Engineer Exam Lab Start free trial
Menu

Independent study resource, not affiliated with NCEES, Pearson VUE, or any state licensing board. You register for the exams and pay their fees only at ncees.org. This site collects no logins and offers no downloads.

FE daily problem for October 4, 2026 (Pipe flow, Darcy-Weisbach)

By Dr. Mohamed Elansary, PhD Environmental EngineeringUpdated

This is the FE practice problem that Engineer Exam Lab members worked on October 4, 2026. The topic is pipe flow, Darcy-Weisbach, from the FE exam specification. Try it with the FE Reference Handbook open before you read on. The worked solution below gives the handbook section and page, the equation, every substitution with units, a size check, and the mistake behind each wrong answer.

The problem

Daily problem · FE, Pipe flow, Darcy-Weisbach

Water flows at 0.0145 m³/s through a 100 mm diameter pipe that is 920 m long. The Darcy friction factor for the pipe is 0.032. The head loss due to friction over the pipe length is most nearly:

  • A 15.6 m
  • B 3.20 m
  • C 27.7 m
  • D 51.2 m

Handbook: Fluid Mechanics, Head Loss Due to Flow (Darcy-Weisbach equation), FE Reference Handbook 10.6

Commit to an answer before you scroll. Writing the given values with their units first is the fastest way to spot what the question really asks for.

Worked solution, step by step

  • Answer: D (51.2 m)
  • Given: Q = 0.0145 m³/s, D = 100 mm, L = 920 m, f = 0.032, g = 9.807 m/s² (handbook)
  • Find: head loss due to friction, hf (m)
  • Handbook: Fluid Mechanics, Head Loss Due to Flow (Darcy-Weisbach equation), page 187
  • Equation: hf = f(L/D)V²/(2g), with V = Q/A and A = πD²/4

Substitute, keeping the units on every value:

  1. D = 100 mm = 0.100 m
  2. A = πD²/4 = π(0.100 m)²/4 = 0.007854 m²
  3. V = Q/A = (0.0145 m³/s)/(0.007854 m²) = 1.846 m/s
  4. hf = f(L/D)V²/(2g) = 0.032 × (920 m/0.100 m) × (1.846 m/s)²/(2 × 9.807 m/s²) = 51.2 m

Result: 51.2 m, 3 significant figures.

Check: Units (m/m)(m/s)²/(m/s²) = m; V = 1.85 m/s is an ordinary velocity for water in a pipe, and the loss is 55.6 m per 1,000 m of pipe.

Why each wrong option is wrong

Every wrong option on this problem comes from a named mistake, so a wrong pick tells you exactly what to fix:

  • A (15.6 m): used g = 32.174 ft/sec² in an SI problem.
  • B (3.20 m): used A = πD² without the 1/4, so V is 4 times too small and the loss is 16 times too small.
  • C (27.7 m): did not square the velocity.

Where this is in the FE Reference Handbook

This problem uses Fluid Mechanics, Head Loss Due to Flow (Darcy-Weisbach equation), page 187 of FE Reference Handbook 10.6. The handbook is a free PDF in MyNCEES, and on exam day you search the same document on screen, so practice finding the section with the search box instead of from memory. Search for the name of the quantity you need, not the symbol, and check the page heading before you copy an equation.

How to approach problems like this

Work the number out before you look at the options. The wrong options are built from real mistakes, so a value that matches one of them proves nothing on its own. Write the given values with units, find the equation in the handbook with the search box, and substitute with the units attached. When your result lands on an option, run a quick size check: is the magnitude reasonable for the situation, and do the units reduce to what the question asks for? If your result falls between two options, look for a unit conversion you skipped.

Whatever the result, log it. A short error log with one line per missed problem (the topic, the mistake named in the solution, and the handbook page) shows within a few weeks which habits cost you points, and it turns review time into targeted practice instead of rereading.

For ten more problems on this topic, each with a full solution, see the pipe flow, Darcy-Weisbach practice set. Every past daily problem is in the daily problem archive, one page per day.

Frequently asked questions

Is this a real FE exam question?

No. It is an original problem that our problem engine generated from the formulas in the FE Reference Handbook and checked by code before it was posted. Real exam questions are confidential, and the agreement every examinee accepts forbids sharing them.

Why does this problem appear here a day late?

Members of Engineer Exam Lab get each problem first, in the morning, and the worked solution the same evening. The problem and its solution come to this public archive the next day.

How should I use the worked solution?

Compare your work with it line by line, not only the final answer. If you picked a wrong answer, find the note that matches it above; each one names the exact mistake, which is the habit to fix before exam day.

Sources

  1. NCEES FE Reference Handbook 10.6 (free PDF in MyNCEES). Retrieved October 3, 2026.
  2. NCEES FE Civil CBT exam specifications (PDF). Retrieved October 3, 2026.
  3. NCEES FE Environmental CBT exam specifications (PDF). Retrieved October 3, 2026.