Hazen-Williams vs. Darcy-Weisbach: Which Should You Choose?

When it comes to designing and evaluating fluid flow in pipes, the Hazen-Williams and Darcy-Weisbach equations are essential tools for engineers. Both equations allow you to calculate pressure drop from friction in pipes, a crucial part of plumbing and HVAC system design.

Read on for an in-depth breakdown of Hazen-Williams vs. Darcy-Weisbach, encompassing their respective advantages and disadvantages, to help you determine which equation is most suitable for your project.

Hazen-Williams Equation

Commonly used for water flow through pipes, the Hazen-Williams equation is as follows:

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

Note: the constant 10.67 only applies to metric units. For imperial units, use a constant of 4.73:

hf = (4.73 × L × Q^1.852) / (C^1.852 × D^4.87)

Where:

• h_f is the head loss due to friction (m/ft)
• L is the pipe length (m/ft)
• Q is the flow rate (m³/s/ft³/s)
• C is the Hazen-Williams coefficient (dimensionless)
• D is the internal pipe diameter (m/ft)

Hazen-Williams Roughness Coefficient

The Hazen-Williams roughness coefficient (C) represents the relative roughness of the interior surface of a pipe.

It is a dimensionless empirical value used in the Hazen-Williams equation to account for the effect of pipe material on flow resistance.

Higher values of the Hazen-Williams coefficient indicate pipes with smoother interior surfaces, which in turn generally indicate lower head loss.

Here are some common Hazen-Williams roughness coefficients for various pipe materials:

Hazen-Williams Equation: Advantages and Disadvantages

The advantages of the Hazen-Williams formula are:

• Simplicity: The Hazen-Williams equation is easier to use than the Darcy-Weisbach equation, as it doesn’t require iterative calculations.
• Ease: This formula estimates friction loss in a pipeline with just a few parameters.

The disadvantages of the Hazen-Williams formula are:

• Limited use: This equation is only applicable to water flow and cannot be used for other fluids.
• Lower accuracy in some scenarios: It is less accurate for larger pipes and higher flow velocities.

Darcy-Weisbach Equation

The Darcy-Weisbach equation is a more versatile and accurate method for calculating head loss due to friction in fluid flow.

The equation is as follows:

hf = (f × L × V^2) / (2 × g × D)

Where:

• h_f is the head loss due to friction (m/ft)
• f is the Darcy friction factor (dimensionless)
• L is the pipe length (m/ft)
• V is the flow velocity (m/s / ft/s)
• g is the earth’s gravitational acceleration (9.81 m/s² / 32.2 ft/s²)
• D is the internal pipe diameter (m/ft)

Darcy-Weisbach Equation: Advantages and Disadvantages

The advantages of the Darcy-Weisbach formula are:

• Versatility: The Darcy-Weisbach equation can be used for various fluids, not just water.
• Accuracy: It provides more accurate results for a wide range of pipe sizes and flow velocities.

The disadvantages of the Darcy-Weisbach formula are:

• Complexity: The equation is more complex, requiring iterative calculations and additional parameters.
• Friction Factor: The user must determine the Darcy friction factor, which can be challenging to estimate accurately.

Hazen-Williams vs. Darcy-Weisbach: Comparison

Accuracy

While the Hazen-Williams equation is more straightforward, it sacrifices accuracy, especially for larger pipes, higher flow velocities, and a range of temperatures.

The Darcy-Weisbach equation offers higher accuracy across a broader range of applications.

Range of Applications

The Hazen-Williams equation is limited, while the Darcy-Weisbach equation can be applied to various scenarios, making it more versatile and suitable for a wide range of industries and applications.

Ease of Use

The Hazen-Williams equation is easier to use due to its simplicity and fewer required parameters.

However, the Darcy-Weisbach equation, while more complex, provides more accurate and comprehensive results.

Hazen-Williams vs. Darcy-Weisbach: Calculation Example

Let’s perform a comparison calculation for the Hazen-Williams and Darcy-Weisbach equations using the following parameters:

• Flow Rate (Q): 0.05 cubic meters per second (m³/s)(1.77 ft³/s / 793 US gpm)
• Pipe Material: Copper
• Hazen-Williams Coefficient (C): 140
• Darcy-Weisbach Coefficient (ε): 0.0015 mm (5.9 × 10⁻⁵ in / 4.92 × 10⁻⁶ ft)
• Pipe Length (L): 500 meters (1,640 ft)
• Internal Pipe Diameter (D): 0.15 meters/150 mm (0.492 ft / 5.91 in)
• Fluid temperature: 20°C (68°F)
• Fluid density (ρ): 1000 kg/m³ (62.4 lb/ft³)
• Dynamic viscosity (μ): 1.004 × 10⁻³ Pa·s (2.10 × 10⁻⁵ lbf·s/ft²)

Hazen-Williams Formula

• hf = (10.67 × L × Q^1.852) / (C^1.852 × D^4.87)
• hf = (10.67 × 500 × (0.05)^1.852) / (140^1.852 × (0.15)^4.87)
• hf ≈ 23.12 meters head (≈ 75.85 ft)

Darcy-Weisbach Formula

First, we need to calculate the velocity:

• A = π × (D / 2)^2
• A = π × (0.15 / 2)^2 ≈ 0.0177 m² (≈ 0.190 ft²)
• V = Q / A
• V = 0.05 / 0.0177 ≈ 2.82 m/s (≈ 9.25 ft/s)

Next, we need to calculate the Reynolds Number (Re):

• Re = (ρ × V × D) / μ
• Re = (1000 × 2.82 × 0.15) / (1.004 × 10^-3)
• Re ≈ 419566

And we also need to know the Friction Factor (f):

• 1 / √f = -2 × log10((ε / (3.7 × D)) + (2.51 × (ν × √f) / (D × V)))
• 1 / √f = -2 × log10((1.5 × 10^-6) / (3.7 × 0.15) + (2.51 × (1.004 × 10^-6 × √f) / (0.15 × 2.82)))
• Imperial: ε ≈ 4.92 × 10⁻⁶ ft; ν ≈ 1.08 × 10⁻⁵ ft²/s
• Following an iterative process, we find that f ≈ 0.0137

Now we can undertake the Darcy-Weisbach Equation:

• hf = (f × L × V^2) / (2 × g × D)
• hf = (0.0137 × 500 × (2.82)^2) / (2 × 9.81 × 0.15)
• hf ≈ 17.47 meters (≈ 57.32 ft)

As you can see from the above examples, the Darcy Weisbach calculation is more detailed but requires more steps.

Hazen-Williams vs. Darcy-Weisbach: Choosing the Right Equation for Your Needs

When deciding between the Hazen-Williams and Darcy-Weisbach equations, consider the following factors:

• Accuracy: For higher accuracy, especially in larger pipes and high flow velocities, the Darcy-Weisbach equation is the better choice.
• Ease of Use: If simplicity and ease of use are more critical for your application, the Hazen-Williams equation may be preferred.

The two formulas above are for pressure drop through pipes. For the pressure drop through valves, feel free to read our blog on Flow Coefficient.

Hazen-Williams vs. Darcy-Weisbach: Conclusion

Both the Hazen-Williams and Darcy-Weisbach equations have their merits and limitations. The Hazen-Williams equation is simpler and easier to use, but is limited in scope and accuracy. The Darcy-Weisbach equation is more versatile and accurate, but requires more complex calculations.

Ultimately, the choice between the two methods depends on the specific requirements or stage of your project, including fluid type and desired level of accuracy.

See Pipe Sizing Calculations in Action

Want to see how friction loss, flow rates, velocities, pressures, and pipe sizing calculations work in a real design workflow?

Watch the short h2x video below to see how our software helps engineers complete pipework calculations faster and with greater accuracy.

 

 

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The software automatically calculates flow rates, velocities, pressures, pump duties, plant sizing, and recirculation systems, so you can spend less time on manual calculations and more time refining your design.

With a straightforward user interface, h2x helps engineers produce high-quality designs more efficiently while staying aligned with industry regulations and project requirements.

h2x has already been used to size pipework on thousands of projects around the world.

Book a demo today to see how h2x can improve your design and calculation workflow.

Hazen-Williams vs. Darcy-Weisbach FAQs

Is the Darcy-Weisbach equation suitable for all pipe materials?

Yes, the Darcy-Weisbach equation can be used for all pipe materials, as long as the appropriate friction factor is determined.

How do I determine the Darcy friction factor?

The Darcy friction factor can be determined using various methods, such as the Moody chart, Colebrook-White equation, or Swamee-Jain equation. Try our free pressure drop calculator which will calculate the friction factor for you.

Why is the Hazen-Williams equation less accurate for larger pipes?

The Hazen-Williams equation becomes less accurate for larger pipes due to its empirical nature and simplifications made during its development.

Which equation is more widely used in industry?

Both equations are widely used in their respective fields.