Hazen-Williams C Values for Common Pipe Materials

Key Formula / Key Facts Box

Overview — What It Is and Why It Matters

The Hazen‑Williams C value is an empirical, dimension‑less number that characterises the relative smoothness of a pipe’s interior surface when water (at approximately 60 °F or 15.6 °C) flows turbulently. Developed for municipal water distribution, the C value replaces the more fundamental Darcy‑Weisbach friction factor with a single coefficient that captures surface texture, age‑related scaling, and manufacturing tolerances.

Accurate C values are crucial because friction loss typically dominates the total dynamic head (TDH) in low‑pressure, high‑flow water‑service networks. An error of 20 % in C can translate into a comparable error in pump sizing, energy consumption, and compliance with fire‑flow or pressure‑regulation codes.

The Method — Derivation and Variants

The original Hazen‑Williams relationship emerged from extensive laboratory testing of water flowing through a variety of pipe materials. The data showed that, for turbulent flow (Re > 10 000), head loss varied roughly as the 1.852 power of flow rate and the –4.87 power of pipe diameter. By fitting these exponents to the experimental data, the empirical equation was obtained.

US‑customary form:

[h_f = K_{US},frac{L,Q^{1.852}}{C^{1.852} D^{4.87}}] where (K_{US}=10.67).

Metric form:

[h_f = K_{SI},frac{L,Q^{1.852}}{C^{1.852} D^{4.87}}] where (K_{SI}=4.727). The SI constant incorporates unit‑conversion factors between gpm → L/s, inches → mm, and feet → m.

• The exponent 1.852 reflects the nonlinear increase of turbulent loss with flow.
• The exponent 4.87 captures the strong inverse relationship with pipe diameter.
• C is dimensionless; higher values indicate smoother interiors (e.g., new PVC), lower values indicate rougher materials (e.g., aged cast iron).

When water temperature deviates markedly from 60 °F, a temperature correction factor (typically 0.85–1.15) may be applied, but most design work uses the base C value.

Worked Example

Example 1 – US Units (Schedule 40 PVC)

Design a domestic water line that delivers 250 gpm through 300 ft of PVC pipe with an inside diameter of 2.027 in. The manufacturer lists C = 150 for new PVC. Compute the friction loss.

1. Insert values into the US‑customary equation.
2. Calculate each term (using a calculator):
   • (Q^{1.852}=250^{1.852}approx 4.48times10^{3})
   • (C^{1.852}=150^{1.852}approx 1.92times10^{3})
   • (D^{4.87}=2.027^{4.87}approx 35.2)
3. Apply the formula:
   [h_f = 10.67timesfrac{300times4.48times10^{3}}{1.92times10^{3}times35.2}approx 215text{ ft}]

Result: friction loss ≈ 215 ft of water (≈ 655 psi), indicating the need for a larger diameter or reduced flow to meet typical residential pressure limits.

Example 2 – SI Units (Ductile‑Iron)

A municipal branch requires 8 L/s through 150 m of ductile‑iron pipe (ID = 150 mm). New ductile‑iron C = 130. Compute head loss.

1. Insert into the SI form.
2. Calculate:
   • (Q^{1.852}=8^{1.852}approx 55.0)
   • (C^{1.852}=130^{1.852}approx 1.55times10^{3})
   • (D^{4.87}=150^{4.87}approx 1.03times10^{6}) (mm⁴·⁸⁷)
3. Convert diameter to meters for the constant (150 mm = 0.150 m) and apply:
   [h_f = 4.727timesfrac{150times55.0}{1.55times10^{3}times0.150^{4.87}}approx 9.8text{ m}]

Result: friction loss ≈ 9.8 m of water (≈ 32 ft), which is acceptable for most pressure‑regulation schemes.

Calculator

For quick computations, use the online Hazen‑Williams calculator: http://pumpcalcs.com/calculators/hazen-williams.

Reference Values & Typical Ranges

Values are drawn from AWWA M36, ASTM D1785, and industry handbooks. Age‑related reduction is typical after 10‑15 years of service.

Application Guidance

• Use the highest applicable C value for new installations; apply a reduction factor for known scaling or corrosion.
• When designing for fire‑flow, adopt conservative (lower) C values to avoid under‑estimating head loss.
• For long‑run mains (> 500 ft), small errors in C compound; consider a sensitivity analysis.
• Combine Hazen‑Williams with Darcy‑Weisbach for high‑temperature or high‑viscosity fluids where the original empirical basis is invalid.
• Document the source of each C value (manufacturer data sheet, code reference) for future maintenance.

Common Mistakes, Limits & Safety Notes

1. Mixing US and SI units in the same calculation – always keep the constant (10.67 or 4.727) consistent with the unit system.
2. Applying Hazen‑Williams to non‑water fluids or to water far from 60 °F without a temperature correction.
3. Using a single C value for a pipe network that contains multiple materials or varying ages; segment the system.
4. Neglecting minor‑loss coefficients (fittings, valves) which can be comparable to friction loss in short runs.
5. Assuming the Hazen‑Williams equation is valid for laminar flow (Re < 2000); in that regime Darcy‑Weisbach should be used.
6. Over‑reliance on rounded C tables – small differences (e.g., 150 vs 145) can affect pump selection in marginal designs.