19.1 Flow, Concentration, and Load Workbook
Key Takeaways
- Most WRE calculation misses start with the wrong basis: flow rate, concentration, mass rate, volume, or detention time.
- MGD, gpm, cfs, mg/L, lb/day, ft3, acre-ft, and minutes must be converted before formulas are mixed.
- Load problems should be written as concentration times flow times a conversion factor, with units carried through the setup.
- Treatment and water-quality questions often ask for the missing variable rather than a direct load calculation.
- A quick magnitude check prevents answers that are dimensionally neat but physically impossible.
Start with the basis, not the formula
WRE calculation questions often look different while using the same unit engine. A wastewater plant load, a chlorine dose, a tank volume, a detention time, and a pollutant allocation all require the same first decision: what is being measured? The answer might be a flow rate, concentration, mass rate, volume, surface loading rate, or time. If you identify the basis before opening the reference, the formula usually becomes obvious.
The core conversion map
| Quantity | Common units | Exam action |
|---|---|---|
| Flow | MGD, gpm, cfs, m3/s | Convert before combining with concentration or area |
| Concentration | mg/L, g/m3, lb/MG | Keep as mass per volume until the load step |
| Mass rate | lb/day, kg/day | Use load equations and check time basis |
| Volume | gal, ft3, acre-ft, MG | Match detention time and storage calculations |
| Area | ft2, acres, m2 | Match hydraulic or surface loading units |
| Time | sec, min, hr, day | Convert once and label the basis |
A reliable workbook line is: given -> target -> basis -> conversion -> equation -> magnitude check. For example, if a question gives 2.5 MGD and 30 mg/L BOD and asks for lb/day, do not start by guessing a treatment formula. Write "flow times concentration equals load" and use the appropriate conversion factor for MGD and mg/L. If the question gives a target load and asks for concentration, rearrange the same relationship.
Detention and storage logic
Detention time is volume divided by flow. The trap is that volume and flow often arrive on different time bases. A basin volume in gallons and a flow in MGD can be used directly only after recognizing that MGD means million gallons per day. A channel volume in cubic feet and a flow in cfs gives seconds. A stormwater storage volume in acre-feet and an inflow in cfs requires conversion before time is meaningful.
Surface and hydraulic loading
Surface loading rate is flow divided by surface area, often used in sedimentation or clarification settings. Hydraulic loading can also appear as flow per area. The units reveal the concept: gpd/ft2, m3/m2-day, or similar. If the answer choices are all flows, solve for flow. If they are all areas, rearrange for area. A common distractor uses volume instead of plan area.
Workbook checks
- State whether the answer should increase or decrease when flow increases.
- Keep concentration and load separate until the last line.
- Convert time once; do not switch days to hours mid-equation.
- Ask whether the answer magnitude fits a plant, pipe, or watershed scale.
- Re-read the requested unit before selecting an answer.
This process is slower for one practice problem but faster on the exam. After enough drills, the basis decision becomes automatic and prevents the highest-cost WRE mistake: using a correct equation on the wrong unit system.
Four-row load drill
Use this drill until the setup feels routine. Row 1: convert plant flow to the day basis. Row 2: write concentration as mass per volume. Row 3: multiply flow and concentration with the correct conversion factor. Row 4: compare the result to the requested unit and expected direction. If concentration doubles while flow stays constant, load should double. If flow is cut in half while concentration stays constant, load should be cut in half. This simple proportional check catches many wrong answer choices before detailed arithmetic is finished.
A WRE problem gives flow in MGD and concentration in mg/L, then asks for a pollutant load in lb/day. What is the best first step?
A basin volume is given in cubic feet and flow is given in cfs. What time unit does volume divided by flow produce before conversion?