Formula
Hazen–Williams, in feet of water per 100 feet, is 0.2083 × (100 / C)^1.852 × Q^1.852 / d^4.8655. Q is US gallons per minute and d is the inside diameter in inches. That is the Spears and PPI TR-14 form. Velocity is 0.4085 × Q / d², which is the same thing as 0.3208 × Q / area.
Darcy hf = f × (L / D) × V² / (2 × 32.174)
Swamee–Jain f = 0.25 / [log10(ε / (3.7 D) + 5.74 / Re^0.9)]²
Reynolds number uses a water viscosity of 1.217×10⁻⁵ ft²/s, about 60°F. Psi is feet times 0.433, from 62.4 lb/ft³ divided by 144. Fittings add an equivalent length: count × (L/D) × diameter in feet. Those L/D values are planning figures, not Crane TP-410. A published K or Cv wins.
Checked two ways. Spears Schedule 40 lists 1.16 ft per 100 ft for 1/2 inch pipe at 1 gpm. The ID implied by their 1.13 ft/s velocity is 0.601 inch, and the formula there is within 2% of 1.16. Separately, 3 inch Schedule 40 steel (ID 3.068) at 100 gpm with ε = 0.00015 ft gives 2.41 ft per 100 ft by Darcy–Weisbach, within 5% of an Engineering Toolbox steel chart near 2.5. Hazen–Williams at C = 120 on that bore is 3.22 ft per 100 ft, about 29% higher. The methods are not interchangeable. PVC Schedule 40 is not the steel ID. The gallons in the pipe are the pipe volume calculator. The tank is the tank volume calculator.
Worked examples
3 inch Schedule 40, ID 3.068, 100 gpm, 100 ft, C = 120, ε = 0.00015 ft, no fittings. Darcy–Weisbach 2.41 ft (1.04 psi). Hazen–Williams 3.22 ft. Velocity 4.34 ft/s.
Two 90° elbows on that line. Each is 30 diameters. 60 × 3.068 / 12 = 15.34 ft of equivalent pipe, added to the 100 ft before both formulas run.
Spears check, not this preset. 1 gpm in a 0.601 inch bore at C = 150 is within 2% of 1.16 ft per 100 ft.
Reference
C factors follow the NFPA 13 pattern for steel and for smooth pipe. PEX is set equal to other smooth thermoplastics. That is an assumption, not a PEX lab C.
| Pipe | C |
|---|---|
| PVC, CPVC, copper, stainless | 150 |
| PEX, assumed smooth thermoplastic | 150 |
| Black steel, wet | 120 |
| Black steel, dry | 100 |
Equivalent length in diameters. Planning values, not Crane.
| Fitting | L/D |
|---|---|
| 90° elbow | 30 |
| 45° elbow | 16 |
| Tee, run | 20 |
| Tee, branch | 60 |
| Gate valve, open | 8 |
| Ball valve, full port | 3 |
| Swing check | 50 |
Questions
Which answer should I use?
Hazen–Williams is the water-works form, and it needs a C factor. Darcy–Weisbach with Swamee–Jain is the fluid-mechanics form, and it needs a roughness. They do not agree on every pipe. On 3 inch Schedule 40 steel at 100 gpm, Darcy at 0.00015 ft roughness is 2.41 ft per 100 ft, within 5% of a published steel chart near 2.5. Hazen–Williams at C = 120 on that same bore is 3.22 ft per 100 ft. Use the method your pipe data was built with.
How close is Hazen–Williams to a published PVC table?
The Spears Schedule 40 table lists 1.16 ft per 100 ft for 1/2 inch pipe at 1 gpm. Their own velocity of 1.13 ft/s implies an ID of 0.601 inch. The formula at that ID is within 2% of 1.16. The nominal steel ID of 0.622 inch is a larger bore, so it loses less head. Match the ID to the pipe you have.
Are the fitting lengths from Crane?
No. The equivalent lengths in diameters are planning values of the usual order of magnitude. They are not a Crane TP-410 K table. A published K or Cv for the valve in your hand wins.
Sources
- Hazen–Williams, Spears PVC technical data and PPI TR-14 form: 0.2083 (100/C)^1.852 Q^1.852 / d^4.8655, feet of water per 100 ft. Checked within 2% of the Spears Schedule 40 row for 1/2 in at 1 gpm when the ID is the one implied by that row’s velocity.
- Darcy–Weisbach with the Swamee–Jain explicit friction factor. Water kinematic viscosity 1.217×10⁻⁵ ft²/s. Commercial steel roughness 0.00015 ft. On 3 in Schedule 40 (ID 3.068) at 100 gpm this is 2.41 ft per 100 ft, within 5% of the Engineering Toolbox steel chart value of about 2.5. Hazen–Williams at C = 120 is 3.22 on the same pipe.
- Fitting L/D values are planning order-of-magnitude figures, not a transcription of Crane TP-410. A published K or Cv wins. PEX at C = 150 is assumed from smooth thermoplastic pipe, not from a PEX-specific test.