Free water-resources theory for the FE Civil and PE Civil (WR&E) exams
Ten guided modules that move from FE fundamentals to PE design-level analysis. Formulas are defined, examples show every step, and exam traps are separated by level. Mapped to the current NCEES FE Civil and PE Civil: Water Resources and Environmental specifications.
How this works
Learn the theory — free
Start with the blue FE foundation material, then move into the amber PE-depth sections for design judgement, multi-step analysis, and system behaviour.
Watch for the traps
Every topic identifies unit traps, modelling assumptions, and the point where an FE calculation becomes a PE design or interpretation question.
Try a full exam simulation — paid
When the theory feels solid, step up from the free topic tasters to a full timed exam simulation with worked solutions.
Current NCEES exam blueprint
This hub follows the official topic names and question ranges currently published by NCEES. The FE Civil specification is effective July 2020. The PE Civil: Water Resources and Environmental specification is effective April 2024 and applies before April 2027.
Water-related FE areas
- Fluid Mechanics 4–6 questions
- Hydraulics and Hydrologic Systems 8–12
- Environmental Engineering 6–9
Expect concise handbook-based calculations across a 110-question breadth exam.
Discipline-specific PE areas
- Hydraulics—Closed Conduit 7–11
- Hydraulics—Open Channel 7–11
- Hydrology 8–12
- Groundwater and Wells 4–6
- Surface Water and Groundwater Quality 5–8
- Drinking Water Distribution and Treatment 6–9
- Wastewater Collection and Treatment 7–11
The April 2024 PE exam has no common breadth block: all 80 questions are WRE-specific. Analysis and Design, Project Planning, Soil Mechanics, Materials, and Project Sitework are also tested; Project Sitework carries 9–14 questions.
Official specifications: FE Civil (effective July 2020) · PE Civil: WRE (effective April 2024, before April 2027). Always check the NCEES site for later revisions.
Ten water-focused learning modules
Fluid Properties & Hydrostatics
Fluid properties, pressure, hydrostatic forces, and the fluid-mechanics assumptions that support both exams.
Topic 2Buoyancy & Flotation
Archimedes’ principle and stability — core fluid-statics reasoning before closed-conduit analysis.
Topic 3Continuity, Energy & Momentum
Continuity, Bernoulli, momentum, flow measurement, and control-volume reasoning.
Topic 4Pipe Flow
Darcy-Weisbach, Hazen-Williams, minor losses, pipe networks, force mains, and wet wells.
Topic 5Pumps & System Curves
Operating point, affinity laws, power, NPSH, distribution demand, storage, and pump operation.
Topic 6Open-Channel Flow
Manning flow, critical depth, hydraulic jumps, culvert control, and stormwater conveyance.
Topic 7Hydrology & Runoff
IDF interpretation, Rational and NRCS runoff, hydrographs, detention, and reservoir routing.
Topic 8Groundwater Flow
Darcy flow, aquifers, steady and transient well drawdown, and contaminant travel velocity.
Topic 9Water Treatment
Mass balance, quality indicators, distribution, coagulation, sedimentation, filtration, and disinfection.
Topic 10Wastewater Treatment
Collection hydraulics, I/I, BOD, activated sludge, nutrients, solids, and clarifier loading.
In a hurry? The formula quick-reference index collects every key equation from all ten topics on one page, each with its variables defined.
Free interactive calculators
Check your hand calculations against these browser-based tools — no account, no download. Each one shows the governing equation so you can see exactly what it is doing.
Manning's Equation
Open-channel discharge for rectangular, trapezoidal, and full circular sections — SI and US units.
CalculatorHazen-Williams Head Loss
Velocity, discharge, and friction loss for water pipes from diameter, C-factor, and slope.
CalculatorRational Method Runoff
Peak runoff rate from runoff coefficient, rainfall intensity, and drainage area.
CalculatorPump Operating Point
Where the pump curve meets the system curve — solve for flow and head with an adjustable sample pump.
Take these formulas with you — free
The essential water resources equations from this page, condensed into a 2-page printable cheat sheet. Free — just enter your email to download.
Ready for the full rehearsal?
$79 one-time
The FE Civil Full-Length Practice Exam is a 110-question timed simulation covering every FE Civil section — water resources included — with detailed worked solutions for every question. Here is the flavour of one water-resources question:
Sample question Open-channel flow
A rectangular concrete channel 2.0 m wide carries a normal depth of 0.80 m on a bed slope of 0.001. Take Manning's n = 0.013. The discharge is closest to:
- 1.4 m³/s
- 2.3 m³/s
- 3.1 m³/s
- 4.0 m³/s
Answer: B. A = 1.60 m², P = 3.60 m, R = 0.444 m. V = (1/0.013)(0.444)2/3(0.001)1/2 = 1.42 m/s, so Q = VA ≈ 2.27 m³/s.
109 more questions like it — fluids, hydraulics, hydrology, groundwater, treatment, and every other FE Civil section — each with a full step-by-step solution.
Frequently asked questions
What is the difference between the FE Civil and PE Civil water-resources topics?
The FE Civil exam is a breadth exam: water appears in three of its seventeen areas — Fluid Mechanics (4–6 questions), Hydraulics and Hydrologic Systems (8–12), and Environmental Engineering (6–9). The PE Civil: Water Resources and Environmental exam is a depth exam with no breadth block since April 2024: eight of its twelve areas are water-specific (closed-conduit and open-channel hydraulics, hydrology, groundwater, water quality, drinking water, wastewater), at professional analysis-and-design depth.
How should I use this site to study?
Work through the ten theory modules in order — each builds on the last. Use the formula index for revision, the free mini-quizzes on each topic page to check understanding, and the calculators to verify your hand calculations. When the theory feels solid, move to timed practice quizzes under exam conditions.
What is free and what is paid?
All theory modules, the formula index, the calculators, and the topic mini-quizzes are free — no account needed. The paid products are full-length timed practice exams and quizzes with detailed worked solutions, sold through our Gumroad store.
Which NCEES specifications does the site follow?
The FE Civil specification effective July 2020 (still the current version) and the PE Civil: Water Resources and Environmental specification effective April 2024 — the version NCEES lists as applying before April 2027. Specifications change, so always confirm against the current documents on ncees.org.
Can I use the calculators instead of hand calculations on the exam?
No — the calculators are study and checking tools. On the exam you will work by hand with the NCEES reference handbook, so practise the manual methods here and use the calculators to confirm your arithmetic and build intuition for how each variable affects the answer.
Is this site affiliated with NCEES?
No. Water Resources Hub is an independent study aid. It is not affiliated with, sponsored by, or endorsed by NCEES, and it is not a substitute for professional engineering judgement.
Who runs Water Resources Hub?
Water Resources Hub is published by Katharine, also known as The Engineered Life — see the About page for more.
Who this is for
FE Civil candidates: use Topics 1–3 as Fluid Mechanics foundations, then study the FE-level portions of Topics 4–10 for Hydraulics and Hydrologic Systems and Environmental Engineering.
PE Civil: Water Resources and Environmental candidates: concentrate on the amber PE-depth sections. The modules use the current NCEES area names and extend the FE equations into networks, routing, collection, treatment, and design interpretation.
This water-focused hub does not replace preparation for the PE areas Project Planning, Soil Mechanics, Materials, Analysis and Design, and Project Sitework. Formulas state units and assumptions plainly; candidates should verify all procedures against the reference handbook and design standards supplied for their exam appointment.