4.2 Analysis and Design Workflow
Key Takeaways
- Analysis and Design is a 6-9 question NCEES area covering mass balance, hydraulic loading, solids loading, and flow measurement.
- Blended concentration is a flow-weighted average, Cmix = sum(QC)/sum(Q), never an arithmetic average of concentrations.
- Pounds per day = flow(mgd) x concentration(mg/L) x 8.34; the 8.34 factor cancels when the answer is a concentration.
- Hydraulic loading rate is Q/A (gpd/ft^2) while detention time is V/Q; depth separates two basins with the same overflow rate.
- Flow-measurement answers hinge on whether field conditions (submergence, calibration range, approach flow) satisfy the device's assumptions.
Analysis and Design Workflow
The NCEES specification gives Analysis and Design a 6-9 question range and names four tools: mass balance, hydraulic loading, solids loading, and hydraulic flow measurement. These are the accounting tools behind water treatment, wastewater treatment, stormwater facilities, sludge handling, groundwater remediation, and distribution systems. The exam routinely hides a one-line calculation inside a paragraph of process context, so a disciplined setup beats fast arithmetic.
The Four-Step Setup
Run the same workflow before touching the calculator:
- Draw the boundary. Mark every inflow, outflow, sidestream, recycle line, bypass, storage term, and loss.
- Name the target. Decide whether the question wants a concentration, a flow, a mass per time, a surface loading, a volume, a detention time, or a meter reading.
- Convert units. Put flow, concentration, area, volume, and time on one consistent basis before comparing answer choices.
- Check reasonableness. A blended concentration must fall between the contributing concentrations unless a reaction, removal step, or chemical addition is present.
Core Relationships
| Task | Setup | What to watch |
|---|---|---|
| Conservative mass balance | mass in = mass out (steady state) | Include every stream crossing the boundary |
| Blending concentration | Cmix = sum(QC) / sum(Q) | Flow-weighted, not arithmetic mean |
| Mass loading | lb/day = Q(mgd) x C(mg/L) x 8.34 | The 8.34 lb/Mgal-per-(mg/L) factor |
| Hydraulic loading (overflow) | HLR = Q / A surface | Use plan area for clarifiers, media area for filters |
| Detention time | t = V / Q | Convert volume and flow to matching time units |
| Solids loading (flux) | mass rate / area | lb/day-ft^2 for thickeners/clarifiers |
| Flow measurement | device equation or rating | Submergence, calibration, location |
Mass Balance
A mass balance is only as good as its boundary. For a conservative constituent at steady state with no reaction, removal, or generation, mass entering equals mass leaving. In WRE problems the constituent may be nitrate, total suspended solids (TSS), biochemical oxygen demand (BOD), hardness, chlorine, sludge solids, or sediment.
For blending, compute each stream's mass rate and divide by total mixed flow. When the problem gives mgd and mg/L and asks for lb/day, use load = Q x C x 8.34, where 8.34 lb/gal is the weight of water. If the requested answer is a concentration, the 8.34 cancels as long as all flows share a volume-time basis. Worked check: 2.0 mgd at 30 mg/L BOD carries 2.0 x 30 x 8.34 = 500 lb/day of BOD.
Recycle streams deserve care. A sidestream return from sludge dewatering or filter backwash can carry a large pollutant mass even at small flow. If that stream crosses the control volume, include it; if it recirculates entirely inside the boundary, do not double-count it. This single mistake produces the most common distractor in blending problems.
Hydraulic and Solids Loading
Hydraulic loading rate (HLR), also called surface overflow rate for settling basins, is flow per unit plan area, Q/A, expressed in gpd/ft^2. It governs clarifiers, sand filters, infiltration basins, and rapid-mix units. Typical design anchors worth recognizing: primary clarifier overflow rates near 800-1,200 gpd/ft^2 at average flow, and rapid sand filters near 2-3 gpm/ft^2.
Detention time, t = V/Q, depends on depth as well as area, so a shallow basin and a deep basin can share the same overflow rate yet differ in detention time. A clarifier sized only by overflow rate may still fail a detention-time criterion, and vice versa, so read which one the question demands.
Solids loading adds concentration to the picture. A secondary clarifier is checked for both overflow rate and solids flux (lb/day-ft^2); a gravity thickener is checked in lb/day-ft^2; an activated-sludge process is checked against solids retention time and mass wasting. Always write the requested loading unit first, because the unit tells you which denominator (area or volume) belongs in the calculation.
| Process unit | Loading metric | Typical units |
|---|---|---|
| Primary/secondary clarifier | Overflow rate | gpd/ft^2 |
| Secondary clarifier | Solids flux | lb/day-ft^2 |
| Gravity thickener | Solids loading | lb/day-ft^2 |
| Trickling filter | Organic loading | lb BOD/day per 1,000 ft^3 |
| Sand filter | Filtration rate | gpm/ft^2 |
Flow Measurement
Hydraulic flow measurement converts a field signal into discharge. Weirs and Parshall flumes relate head to flow (e.g., a rectangular weir follows Q proportional to H^1.5). Meters read velocity (propeller), pressure differential (venturi, orifice), magnetic response (no head loss, needs conductive fluid), or transit time (ultrasonic). Rating curves relate stage to discharge at a specific station and become invalid after channel change or scour.
On the PE exam the decisive question is rarely the meter brand; it is whether the field condition satisfies the method's assumptions. A flume drowned by downstream submergence, a weir without a proper approach (low velocity of approach, full nappe ventilation), a meter operated outside its calibrated range, or a rating curve used after a flood reshaped the channel will all report misleading flow. When answer choices mix calculation and judgment, choose the option that protects the measurement basis before trusting the number.
Common trap: applying the free-flow flume equation when the problem states the tailwater is high enough to submerge the throat.
A process stream of 3.5 mgd at 24 mg/L total suspended solids is mixed with a recycle stream of 0.7 mgd at 180 mg/L. If no solids are removed or generated during mixing, what is the mixed concentration?
Two clarifiers carry the same surface overflow rate, but Basin A is 8 ft deep and Basin B is 16 ft deep over equal plan areas and flow. Which statement is correct?