FE and PE exam practice, one worked problem a day.
Clear, sourced answers about the FE and PE exams, plus a new practice problem every day with its full solution.
Sample problem · FE, Pipe flow, Darcy-Weisbach
A 12 in. diameter pipe that is 2,050 ft long carries 1,650 gpm of water. The Darcy friction factor for the pipe is 0.033. The head loss due to friction in the pipe is most nearly:
Handbook: Fluid Mechanics, Head Loss Due to Flow (Darcy-Weisbach equation), FE Reference Handbook 10.6
Show the worked solution
- Answer
- A (23.0 ft)
- Given
- Q = 1,650 gpm, D = 12 in., L = 2,050 ft, f = 0.033, g = 32.174 ft/sec² (handbook), 7.481 gal/ft³ (handbook)
- Find
- head loss due to friction, hf (ft)
- Handbook
- Fluid Mechanics, Head Loss Due to Flow (Darcy-Weisbach equation); Units and Conversion Factors (7.481 gal per ft³), pages 3 and 187
- Equation
hf = f(L/D)V²/(2g), with V = Q/A and A = πD²/4- Substitute
Q = (1,650 gal/min)/(7.481 gal/ft³ × 60 sec/min) = 3.676 ft³/secD = 12 in./(12 in./ft) = 1.000 ftA = πD²/4 = π(1.000 ft)²/4 = 0.7854 ft²V = Q/A = (3.676 ft³/sec)/(0.7854 ft²) = 4.680 ft/sechf = f(L/D)V²/(2g) = 0.033 × (2,050 ft/1.000 ft) × (4.680 ft/sec)²/(2 × 32.174 ft/sec²) = 23.0 ft
- Result
- 23.0 ft, 3 significant figures
- Check
- units (ft/ft)(ft/sec)²/(ft/sec²) = ft; V = 4.68 ft/sec is an ordinary velocity for water in a pipe, and the loss is 1.12 ft per 100 ft of pipe.
- Why the others are wrong
- B: used g = 9.807 m/s² in a USCS problem
- C: used the radius instead of the diameter in L/D, which doubles the loss
- D: did not square the velocity
How the lab works
- 6:00 AM Central, every dayA new FE problem posts in the community: the situation, the given values with units, and what to find.
- 6:00 PM Central, the same dayThe full worked solution posts as a reply: the handbook section and page, the equation, the substitution with units, and why each wrong option is wrong.
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How every problem is made
- Software generates each problem from the formulas in the NCEES reference handbooks, with realistic values and units.
- Code solves it again and checks the answer before anything is posted.
- Each wrong option comes from a named mistake, such as a unit slip or the wrong equation, and the solution says which.
- A second AI model checks the wording, and posts written by AI carry a robot mark in the community.
Problems are original. Nothing is copied from NCEES practice exams or paid question banks, and nobody posts content from a real exam.
Start with the facts
- What is the FE exam?Who it is for and where it fits on the path to a P.E. license.
- Which FE exam should you take?Seven disciplines, one shared core, and how to choose.
- Which calculators are allowed?The approved models for 2026 and the rules in the room.
- How to use the FE Reference HandbookSearch the on-screen PDF fast; Ctrl + F does not work.
- FE pass rates by disciplineThe latest NCEES numbers and who they count.
- A 60-day FE study planWeek by week, built on your discipline's specification.
- PE Civil exam formatEighty questions, eight hours, five modules.
- PE Civil design standards in April 2027What changes and what stays the same.
Practice by topic
- Pipe flow head loss (Darcy-Weisbach)Ten problems with full solutions.
- Truss member forcesMethod of joints, tension or compression.
- Clarifier overflow rate and detention timeFill-in problems for FE Environmental.
- Time value of moneyEngineering economics, on every FE exam.
- Effective stressLayered soil profiles with a water table.
- Rational method peak runoffComposite coefficients, U.S. units.
- Ethics and the Model RulesSelect all that apply.
- Free sample setFive problems from five exam areas.
Written by Dr. Mohamed Elansary, PhD Environmental Engineering. Every number on this site comes from NCEES, a state licensing board, or a published price page, with the source and date on the page, or from the problem engine.