FE Environmental Water and Wastewater Practice Problems

Work 3 free FE Environmental water and wastewater practice problems with complete solutions, governing equations and checks. Attempt the setup before reading the answer.

Free sample problem

A granular media filter with a $20$ ft by $24$ ft plan area operates at a filtration rate of $4.0$ gpm/ft $^2$ for a $60$ h run, then is backwashed at $18$ gpm/ft $^2$ for $10$ min. The backwash water expressed as a percentage of the water filtered during the run is most nearly:

(A)0.062 %
(B)1.25 %
(C)3.1 %
(D)12.5 %

Show worked solution

Answer: (B)

Backwash consumes about $1.25$ percent of production: the wash rate is 4.5 times the filtration rate, but the run lasts 360 times as long as the wash.

Plan area cancels from both volumes, leaving a ratio of rate times duration in gallons per square foot.

\frac{V_{bw}}{V_f} = \frac{(18)(10)}{(4.0)(60 \times 60)}

Run length in minutes is $3{,}600$ , so $180$ gal/ft $^2$ of wash water stands against $14{,}400$ gal/ft $^2$ filtered.

\frac{180}{14{,}400} = 0.0125 = 1.25\%

FE Reference Handbook — Water and Wastewater: Granular Media Filtration, Filtration and Backwash Rates

Why the other choices appear

(A)Inverts the rate ratio, computing (4.0/18)(10/3,600) = 6.2 x 10⁻⁴ = 0.062%.
(C)Takes the run as 24 h, comparing 86,400 gal of backwash with 2,764,800 gal filtered.
(D)Reads the run length as 6 h, a decimal slip that inflates the ratio tenfold to 12.5%.

Two more free problem types

Try a different setup before reading the solution. These additional original questions are separate from the sold practice forms, so solving them does not reveal another question from a full practice form.

A steady concentration balance before treatment

Two water streams enter a perfectly mixed junction: 2 L/s at 40 mg/L and 3 L/s at 10 mg/L of a conservative dissolved substance. There is no reaction, accumulation, or loss. What is the combined outlet concentration?

(A)10 mg/L
(B)22 mg/L
(C)25 mg/L
(D)40 mg/L

Show worked solution

Answer: (B)

The outlet concentration is 22 mg/L, a flow-weighted average.

Conservative solute mass flow is concentration multiplied by water flow. Sum the inlet solute loads and divide by the total flow.

C_{out}=\frac{Q_1C_1+Q_2C_2}{Q_1+Q_2}=\frac{2(40)+3(10)}{5}=22\ \mathrm{mg/L}

The incoming solute load is 110 mg/s. Five litres per second at 22 mg/L carries exactly 110 mg/s; both flow and solute are conserved.

The result lies between 10 and 40 mg/L. Reaction, evaporation or incomplete mixing would require a different model; none is present in the stated junction.

FE Reference Handbook: Environmental Engineering — steady mass balance and conservative mixing.

Why the other choices appear

(A)This ignores the higher-concentration inlet.
(C)This takes an unweighted arithmetic average despite unequal flows.
(D)This ignores dilution from the second inlet.

A plug-flow removal model and hydraulic time

A plug-flow contactor treats 0.020 cubic metres per second. A dissolved contaminant obeys first-order decay with k = 0.15 per minute. What minimum contactor volume achieves 90% removal under ideal plug-flow conditions?

(A)7.20 m³
(B)12.00 m³
(C)18.42 m³
(D)27.63 m³

Show worked solution

Answer: (C)

The required ideal plug-flow volume is about 18.42 cubic metres.

Ninety percent removal leaves an outlet-to-inlet ratio of 0.10, not 0.90. The ideal plug-flow decay law determines hydraulic residence time.

C_{out}/C_{in}=e^{-k\tau},\qquad \tau=-\ln(0.10)/0.15=15.3506\ \mathrm{min}

Convert flow to 1.2 cubic metres per minute so it matches the decay constant before multiplying by time.

V=Q\tau=(0.020)(60)(15.3506)=18.4207\ \mathrm{m}^3

The volume divided by flow gives 921.03 seconds, or 15.3506 minutes. Substitution gives exp(-0.15 times 15.3506) = 0.10. A completely mixed reactor would require a different volume formula.

FE Reference Handbook: Environmental Engineering — first-order kinetics and ideal plug-flow residence time.

Why the other choices appear

(A)This uses a different residence time without solving the logarithmic relation.
(B)This assumes ten minutes without enforcing 90% removal.
(D)This adds an unsupported safety multiplier to the ideal model.

Download all 14 additional questions, diagrams and complete solutions (free PDF). Download the editable practice review sheet (CSV).

Original questions and diagrams by EngineerProof, September 30, 2026. Personal study and unchanged redistribution with attribution are permitted. The questions are independent practice, not official NCEES material. Report a correction.

The complete FE Environmental practice exam contains 14 problems in this area and 110 problems overall, with an answer key, full solutions, and a score sheet by knowledge area.

Free FE Environmental problems in the other knowledge areas

Mathematics · Probability and Statistics · Ethics and Professional Practice · Engineering Economics · Fundamental Principles · Environmental Chemistry · Health Hazards and Risk Assessment · Fluid Mechanics and Hydraulics · Thermodynamics · Surface Water Resources and Hydrology · Groundwater, Soils, and Sediments · Air Quality and Control · Solid and Hazardous Waste · Energy and Environment

Retaking the FE exam? The FE Environmental retake plan turns the NCEES diagnostic report into an area-by-area plan, starting from the 37 percent repeat pass rate. The same guide covers testing windows, the attempt limit, and the registration fee.