FE Civil Practice Question Solution included after investigation
CASE E-050 · FE

The Channel That Carried 5.69 Cubic Meters per Second

The flow area alone was not enough. Hydraulic radius and slope set the channel discharge.

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Case E-050 engineering failure visual
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Follow the investigation process used in the field — in five guided steps.

1

Inspect

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2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A rectangular concrete channel is 3 m wide and carries water 1 m deep on a slope of 0.0016. Use Manning n=0.015. A quick calculation substitutes depth y=1 m directly for hydraulic radius and overpredicts discharge. Calculate the correct hydraulic radius and discharge.

Fluid Mechanics Hydraulics Civil Design Verification Root Cause Analysis Safe Correction
E-050
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

Water depth was substituted directly for hydraulic radius.

What was missed

The channel sidewalls contribute to wetted perimeter.

Corrected model

Compute A, wetted perimeter, and R=A/Pw before applying Manning's equation.

QUICK ANSWER

For a 3 m wide, 1 m deep rectangular channel, A=3 m² and wetted perimeter is 5 m, so R=0.6 m. Using n=0.015 and S=0.0016, Manning's equation gives Q≈5.69 m³/s.

ENGINEERING TAKEAWAY

Use the actual hydraulic radius R=A/Pw in Manning's equation Q=(1/n) A R^(2/3) S^(1/2).

CASE QUESTIONS

Questions this case should settle.

What is hydraulic radius for a rectangular channel?

Flow area divided by wetted perimeter, R=A/Pw.

What is Q for b=3 m, y=1 m, n=0.015, S=0.0016?

Approximately 5.69 m³/s.

NEXT FE PRACTICE QUESTION

The Faster Pipe Section That Lost 16 kPa of Pressure

Fluid Mechanics Hydraulics · 5–10 min

Continue Practice →
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