Hazen Williams Water

Overview

The Hazen-Williams equation is an empirical formula widely used in civil and plumbing engineering to estimate frictional head loss for water flowing in pressurized pipes. It offers a simpler alternative to the Darcy-Weisbach equation because it avoids iterative calculations, though at the cost of reduced accuracy and a narrower range of valid conditions.

The Darcy-Weisbach equation combined with the Moody diagram remains the most rigorous model for pipe friction loss. The Hazen-Williams method is preferred when quick estimates are needed for water distribution systems operating under typical conditions.

Key Formulas

The Hazen-Williams equation for head loss per 100 feet of pipe:

$h_{100ft} = 0.2083 \left(\frac{100}{C}\right)^{1.852} \frac{q^{1.852}}{d^{4.8655}}$

For SI units, the equivalent form gives head loss per 100 meters of pipe:

$h_{100m} = 10.67 \left(\frac{1}{C}\right)^{1.852} \frac{Q^{1.852}}{d^{4.8704}}$

Head loss for an arbitrary pipe length scales linearly:

$h_L = h_{100ft} \times \frac{L}{100}$

Flow velocity from volumetric flow rate and pipe inner diameter:

$v = \frac{0.4087 \cdot q}{d^2}$

Variables

Roughness Coefficient (C Values)

The roughness coefficient $C$ depends on pipe material and condition. Higher values indicate smoother interiors and lower friction losses.

Flow Velocity Chart

The relationship between flow rate, pipe diameter, and velocity is critical for sizing. Excessive velocity causes noise, erosion, and increased head loss; too-low velocity risks sediment buildup.

Common design guidelines suggest keeping water velocity between 2 and 8 ft/s in distribution piping.

Calculator

Unit Converter

Example Calculation

Given:

• Flow rate: $q = 200 \text{ gal/min}$
• Pipe: 3-inch PEH pipe DR 15, inside diameter $d = 3.048 \text{ in}$
• Roughness coefficient: $C = 140$
• Pipe length: $L = 30 \text{ ft}$

Step 1 — Head loss per 100 ft:

$h_{100ft} = 0.2083 \left(\frac{100}{140}\right)^{1.852} \frac{200^{1.852}}{3.048^{4.8655}} \approx 9.0 \text{ ft H}_2\text{O / 100 ft}$

Step 2 — Actual head loss for 30 ft:

$h_{30ft} = 9.0 \times \frac{30}{100} = 2.7 \text{ ft H}_2\text{O}$

Step 3 — Flow velocity:

$v = \frac{0.4087 \times 200}{3.048^2} \approx 8.82 \text{ ft/s}$

This velocity exceeds typical guidelines (2–8 ft/s), suggesting a larger pipe diameter may be warranted to reduce noise and erosion risk.

Design Notes

• Empirical limitation: The Hazen-Williams equation lacks a theoretical basis. Roughness coefficients are derived from experiments at velocities near 1 m/s (≈3 ft/s) and may not extrapolate well outside that range.
• Reynolds number: The equation is relatively accurate only when $Re > 10^5$, corresponding to fully turbulent flow.
• Temperature range: Validated for water at 40–75°F (5–25°C) with kinematic viscosity ≈ 1.1 cSt. At 130°F (54.4°C) where ν ≈ 0.55 cSt, predicted head loss can be significantly in error.
• Water only: This method applies exclusively to water. For other liquids or gases, use the Darcy-Weisbach equation.
• Pipe aging: C values decrease with age due to corrosion, tuberculation, and biological growth. Design with a conservative (lower) C to account for service degradation.
• Alternative for open channels: Manning's formula is the standard empirical method for gravity-driven flow in open channels, not Hazen-Williams.

Limitations

The Hazen-Williams equation is empirical and should be used only for water in ordinary distribution temperature ranges. It is not suitable for other liquids, gases, laminar flow, transitional flow, very hot water, or systems where viscosity changes strongly. For general fluid mechanics calculations, use the Darcy-Weisbach equation with a friction factor from the Colebrook equation or Moody diagram.

Related Mobile Apps from The Engineering ToolBox

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Unit Conversions

Restored Original Source Tables

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References

• Hazen-Williams Water — Engineering ToolBox