Hazen-Williams Pipe Flow Calculator — Head Loss

Calculate

Hazen-Williams is calibrated to water at ordinary temperatures (40–75 °F / 4–25 °C). Selecting any other fluid returns NOT-APPLICABLE and points to Darcy-Weisbach.

The material sets the starting C value. C is a roughness coefficient — higher means smoother pipe with less head loss. New plastic is about 150; aged metal is 100 or lower.

Design C is used for new-system sizing. For existing pipes or long-term analysis, aged C accounts for corrosion, scaling, and tuberculation. The C value shown below is the result of this selection.

Enter a custom C to override the material table. Useful for measured field values or project-specific basis. Leave blank to use the material table C. Normal range: 60–160.

Hazen-Williams uses the inside diameter. Nominal pipe size is not the bore — a 3-inch Schedule 40 pipe has a 3.068-inch inside diameter, not 3.000.

Enter the actual pipe bore — the inside dimension the water flows through. For Schedule 40 steel: 3 in nominal → 3.068 in bore. Use the Nominal + Schedule mode to look up the bore automatically.

Flow rate of water in the pipe. Required for Head Loss and Diameter solve modes, and for Check mode. Leave blank when solving for Flow Rate — it is the computed output in that mode.

Length of the straight pipe run. Add fitting losses via Equivalent Fitting Length below, or use the K-method separately.

Allowable head loss for the run. Used when solving for Flow Rate or Diameter, and in Check mode. Choose the basis (total, per 100 ft, slope %, or pressure drop) with the selector below. Leave blank when solving for Head Loss — it is the computed output.

How the head loss value above is expressed. The calculator converts any basis to the total head loss for the run before computing.

Optional velocity design limit. Typical water distribution: 5 ft/s preferred, 8 ft/s common maximum. In Diameter mode, the pipe is also sized to stay within this limit. In Check mode, a separate velocity ratio is reported.

Equivalent pipe length for fittings, valves, and entrance/exit losses. Added to the straight length for the total effective length. Use the K-method for more precise fitting losses.

What to Look at First

Head loss or solved quantity. In Solve mode, the first output is the unknown you chose — head loss in ft (or m), maximum flow rate in gpm (or L/s), or the required pipe size. In Check mode, read the head-loss and velocity ratios against your limits.

C coefficient used. The result block shows the C value, material, and condition applied. Because head loss varies with C to the −1.85 power, a 30-point change in C can more than double the head loss. Confirm C matches your design basis before using the result.

Velocity alongside head loss. Head loss alone can pass while velocity exceeds the design limit. The result always reports velocity, and in Check mode reports a separate velocity ratio if a limit is entered.

Inside diameter vs nominal size. The Hazen-Williams equation uses the inside diameter raised to the −4.87 power. A 3-inch nominal Schedule 40 pipe has a 3.068-inch bore, not 3.000 — entering nominal size as the ID understates head loss significantly for larger differences. Enter the inside diameter directly or use the Nominal + Schedule selector to pull the correct bore from the pipe table.

How to Use This Calculator

  1. Choose Calculation Mode: Solve (compute head loss, flow rate, or pipe diameter) or Check (evaluate a proposed pipe against limits).

  2. In Solve mode, choose what to solve for: Head Loss (given flow, diameter, and length), Flow Rate (given diameter, length, and allowable head loss), or Diameter (given flow, length, and at least one limit).

  3. Select Unit System — Imperial (gpm, in, ft, psi) or Metric (L/s, mm, m, kPa). All inputs and outputs switch accordingly.

  4. Confirm the fluid is Water. For any other fluid, the calculator will not apply Hazen-Williams and will redirect you to Darcy-Weisbach.

  5. Choose Pipe Material and Condition (New / Design / Aged). The calculator sets C from the material table. Review the C value shown — it is the design basis for the result.

  6. Enter the inside diameter directly, or choose Nominal Size + Schedule to pull the correct bore from the ASME B36.10M pipe table.

  7. Enter the known values for your chosen solve-for: flow rate and pipe length for head loss; pipe diameter and length and allowable head loss for flow rate; flow rate and length plus at least one limit for diameter.

  8. Optionally enter a velocity limit and an equivalent fitting length for fittings.

  9. Click Calculate. Read the result, the C used, the velocity, and in Check mode the head-loss and velocity ratios.

All results are friction (major) loss for the entered run. Fittings are not included unless an equivalent length is entered. Elevation, pump head, and minor losses are separate. Hazen-Williams is valid for water near ordinary temperatures (40–75 °F) in turbulent flow.

Inputs & Outputs

Inputs

•Calculation Mode : Options: Solve — compute an unknown (head loss, flow, or diameter), Check — evaluate a proposed pipe against limits
•Solve For : Options: Head Loss — given flow, pipe, and length, Flow Rate — given pipe, length, and allowable head loss, Diameter — given flow, length, and head-loss or velocity limit
•Unit System : Options: Imperial — gpm, in, ft, psi, Metric — L/s, mm, m, kPa
•Fluid : Options: Water (ordinary temperature), Other fluid — Darcy-Weisbach required
•Pipe Material : Options: PVC / HDPE (thermoplastic), Cement-lined ductile iron, Unlined steel (C ≈ 120 design), Cement-lined steel, Aged / tuberculated metal (C ≈ 100), Old unlined cast iron (C ≈ 60–80)
•Condition : Options: New — as-installed, clean bore, Design — typical design value, Aged — future or existing aged condition
•C Coefficient Override (optional)
•Diameter Entry : Options: Direct inside diameter (enter actual bore), Nominal size + schedule (ID from pipe table)
•Inside Diameter (in / mm)
•Nominal Pipe Size : Options: ½ in (DN15), ¾ in (DN20), 1 in (DN25), 1¼ in (DN32), 1½ in (DN40), 2 in (DN50), 2½ in (DN65), 3 in (DN80), 4 in (DN100), 6 in (DN150), 8 in (DN200), 10 in (DN250), 12 in (DN300)
•Schedule : Options: Schedule 40 (standard wall), Schedule 80 (heavy wall)
•Flow Rate (gpm / L/s)
•Pipe Length (straight run) (ft / m)
•Head Loss / Allowable Head Loss (ft / psi / ft per 100 ft / m / kPa / m per 100 m)
•Head Loss Basis : Options: Total head loss — ft or m for the full run, Head loss per 100 ft (or per 100 m), Percent slope — ft per 100 ft as a percent, Available pressure drop — psi or kPa
•Velocity Limit (optional) (ft/s / m/s)
•Equivalent Fitting Length (optional) (ft / m)

Outputs

•Head loss (Solve — Head Loss mode) (ft / m)
•Slope — head loss per 100 ft (or per 100 m) (ft/100 ft / m/100 m)
•Pressure loss (psi / kPa)
•Velocity (ft/s / m/s)
•C coefficient used + condition + material
•Equation form applied (US or SI)
•Reynolds number (turbulence validity check)
•Solved flow rate (Solve — Flow Rate mode) (gpm / L/s)
•Required inside diameter (Solve — Diameter mode) (in / mm)
•Selected standard pipe size (Solve — Diameter mode)
•Governing limit — head loss or velocity (Diameter / Check mode)
•Head-loss ratio and velocity ratio vs limits (Check mode)

Formula

Hazen-Williams Formula

The Hazen-Williams equation gives friction (major) head loss for water in a full pressurized pipe.

US Customary Form (canonical — build gate)

h_f = 0.002083 × L × (100/C)^1.852 × Q^1.852 / d^4.8655

Where:

  • h_f = friction head loss [ft]
  • L = pipe length [ft]
  • C = Hazen-Williams roughness coefficient (dimensionless)
  • Q = flow rate [US gpm]
  • d = inside diameter [in]

The (100/C)^1.852 term is essential — it applies the roughness correction relative to C = 100. Dropping or misplacing this term is the most common coding error in HW calculators.

SI Form

h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.8704)

Where:

  • h_f [m], L [m], Q [m³/s], D [m]

The constant differs by unit system (0.002083 US, 10.67 SI) — they are not interchangeable.

Velocity

V = Q / A    (A = π/4 × d²)

Pressure Loss

pressure_loss_psi = h_f_ft × 0.4332
pressure_loss_kPa = h_f_m × 9.807

Solving for Flow Rate

Q = [h_f × d^4.8655 / (0.002083 × L × (100/C)^1.852)]^(1/1.852)

Solving for Diameter

d = [0.002083 × L × (100/C)^1.852 × Q^1.852 / h_f]^(1/4.8655)

Diameter is computed for both the head-loss limit and the velocity limit; the larger governs. The result is snapped up to the next standard size (ASME B36.10M Sch 40 or Sch 80).

Reynolds Number Validity Check

Re = V × D / ν_water

Where ν_water ≈ 1.004 × 10⁻⁶ m²/s at 20 °C.

  • Re < 2,000 → NOT-APPLICABLE (laminar). Use Darcy-Weisbach.
  • Re 2,000–4,000 → transitional warning. Result shown but unreliable.
  • Re > 4,000 → turbulent. HW valid.
Variable Meaning US Units SI Units
h_f Friction head loss ft m
L Pipe length ft m
Q Flow rate gpm m³/s
d / D Inside diameter in m
C HW roughness coefficient — —
V Velocity ft/s m/s
Re Reynolds number — —

Key Facts

  • The Hazen-Williams equation uses a single roughness coefficient C instead of a friction factor, so it needs no Reynolds number, no viscosity, and no iteration — which is why it is the standard method for water distribution.
  • Head loss varies with C to the −1.85 power: a line at C 100 has roughly twice the head loss of the same line at C 150, at the same flow and diameter.
  • Head loss rises with flow to the 1.85 power — doubling the flow roughly triples the head loss.
  • Head loss falls with diameter to the −4.87 power — going up one pipe size cuts head loss sharply.
  • The constant in the US formula (0.002083) and the SI formula (10.67) are not interchangeable; using one with the other unit system is a common error.
  • The inside diameter governs the calculation, not the nominal pipe size. A 3-inch Schedule 40 pipe has a 3.068-inch bore, not 3.000.
  • Hazen-Williams is valid only for water at ordinary temperatures in turbulent flow. For oils, gases, hot water, or laminar flow, use Darcy-Weisbach.
  • The equation covers friction (major) head loss only — elevation, pump head, minor losses from fittings, and residual pressure are separate parts of the system calculation.

Applications

  • Finding the friction head loss in a water main, service line, or riser for a given flow and pipe size.
  • Sizing a pipe to stay within an allowable head loss or a target velocity for a water-distribution or irrigation line.
  • Finding the flow a pipe can carry within an available head or pressure drop.
  • Checking a proposed pipe against both a head-loss limit and a velocity limit.
  • Estimating pressure loss in psi or kPa across a pipe run for a pump or system-head calculation.
  • Comparing head loss for new vs aged pipe by changing the C coefficient.
  • Fire-protection and sprinkler hydraulics where the standard specifies Hazen-Williams with set C values (NFPA 13, NFPA 20).
  • Irrigation main and lateral sizing using the standard water-distribution method.

Example Calculation

Example 1 — Head Loss for a Known Pipe

Given (Imperial, Solve — Head Loss):

  • Flow rate: 100 gpm
  • Inside diameter: 3.068 in (3 in Schedule 40 pipe)
  • Pipe length: 100 ft
  • C = 130 (unlined steel, design)

Formula:

h_f = 0.002083 × L × (100/C)^1.852 × Q^1.852 / d^4.8655

Velocity: 100 gpm through a 3.068 in pipe ≈ 4.33 ft/s

Result: Head loss ≈ 2.9 ft over 100 ft (about 2.9 ft per 100 ft); pressure loss ≈ 1.3 psi

Example 2 — How the C Coefficient Changes the Result

The same 3.068 in pipe and 100 gpm flow, but varying C:

  • C = 150 (new PVC): head loss ≈ 2.1 ft per 100 ft
  • C = 130 (design unlined steel): head loss ≈ 2.9 ft per 100 ft
  • C = 100 (aged/tuberculated): head loss ≈ 4.5 ft per 100 ft

Head loss varies with C to the −1.85 power, so the C chosen for the design condition matters as much as the pipe size. Aged pipe at C 100 has roughly twice the head loss of new plastic at C 150.

Example 3 — Non-Water Fluid (NOT-APPLICABLE)

The same pipe and flow, but the fluid is a light oil rather than water. Hazen-Williams does not apply — it has no viscosity term and is calibrated to water. The calculator returns NOT-APPLICABLE and directs you to Darcy-Weisbach.

Example 4 — Required Pipe Diameter

Given (Imperial, Solve — Diameter):

  • Flow: 200 gpm
  • Length: 100 ft
  • C = 130
  • Allowable head loss: 5 ft per 100 ft
  • Velocity limit: 8 ft/s

The calculator solves for the required inside diameter from both limits and takes the larger. Suppose head loss governs at about 3.7 in required ID. The next Schedule 40 standard size up is 4 in (actual ID 4.026 in), which is selected. The velocity at 4.026 in is well within 8 ft/s.

Example 5 — Check Mode

Given (Imperial, Check):

  • Flow: 100 gpm
  • Pipe: 2½ in Schedule 40 (ID 2.469 in)
  • Length: 100 ft
  • C = 130
  • Allowable head loss: 10 ft per 100 ft
  • Velocity limit: 8 ft/s

Computed head loss exceeds the 10 ft/100 ft limit (ratio > 1.0); velocity is also checked. The result shows which constraint governs and prompts sizing up.

Standards & References

Units

The calculator works in US customary units by default and converts to metric on selection. Flow is in gallons per minute (gpm) or litres per second (L/s); diameter in inches or millimetres; length and head loss in feet or metres; pressure loss in psi or kPa. The unit system is kept consistent from input to output because the Hazen-Williams constant changes with units — 0.002083 in the US form, 10.67 in the SI form. The coefficient C is dimensionless and the same number in both systems. A head loss in feet converts to psi by multiplying by 0.4332, and to metres by multiplying by 0.3048.

Limitations

  • This calculator covers friction (major) head loss only for water flowing full in a pressurized pipe.
  • Hazen-Williams is valid only for water at ordinary temperatures (40–75 °F / 4–25 °C) in turbulent flow.
  • It does not apply to other fluids (oils, chemicals, gases), hot water, laminar flow, or open-channel or partially full gravity flow.
  • Fittings, valves, and entrance and exit losses are not included unless equivalent length is entered.
  • Elevation or static head, pump head, residual pressure, and minor losses are outside scope — the friction loss is one input to those larger calculations.
  • The inside diameter is used; the schedule must match the actual pipe. The C coefficient is a user-selected design value.
  • The calculator does not check pressure rating, surge or water hammer, or erosion limits beyond flagging velocity above 15 ft/s.
  • Results are design estimates. Final design follows the project's hydraulic basis and professional judgment.

Common Mistakes to Avoid

  • Dropping or misplacing the (100/C) term. The US form is 0.002083 × L × (100/C)^1.852 × Q^1.852 / d^4.8655 — folding C into the flow term or omitting the 100 gives a wrong head loss.
  • Mixing the unit constants. The US constant 0.002083 goes with gpm, inches, and feet; the SI constant 10.67 goes with m³/s and metres. Using one with the other unit system is a silent error.
  • Using the nominal pipe size instead of the inside diameter. The inside diameter depends on the schedule, not just the nominal size.
  • Using a new-pipe C for an aged existing pipe. Existing pipes often need a lower C because aging raises the head loss substantially.
  • Treating C as a fixed constant. C is a design choice by material and age — pick the C for the design condition.
  • Applying Hazen-Williams to fluids other than water at ordinary temperatures. It is the wrong model for oils, gases, hot water, and laminar flow.
  • Checking head loss but ignoring velocity. A pipe can be within its head-loss limit and still run too fast, bringing noise, erosion, and surge risk.
  • Treating friction loss as the total system head. Elevation, pump head, residual pressure, and minor losses are separate.

Frequently Asked Questions

What is the Hazen-Williams equation used for?
It calculates the friction head loss of water flowing through a full, pressurized pipe using a single roughness coefficient C. It is widely used for water distribution, fire-protection and sprinkler hydraulics, and irrigation because it is quick and needs no iteration or fluid viscosity.
What is the C coefficient in the Hazen-Williams equation?
C is the roughness coefficient, a number that describes how smooth the pipe wall is. It is read from a table by material and condition: new plastic and cement-lined pipe are around 140–150, new steel roughly 120–130, and aged or tuberculated metal drops toward 100 or below. A higher C means a smoother pipe with less head loss.
Why does the C value matter so much?
Because head loss varies with C to the −1.85 power, so a change in C has a large, non-linear effect. A line at C 100 has about twice the head loss of the same line at C 150 for the same flow and size. This is why the C chosen for the design condition — new pipe or aged pipe — matters as much as the pipe diameter.
What is the difference between the US and SI forms of the equation?
The two forms use different constants because the units differ: the US form uses 0.002083 with flow in gpm, diameter in inches, and length and head loss in feet, while the SI form uses 10.67 with flow in m³/s and lengths in metres. The constants are not interchangeable, and the C coefficient is the same number in both systems.
When should I use Darcy-Weisbach instead of Hazen-Williams?
Use Darcy-Weisbach for any fluid other than water, for hot water, for gases or oils, and for laminar or transitional flow. Hazen-Williams has no viscosity or temperature term and is calibrated to water at ordinary temperatures in turbulent flow — outside that range it is the wrong model.
Can Hazen-Williams be used for hot water?
Not reliably. The equation has no viscosity or temperature term and is calibrated for ordinary-temperature water, roughly 40–75 °F. Hot water is less viscous and behaves differently, so for hot-water or temperature-sensitive design, Darcy-Weisbach with viscosity input is the correct choice.
Does Hazen-Williams include elevation or static head?
No. It calculates friction loss only — the loss from water rubbing against the pipe wall. Elevation or static head, residual pressure at the outlet, pump head, and minor losses from fittings are separate terms in the total system-head calculation.
What is head loss per 100 ft?
It is the friction head loss normalized to 100 feet of pipe, a common way to state and compare friction independent of actual run length. Expressing the loss as a slope — feet of head per 100 feet, or a percent — lets pipe sizes and design limits be compared directly, and the total loss is that slope times the real length.

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