Hazen-Williams Calculator

Estimate head loss, flow rate, or required pipe diameter for pressurized water flow in full pipes using the Hazen–Williams equation with common metric and U.S. units.

Configuration

Choose what you want to solve for. The Hazen–Williams equation is typically applied to pressurized water flowing full in a pipe.

Pipe & Flow Properties

Enter basic pipe geometry, length, roughness coefficient, and either flow rate or head loss. The calculator converts all values to a consistent internal system before applying the Hazen–Williams equation.

Results Summary

The main result is shown below, with quick stats for head loss, velocity, hydraulic gradient, and equivalent pressure drop.

Pressurized Pipe Flow Guide

Hazen-Williams Calculator: Flow, Velocity & Head Loss

A practical, code-aware walkthrough of how to use a Hazen-Williams Calculator to size water pipes, estimate head loss, and interpret velocity and pressure drop so your designs stay realistic and buildable.

8–12 min read Updated 2025 Potable & fire water systems

Quick Start: Using the Hazen-Williams Calculator Safely

The Hazen-Williams equation is an empirical formula for head loss in full, pressurized water pipes. It is very convenient for potable and fire-water systems, but only if you respect its limits. Use this section as a checklist whenever you plug values into the calculator.

  1. 1 Confirm that you are dealing with pressurized water at normal temperatures (roughly 5–25 °C / 40–80 °F) in a pipe that is intended to run completely full.
  2. 2 Choose the solve mode in the Hazen-Williams Calculator: head loss / pressure drop, allowable flow, or required diameter, depending on your design question.
  3. 3 Enter the pipe length and diameter using a consistent unit system (all SI or all US customary). If your calculator supports multiple units, pick the ones that match your drawings (e.g., mm & m, or in & ft).
  4. 4 Select a realistic Hazen-Williams roughness coefficient \(C\). Smooth plastic (PVC/HDPE) might be \(C \approx 140\text{–}150\), new ductile iron \(C \approx 120\text{–}140\), and older corroded steel significantly lower.
  5. 5 Enter the flow rate (or the target head loss / allowable pressure drop) and run the calculation. Check that the resulting velocity is within your design range (often 0.6–3 m/s or 2–10 ft/s, depending on application and local standards).
  6. 6 Review the calculator’s quick stats (friction slope, velocity, head loss per 100 m or 100 ft). Compare them against your design criteria, e.g. maximum head loss per kilometre or per 100 ft, or fire-protection code limits.
  7. 7 Apply a sanity check: if the numbers look unusual compared to similar projects (for example, velocities higher than 5 m/s in a distribution main), re-check your units, pipe diameter, and \(C\) value before finalizing.

Fast workflow: start with your preferred diameter, check velocity and head loss, then iterate diameter until both are acceptable. The Hazen-Williams Calculator makes that iteration painless.

Important limitation: Hazen-Williams is only valid for water-like fluids in turbulent flow. Do not use it for oils, chemicals, high-viscosity liquids, or laminar regimes — use Darcy–Weisbach instead.

Choosing Your Method: What Are You Solving For?

In practice, engineers use the Hazen-Williams equation in three main ways. Your calculator is structured around these typical questions, so picking the right mode keeps the workflow simple and the outputs meaningful.

Method A — Check Head Loss in an Existing Line

“Given the flow, pipe size, material, and length, how much head do I lose?”

  • Ideal when the pipe size and material are fixed (retrofits, existing networks).
  • Useful for verifying that a pump or reservoir can still deliver the required pressure.
  • Pairs nicely with field tests (static vs. residual pressure at hydrants).
  • Doesn’t tell you if a different size would be cheaper or better.
  • Relies heavily on a good estimate of \(C\) for aged pipes.
Head-loss form (SI): \( h_f = 10.67\,L\,\dfrac{Q^{1.852}}{C^{1.852} d^{4.87}} \)

Method B — Find the Flow for a Head-Loss Limit

“Given a maximum allowable head loss, how much water can I move through this pipe?”

  • Useful for pump sizing and system upgrades with strict pressure constraints.
  • Helps you translate head-loss limits (e.g., ft per 100 ft) into flow rates.
  • Requires careful attention to units and the exponent when rearranging for \(Q\).
  • Still sensitive to uncertainty in \(C\).
Flow form (conceptual): \( Q = \left[\dfrac{h_f}{K\,L}\,C^{1.852} d^{4.87}\right]^{1/1.852} \)

Method C — Select a Diameter that Meets Both Head Loss & Velocity

“What pipe size gives me acceptable head loss and a reasonable velocity for this flow?”

  • Matches how you actually pick line sizes in water-distribution design.
  • Makes it easy to iterate: try a diameter, evaluate head loss and velocity, tweak.
  • Requires judgement about acceptable velocities (noise, erosion, water hammer).
  • May need multiple trials before you converge on a cost-effective diameter.
Velocity check: \( v = \dfrac{4Q}{\pi d^2} \)   → compare to your target band (e.g., 0.6–3 m/s).

Good habit: use one method as your primary design approach, then cross-check with another. For example, size a pipe with the diameter method, then re-run the calculator in “head-loss” mode to verify results.

What Moves the Hazen-Williams Number the Most

The Hazen-Williams formula is highly non-linear. Small changes in some parameters can create big changes in head loss or allowable flow. The chips below highlight the levers that matter most.

Pipe diameter \(d\)

Head loss scales roughly with \(d^{-4.87}\). Increasing diameter slightly can slash friction loss, often more cost-effectively than adding pumping capacity.

Flow rate \(Q\)

Head loss scales with \(Q^{1.852}\). Doubling flow almost quadruples friction loss. The calculator makes this sensitivity obvious in the quick stats.

Roughness coefficient \(C\)

Smooth pipes (high \(C\)) have lower head loss. As pipe ages and roughness grows, the effective \(C\) drops, increasing friction. Conservative design often means using a lower \(C\) for long-term conditions.

Pipe length \(L\)

Hazen-Williams is a distributed loss model: doubling the length doubles the friction head. The calculator typically reports both total head loss and loss per 100 m or 100 ft.

Units & constants

The numerical constant (e.g., 10.67 for SI or 4.73 for US customary) depends on your units. A trustworthy calculator handles the conversions internally so you do not have to.

Minor losses (not in the formula)

Hazen-Williams covers friction along a straight equivalent length. Bends, valves, tees, and meters introduce minor losses that must be added separately, often via equivalent length or \(K v^2/2g\).

Worked Examples Using the Hazen-Williams Calculator

Example 1 — Head Loss and Velocity in a PVC Distribution Line (SI)

You are evaluating a buried PVC water main feeding a small subdivision. The design data are:

  • Flow rate \(Q\): 0.020 m³/s (20 L/s)
  • Internal diameter \(d\): 150 mm (0.15 m)
  • Pipe length \(L\): 250 m
  • Material: PVC, assume \(C = 145\)
1
Friction slope from Hazen-Williams. The SI form for friction slope \(S_f\) (head loss per metre) is:
\[ S_f = \frac{h_f}{L} = 10.67\,\frac{Q^{1.852}}{C^{1.852} d^{4.87}} \]
Plugging in \(Q = 0.020\), \(C = 145\), \(d = 0.15\), the calculator returns \(S_f \approx 0.0078\).
2
Total head loss.
\[ h_f = S_f\,L \approx 0.0078 \times 250 \approx 1.95\ \text{m} \]
So friction costs you about 2 m of head along this reach (ignoring minor losses).
3
Velocity check. The calculator also reports velocity using:
\[ v = \frac{4Q}{\pi d^2} \]
Here, \(v \approx 1.1\ \text{m/s}\), which is comfortably within typical distribution-system targets.
4
Pressure drop. If the water density is \(\rho \approx 1000\ \text{kg/m}^3\), the friction-related pressure drop is:
\[ \Delta p = \rho g h_f \approx 1000 \times 9.81 \times 1.95 \approx 19{,}000\ \text{Pa} \approx 19\ \text{kPa} \]
The calculator may report this directly as kPa or bar, depending on your chosen units.

Example 2 — Maximum Flow for a Head-Loss Limit (US Customary)

A fire-protection line must not lose more than 20 ft of head between a pump and a remote hydrant. The line is 8 in ductile iron, 1200 ft long. You want to estimate the maximum flow while staying within this friction limit.

  • Head-loss limit \(h_f\): 20 ft
  • Length \(L\): 1200 ft
  • Diameter \(d\): 8 in (0.667 ft)
  • Material: ductile iron, assume \(C = 130\)
1
Compute friction slope.
\[ S_f = \frac{h_f}{L} = \frac{20}{1200} \approx 0.0167 \]
This is the allowable head-loss gradient along the line.
2
Hazen-Williams in US units. For many US-unit implementations:
\[ S_f = 4.73\,\frac{Q^{1.852}}{C^{1.852} d^{4.87}} \]
where \(Q\) is in ft³/s and \(d\) in ft. The calculator rearranges internally to solve for \(Q\).
3
Solve for flow \(Q\). Conceptually:
\[ Q = \left[\frac{S_f\,C^{1.852} d^{4.87}}{4.73}\right]^{1/1.852} \]
With \(S_f = 0.0167\), \(C = 130\), \(d = 0.667\ \text{ft}\), the calculator returns approximately \(Q \approx 2.1\ \text{ft}^3/\text{s}\) (\(\approx 950\ \text{gpm}\)).
4
Check velocity and codes. The calculator reports velocity; you verify it against fire-protection guidance, noise and erosion limits, and any local code requirements before finalizing.

Common Layouts & Variations in Hazen-Williams Applications

Hazen-Williams is most at home in pressurized water-distribution systems. Different layouts influence how you apply the equation and how you interpret the calculator outputs.

ConfigurationTypical UsesHazen-Williams Notes
Building Service & Domestic BranchesSmall commercial and residential water services, internal risers. Short runs; friction is often modest. Hazen-Williams is used mainly to confirm that velocities are reasonable and that pressure at fixtures remains adequate.
Municipal Distribution MainsGridded networks feeding neighbourhoods and streets. Long runs and multiple branches. The calculator is used segment-by-segment, often combined with network solvers. Friction slope and \(C\) selections are critical.
Fire Protection LoopsHydrant loops, sprinkler mains, fire pumps. High design flows, strict residual-pressure requirements. Hazen-Williams is embedded in many fire codes; the calculator helps iterate between pipe size, flow, and pressure drop.
Irrigation LateralsGolf courses, parks, agricultural sprinklers. Long laterals with multiple outlets. Hazen-Williams may be combined with emitter orifice equations. Watch for sections that are not fully pressurized or that operate near laminar conditions.
Pump Discharge HeadersShort, high-flow sections between pumps and manifolds. Friction and minor losses can both be significant. Use Hazen-Williams for friction and add equivalent lengths or \(K\)-values for fittings and control valves.
  • Confirm that each segment is full and pressurized for Hazen-Williams to be valid.
  • Use separate calculations or software for partially full sewers or open channels.
  • Document the \(C\) values you assume for each material and age condition.
  • Compare calculator outputs against similar past projects as a reasonableness check.
  • Where codes specify a method (e.g., NFPA), follow the prescribed \(C\) and safety factors.

Specs, Logistics & Sanity Checks

The numbers from a Hazen-Williams Calculator are only as good as the data and engineering judgement that go into them. Use this section to translate computed results into practical design and construction decisions.

Choosing \(C\) and Pipe Materials

Published tables list typical Hazen-Williams coefficients. Smooth plastic and cement-mortar-lined ductile iron tend to have higher \(C\); older unlined metal pipes are lower.

  • Use new-pipe \(C\) for short-term performance checks.
  • Use a reduced \(C\) for end-of-life or conservative designs.
  • Align \(C\) values with any governing standards or local utility practice.

Field Verification & Calibration

For existing systems, you can back-calculate an effective \(C\) by comparing measured and calculated pressure drops at known flows.

  • Measure static and residual pressure at hydrants during flow tests.
  • Record actual flows from pitot tubes or calibrated meters.
  • Use the calculator to adjust \(C\) until modeled and measured pressures agree.

Sanity Checks Before Finalizing

Before you freeze a design, review these quick checks directly against the calculator outputs:

  • Velocity within your target band for noise, erosion, and water-quality control.
  • Head loss per 100 m or 100 ft consistent with your network design criteria.
  • Pressure at critical nodes (e.g., remote hydrants, upper floors) above minimum allowable.

Design workflow: start with code or utility criteria (minimum pressures, maximum velocities), use the Hazen-Williams Calculator to size and check pipes, then document all assumptions in your design report.

Do not mix methods blindly: if you calibrate parts of a network with Darcy–Weisbach, keep the same reference conditions when comparing to Hazen-Williams results.

Frequently Asked Questions

When should I use the Hazen-Williams equation instead of Darcy–Weisbach?
Hazen-Williams is convenient for pressurized water in turbulent flow, especially in potable and fire-protection systems where standards and design tables are built around it. Use Darcy–Weisbach when you need a method that works for other fluids, wide temperature ranges, or laminar flow, or when you want consistency across many different pipe materials and fluids.
What units does this Hazen-Williams Calculator use?
The calculator typically lets you pick either SI units (m, mm, L/s, m³/h, kPa) or US customary units (in, ft, gpm, psi). Internally, it converts everything to a consistent system and applies the correct numerical constant so that the Hazen-Williams equation remains valid.
What are typical Hazen-Williams \(C\) values for common pipe materials?
Smooth plastic pipes such as PVC and HDPE often use \(C\) in the range of 140–150, new ductile iron around 120–140, and older steel or cast iron significantly lower. Always check the values recommended by local standards, manufacturers, or the authority having jurisdiction.
Can I use Hazen-Williams for wastewater, slurries, or other liquids?
Not reliably. Hazen-Williams is calibrated for clean water at normal temperatures and in turbulent regimes. For wastewater, slurries, oils, or highly viscous liquids, you should use methods based on Darcy–Weisbach and Moody friction factors, which account for viscosity and a wider range of flow conditions.
Does Hazen-Williams include minor losses from valves and fittings?
No. The basic Hazen-Williams equation accounts for distributed friction along a pipe length only. You must add minor losses from valves, bends, tees, meters, and other appurtenances separately, either via equivalent length or \(K v^2/2g\) methods, and combine them with the friction loss for total head loss.
Is Hazen-Williams valid for partially full pipes or very low flows?
Hazen-Williams assumes a completely full, pressurized pipe with turbulent flow. It is not appropriate for partially full sewers, open channels, or laminar flow. For those cases, use open-channel hydraulics and friction relationships that explicitly handle depth and flow regime.
Scroll to Top