12.1 Concentration, Load, and Mass-Rate Conversions

Concentration, Load, and Mass Rate

The April 2024 PE Civil Water Resources and Environmental specification expects candidates to move comfortably between concentration, flow, and load. This shows up in surface water quality, groundwater contamination, wastewater treatment, solids loading, and total maximum daily load problems. The exam often gives familiar water-quality units, then hides the actual task in the final sentence: find a load, a required concentration, a percent reduction, or the mixed concentration after two streams combine.

Concentration is pollutant mass per water volume, commonly mg/L. Load is pollutant mass per time, such as lb/day or kg/day. Mass rate is the same idea written generically; it tells how much pollutant crosses a boundary each unit of time. A concentration by itself does not tell environmental impact unless the flow is known. A small flow at 1,000 mg/L may carry less mass than a large flow at 20 mg/L.

Conversion Shortcuts

The 8.34 factor comes from water density and unit conversion. It is not magic, and it is not interchangeable with metric formulas. If the problem gives cfs, gpm, acre-ft/day, or L/s, convert flow first or use a fully dimensional method.

Calculation Workflow

1. Circle the requested output and its unit.
2. Put every flow on one basis, usually MGD or m^3/day.
3. Put every concentration on one basis, usually mg/L.
4. Convert each stream to load before adding or subtracting pollutant mass.
5. If the answer must be a concentration, divide the resulting load by the resulting flow and conversion factor.
6. Check that a blended conservative concentration falls between the input concentrations.

Mixing and Dilution

For a conservative pollutant with no reaction, settling, volatilization, decay, or chemical addition, the mixed concentration is a flow-weighted average:

Cmix = sum(Qi Ci) / sum(Qi)

This formula works when the same flow units are used throughout. Do not average concentrations unless the flows are equal. If a 4 MGD stream at 5 mg/L mixes with a 1 MGD stream at 45 mg/L, the result is (4 x 5 + 1 x 45) / 5 = 13 mg/L. The high-strength stream is only 20 percent of the flow but contributes most of the pollutant mass.

Load-Based Removal

When flow changes through a process, percent removal must be based on load rather than concentration alone. This is common when sludge wasting, recycle streams, infiltration, evaporation, or chemical addition changes the water volume. For example, if influent is 2.0 MGD at 180 mg/L and effluent is 1.8 MGD at 30 mg/L, influent load is 2.0 x 180 x 8.34 = 3,002 lb/day. Effluent load is 1.8 x 30 x 8.34 = 450 lb/day. Removal is (3,002 - 450) / 3,002 = 85 percent.

Exam Traps

Use the concentration-load relationship as a unit audit. A load answer should have mass per time. A concentration answer should have mass per volume. A hydraulic answer such as gpd/ft^2 is not a pollutant load unless a concentration is also included. Before selecting a multiple-choice answer, estimate the order of magnitude. A municipal plant with MGD flow and tens of mg/L concentration should often produce hundreds or thousands of lb/day, not single digits.