FE Civil Practice Question Solution included after investigation
CASE E-048 · FE

The Pipe That Halved Its Diameter and Quadrupled Its Velocity

The diameter fell by half. The velocity did not merely double—it rose from 1.5 to 6.0 m/s.

▶ INTERACTIVE CASE FILE • 5–10 MIN • CLICK TO INVESTIGATE

Inspect, commit, prove, fix, and sign off.

Case E-048 engineering failure visual
HOW THIS WORKS

Think like
a real engineer.

Follow the investigation process used in the field — in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

See the full debrief and key takeaways.

Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

Water flows steadily through a 200 mm diameter pipe at 1.5 m/s and then enters a 100 mm diameter section. A note predicts the downstream velocity is 3.0 m/s because the diameter is halved. Calculate the actual downstream velocity and identify the area-scaling error.

Fluid Mechanics Hydraulics Civil Design Verification Root Cause Analysis Safe Correction
E-048
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
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DEBRIEF (LOCKED)

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Find the root cause, confirm the fix, and see how this connects to the exam.

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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

Velocity was scaled inversely with diameter rather than area.

What was missed

Circular area varies with D squared.

Corrected model

Use A1V1=A2V2 for steady incompressible flow.

QUICK ANSWER

For steady incompressible flow, A1V1=A2V2. Because circular area is proportional to D², reducing diameter from 0.20 m to 0.10 m reduces area by four. Therefore velocity rises from 1.5 m/s to 6.0 m/s.

ENGINEERING TAKEAWAY

For steady incompressible flow, Q=A V. In a circular pipe, A=pi D²/4, so velocity is inversely proportional to D² at fixed Q.

CASE QUESTIONS

Questions this case should settle.

What happens to velocity if pipe diameter is halved at constant flow?

Velocity becomes four times larger.

Why not just use the diameter ratio?

Continuity uses cross-sectional area, and circular area is proportional to diameter squared.

NEXT FE PRACTICE QUESTION

The Channel That Carried 5.69 Cubic Meters per Second

Fluid Mechanics Hydraulics · 5–10 min

Continue Practice →
WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — and beyond.

  • Apply core engineering concepts to real-world problems
  • Practice structured troubleshooting and analysis
  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
Do I need prior knowledge to use these cases?

Basic subject familiarity helps, but every case is designed to teach through the investigation itself.

How long does a case take?

Most cases are designed for a focused 5–10 minute investigation.

Are the cases aligned with engineering exams?

Each case is mapped to a verified exam, subject, topic, and misconception before publication.

What happens after I complete a case?

The sealed debrief unlocks with the root cause, corrected reasoning, fix, and takeaway.