Pipe Flow Calculator

Hazen-Williams head loss, velocity and pressure drop for water in pressurised pipes — PVC, copper, steel or cast iron, residential and commercial flow rates.

Pipe

in
Inside dim, not nominal — ¾″ copper has ID 0.811″.
ft
Straight run + fitting equivalents (e.g. 1″ elbow ≈ 2 ft).

Flow

gpm
Residential fixture demand: shower 2.5, sink 1.5, washing machine 4. Peak service 8-25 gpm.

Calculation results

Velocity

— ft/s

Head loss

— ft

Pressure drop

— psi

Reynolds number

—

1 ft of water = 0.4335 psi. Head loss along the pipe + elevation change + minor losses = total pressure drop seen at the fixture.

Informational only. Hazen-Williams is empirical and valid for water at typical temperatures (40-75 °F / 5-25 °C) in turbulent flow at velocities 2-10 ft/s. For other fluids, large temperature swings or very low/high Reynolds numbers, use Darcy-Weisbach with the appropriate friction factor.

Hazen-Williams formula

Empirical formula for head loss of water in pressurised pipes. Used widely in water-supply, fire-protection and irrigation design because it is direct (no Reynolds-dependent friction factor iteration). Valid for water in fully turbulent flow at typical temperatures.

hf = 4.52 × L × Q1.852 / (C1.852 × D4.87)

where hf is head loss in feet, L is pipe length in feet, Q is flow in gpm, D is inside diameter in inches and C is the Hazen-Williams coefficient for the pipe material.

velocity (ft/s) = 0.408 × Q / D²
pressure drop (psi) = hf × 0.4335

Worked example — 1″ PVC, 100 ft, 10 gpm

  • C = 150 (PVC)
  • v = 0.408 × 10 / 1² = 4.08 ft/s
  • hf = 4.52 × 100 × 101.852 / (1501.852 × 14.87)
  • = 4.52 × 100 × 71.12 / (12,338 × 1) = 2.61 ft
  • Pressure drop = 2.61 × 0.4335 = 1.13 psi

Hazen-Williams C reference

MaterialC valueNotes
PVC, CPVC, PEX, HDPE150Smooth plastic; consistent across age
Copper, drawn130-140140 new; drops to 130 with mineral buildup
Steel, new140Drops to 100-120 with corrosion
Cast iron, new130Asphalt-coated or cement-lined
Cast iron, 10-20 yr old100-110Internal tuberculation reduces effective ID
Cast iron, 30+ yr old80-100Replacement candidate
Galvanised steel120Drops to 80-100 in 20 years
Concrete120-140Smooth precast 140; rough 120

Sizing rules of thumb

  • Velocity ceiling: 8 ft/s for water lines. Above this, erosion accelerates and pipes can become noisy ("water hammer", whoosh sounds).
  • Velocity floor: 2 ft/s minimum to keep particles suspended (no sediment settling).
  • Pressure drop budget: typical residential service starts at 60 psi at the street. Lose 5-10 psi to building service line, 10-15 psi to vertical lift (1 storey = 5 psi), 5-10 psi to fixture branches. Target 30-50 psi at the fixture.
  • Fitting equivalent length: a 90° elbow ≈ 2 ft of straight pipe; a gate valve fully open ≈ 1 ft; a tee through-flow ≈ 4 ft. Add these to the straight run for "equivalent length" in the formula.

Frequently asked questions

What is the Hazen-Williams formula?
An empirical formula for head loss of water in pressurised pipes: h_f = 4.52 × L × Q^1.852 / (C^1.852 × D^4.87), where h_f is feet of head loss, L is pipe length in feet, Q is flow in gpm, D is inside diameter in inches, C is the material coefficient. Widely used because it is direct — no Reynolds iteration like Darcy-Weisbach.
When should I use Darcy-Weisbach instead?
For non-water fluids, gases, very low or very high Reynolds numbers, or any application where the assumptions break down (Hazen-Williams assumes water, turbulent flow, typical temperatures). Darcy-Weisbach with the Colebrook friction factor is the more rigorous (but more complex) formula.
What is a typical Hazen-Williams C for PVC?
C = 150 for PVC, CPVC, PEX and HDPE. Plastic does not corrode internally so C stays at 150 throughout the pipe life — unlike metal pipes where C drops with age.
What is the maximum velocity for water in pipes?
8 ft/s is the practical residential ceiling (10 ft/s in some codes). Above 8 ft/s pipes become noisy from water hammer, erosion accelerates (especially in copper), and pressure drop grows quadratically with velocity. Aim for 4-6 ft/s in typical service.
How much pressure drop in a 1 inch pipe?
1″ PVC at 10 gpm loses about 2.6 ft (1.1 psi) per 100 ft. At 20 gpm, loss quadruples to ~10 ft per 100 ft (4.3 psi). Older steel/iron pipes at the same flow can lose 2-3× more.
How do I convert head loss to pressure?
Multiply head loss in feet by 0.4335 to get psi. So 10 ft of head loss = 4.335 psi. Inversely: 1 psi = 2.31 feet of head. This conversion uses water at 60 °F and standard gravity.
What is Reynolds number for water in pipes?
For water at 60 °F: Re ≈ 7,740 × velocity (ft/s) × diameter (in). Flow is laminar below Re 2,300, transitional 2,300-4,000, turbulent above 4,000. Residential water flow is almost always turbulent (Re 10,000-100,000+).