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Hazen–Williams calculator

Head loss or flow for water in a full pipe, from the Hazen–Williams C factor.

Free, right in your browser. Every result shows its work.

gpm
in
ft

Handbook C: 150 plastic · 140 ductile iron · 130 concrete, copper, new cast iron · 120 new welded steel · 100 20-year-old cast iron. Use the value a problem gives.

Result

Head loss, h_f
5.87ft of water
Pressure drop
2.544psi
Velocity
3.191ft/s
Loss per 100 ft
0.587ft
  1. 1.Q = 500 gpm = 1.114 ft³/s; D = 8/12 = 0.6667 ft
  2. 2.h_f = 4.73 L Q^1.852 / (C^1.852 D^4.87) = 4.73 × 1000 × 1.114^1.852 / (120^1.852 × 0.6667^4.87) = 5.87 ft
  3. 3.V = Q/A = 3.191 ft/s
  4. 4.Δp = h_f × 62.4 / 144 = 2.544 psi

How it's tested on the exam

Shows up on: PE Civil (Water Resources & Environmental) · PE Mechanical (HVAC & Refrigeration) · PE Mechanical (Thermal & Fluid Systems)

  • Water only, turbulent only. Hazen–Williams has no viscosity term — it's an empirical fit for water at ordinary temperatures, not for oil or air.
  • Match the form to its units. The constant changes with units (4.73 with cfs and feet; 10.44 per foot with gpm and inches; 10.67 in SI). Using a constant with the wrong units is the classic miss.
  • Higher C means smoother pipe and less loss. Older pipe has a lower C — design problems often ask you to use an aged value.
  • Head loss scales with Q^1.852, not Q². Doubling the flow multiplies the loss by about 3.6.

Worked example

500 gpm of water flows through 1,000 ft of 8-in pipe with C = 120. Find the head loss.

  1. 1.Q = 500 / 448.8 = 1.114 ft³/s; D = 8/12 = 0.6667 ft
  2. 2.h_f = 4.73 × 1,000 × 1.114^1.852 / (120^1.852 × 0.6667^4.87) = 5.87 ft
  3. 3.Δp = 5.87 × 62.4 / 144 = 2.54 psi

h_f ≈ 5.9 ft of water (≈ 2.5 psi).

Where it is in the Handbook

  • Closed Conduit Flow and Pumps — Hazen-Williams Equation — PE Civil Reference Handbook
  • Hydraulics, Fluids, and Pipe Flow — Pressure Drop of Water Flowing in Circular Pipe (Hazen-Williams) — PE Mechanical Reference Handbook

Section names as printed in the current NCEES PE Reference Handbooks (Mechanical 2.1, Civil 2.2); numbering can shift between versions. On exam day you'll use your own approved calculator — here's which models NCEES allows.