When should I use Hazen-Williams equation?

Use Hazen-Williams for water flow in pipes larger than 2 inches, at normal temperatures (40-75°F), with velocities under 10 ft/s. It's simpler and commonly used for water distribution systems.

When should I use Darcy-Weisbach equation?

Use Darcy-Weisbach for any fluid (not just water), any pipe size, extreme temperatures, or when higher accuracy is needed. It requires calculating the friction factor using Moody diagram or Colebrook equation.

Hazen-Williams vs Darcy-Weisbach: When to Use Each on the PE Exam

One of the most common questions on the PE Civil exam involves pipe flow and head loss calculations. You'll typically have two equations to choose from: Hazen-Williams and Darcy-Weisbach. This guide explains when to use each and provides a decision flowchart for exam day.

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Quick Comparison Table

Feature	Hazen-Williams	Darcy-Weisbach
Fluid Type	Water only	Any fluid
Temperature Range	40-75°F (4-25°C)	Any temperature
Pipe Size	> 2 inches	Any size
Flow Regime	Turbulent only	Laminar or turbulent
Accuracy	Good for water systems	More theoretically rigorous
Complexity	Simple, direct calculation	Requires friction factor lookup
Common Use	Water distribution, fire protection	Chemical plants, research, any fluid

The Equations

Hazen-Williams Equation (US Units)

h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87)

Or for velocity: V = 1.318 × C × R^0.63 × S^0.54

Darcy-Weisbach Equation

h_f = f × (L/D) × (V²/2g)

Where f = friction factor from Moody diagram or Colebrook equation

Decision Flowchart

Which Equation Should I Use?

Is the fluid water?
- No → Use Darcy-Weisbach
- Yes → Continue to step 2
Is the temperature between 40-75°F?
- No → Use Darcy-Weisbach
- Yes → Continue to step 3
Is the pipe larger than 2 inches?
- No → Use Darcy-Weisbach
- Yes → Continue to step 4
Does the problem give you a C value (Hazen-Williams coefficient)?
- Yes → Use Hazen-Williams
- No, but gives roughness (ε) → Use Darcy-Weisbach

Hazen-Williams C Values

Pipe Material	C (new)	C (20 years)
PVC, HDPE	150	140
Ductile Iron (cement lined)	140	130
Cast Iron (cement lined)	130	100
Steel (new)	140	100
Concrete	130	120
Galvanized Iron	120	80

PE Exam Tip: If the problem mentions "fire protection" or "water distribution," it's almost always expecting Hazen-Williams. NFPA standards use C = 120 for design calculations.

Darcy-Weisbach Friction Factor

The challenge with Darcy-Weisbach is finding the friction factor (f). You have three options:

Option 1: Moody Diagram

Look up f based on Reynolds number (Re) and relative roughness (ε/D). The PE reference handbook includes the Moody diagram.

Option 2: Swamee-Jain Equation (Direct Solution)

Swamee-Jain Equation

f = 0.25 / [log₁₀(ε/3.7D + 5.74/Re^0.9)]²

This gives the same result as the Colebrook equation but can be solved directly - perfect for calculators!

Option 3: Laminar Flow (Re < 2000)

Laminar Flow Friction Factor

f = 64 / Re

Worked Example Comparison

Problem: Calculate head loss in 1000 ft of 12-inch ductile iron pipe carrying 2000 gpm of water at 60°F.

Hazen-Williams Solution (C = 140)

Q = 2000 gpm = 4.46 cfs
D = 12 in = 1.0 ft
h_f = 10.67 × 1000 × 4.46^1.852 / (140^1.852 × 1.0^4.87)
h_f = 8.7 ft

Darcy-Weisbach Solution (ε = 0.0004 ft)

V = Q/A = 4.46 / (π × 0.5²) = 5.68 ft/s
Re = VD/ν = 5.68 × 1.0 / (1.21 × 10^-5) = 469,000
ε/D = 0.0004 / 1.0 = 0.0004
From Moody diagram or Swamee-Jain: f ≈ 0.017
h_f = 0.017 × (1000/1.0) × (5.68²/64.4)
h_f = 8.5 ft

Both methods give similar results for this typical water flow scenario, which is why Hazen-Williams is preferred for its simplicity.

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