported as CaCO₃ or as N is a different mass than the same species expressed as itself. Keep the basis the problem uses all the way through.
• Flow at the wrong point. In a stream problem, use the flow where the limit applies, including effluent that enters above it and net of diversions. The area page's TMDL and oxygen-sag traps build on this step.

How to study it

Write units on every term until the cancellation is automatic: mg/L × MGD × 8.34 → lb/day. Then drill four versions of the same problem in a row: pure chemical, a percent-purity solid, a liquid solution with SG, and a blend solved backward for flow. Carry the step into BOD loading and activated sludge and CT, sedimentation and filtration, where it is usually the first line of a longer problem.

Part of the Surface Water and Groundwater Quality area of the PE Civil WRE exam. → Start practicing free — the whole practice bank, free with an account.