Fire Pipe Pressure Loss Calculator
How the formula works
Water flowing in a pipe loses pressure because of friction against the pipe wall. For fire protection pipes, the standard way to estimate this loss is the Hazen-Williams formula, which is the formula used in NFPA 13 hydraulic calculations.
1. Friction loss per unit length
p = k x Q^1.85 / (C^1.85 x d^4.87)
2. Total friction loss
Friction loss = p x (pipe length + fittings equivalent length)
3. Elevation pressure
Elevation pressure = 0.0981 bar per metre (0.433 psi per foot) x rise. A rise adds pressure loss, a drop reduces it.
4. Velocity
v = 21.22 x Q / d^2 (flow in L/min, diameter in mm, velocity in m/s)
v = 0.4085 x Q / d^2 (flow in gpm, diameter in inches, velocity in ft/s)
5. Required internal diameter
d = (k x Q^1.85 x L / (C^1.85 x P))^(1/4.87), where P is the allowable friction loss. The next larger standard pipe is then selected.
6. Maximum flow
Q = (P x C^1.85 x d^4.87 / (k x L))^(1/1.85)
Where
- Q = flow (L/min or gpm), d = internal pipe diameter (mm or inches), C = Hazen-Williams roughness factor
- L = total equivalent length (pipe plus fittings), P = pressure (bar or psi)
- k = 6.05 x 10^5 for bar, L/min, mm and m, or k = 4.52 for psi, gpm, inches and feet
Typical C-factors (NFPA 13 style)
- Black steel, wet pipe and deluge: 120
- Black steel, dry pipe and pre-action: 100
- Galvanized steel: 120
- Copper tube or stainless steel: 150
- Listed plastic pipe (CPVC, PE): 150
- Cement-lined ductile iron: 140
- Unlined cast or ductile iron: 100
How to use the calculator
- Select the calculation and the unit system.
- Enter the flow, or select the pipe schedule and nominal size, depending on the calculation.
- Select the pipe material. Choose Custom if you know the C-factor.
- Enter the pipe length. Add a fittings allowance and the elevation rise if needed.
- Click Calculate, then Download PDF Result if you need a record.
Important notes
- Typical values only. The code, the pipe supplier data and the project specification are final.
- The fittings allowance is a percentage of pipe length. For final design, add the real equivalent length of every elbow, tee, valve and strainer.
- Velocity above about 6 m/s (20 ft/s) is usually avoided in design. Underground fire mains are often kept lower, so check your specification.
- Schedule 40 and Schedule 10 steel diameters are used. For copper, plastic or lined pipe use the Custom internal diameter option.
Worked example
Example 1 – Pressure loss, metric
Flow 1000 L/min, DN 100 Schedule 40 steel pipe (internal diameter 102.26 mm), black steel wet system (C = 120), pipe length 100 m.
p = 6.05 x 10^5 x 1000^1.85 / (120^1.85 x 102.26^4.87) = 0.00499 bar per metre
Friction loss = 0.00499 x 100 = 0.499 bar (7.24 psi)
Velocity = 21.22 x 1000 / 102.26^2 = 2.03 m/s, which is within the typical limit.
Example 2 – Pressure loss with fittings and elevation, imperial
Flow 500 gpm, 4 in Schedule 10 pipe (internal diameter 4.26 in), C = 120, pipe length 300 ft, fittings allowance 20 %, rise 15 ft.
Total equivalent length = 300 + 60 = 360 ft
p = 4.52 x 500^1.85 / (120^1.85 x 4.26^4.87) = 0.05452 psi per foot
Friction loss = 0.05452 x 360 = 19.63 psi
Elevation pressure = 15 x 0.433 = 6.50 psi
Total pressure loss = 26.12 psi (1.80 bar). Velocity = 11.25 ft/s.
Example 3 – Required pipe size, metric
Flow 1500 L/min, C = 120, pipe length 150 m plus 10 % fittings (total 165 m), allowable friction loss 0.5 bar.
Required internal diameter = 132.1 mm
Smallest Schedule 40 pipe: DN 150 (internal diameter 154.1 mm), friction loss 0.237 bar, velocity 1.34 m/s.
Smallest Schedule 10 pipe: DN 125 (internal diameter 134.5 mm), friction loss 0.459 bar, velocity 1.76 m/s.
Example 4 – Maximum flow, metric
DN 125 Schedule 40 copper-type pipe (internal diameter 128.2 mm), C = 150, length 80 m, allowable friction loss 0.3 bar.
Maximum flow = 1942.2 L/min (116.53 m3/h)
Velocity at that flow = 2.51 m/s.
Common mistakes
- Using nominal pipe size instead of the real internal diameter. A DN 100 pipe is not 100 mm inside, and Schedule 10 and Schedule 40 pipes have different internal diameters.
- Using the wrong C-factor. Dry pipe black steel uses a lower C than wet pipe, and an old or corroded pipe can have a much lower C than a new one.
- Forgetting fittings. Elbows, tees, valves and strainers add a lot of equivalent length, so ignoring them makes the loss too low.
- Mixing units. Flow, diameter, length and pressure must all be in the same unit system selected in the calculator.
- Ignoring elevation. A pipe that rises needs extra pressure, and the friction loss alone does not show this.
- Checking only pressure loss and not velocity. A small pipe can meet the pressure limit but have very high velocity, which causes noise, erosion and water hammer risk.
- Applying the Hazen-Williams formula to fluids other than water at normal temperature, or to very small or very large flows outside its range.
- Rounding the required diameter down. You must always select the next larger standard pipe size.
- Treating this result as the full system calculation. A sprinkler or hydrant system needs the loss of every pipe section along the most remote path.
Frequently asked questions
What is the Hazen-Williams formula?
It is an empirical formula that estimates friction loss of water flowing in a full pipe. It is widely used for fire sprinkler, hydrant and water supply design because it is simple and gives reliable results for water at normal temperature.
What is the C-factor?
C is a roughness number. A higher C means a smoother pipe and less friction loss. New plastic and copper pipe have a high C, while old unlined iron has a low C.
What C-factor should I use for fire sprinkler pipe?
As typical NFPA 13 style values, use 120 for black steel wet systems and galvanized steel, 100 for black steel dry and pre-action systems, and 150 for copper and listed plastic pipe. Use the value given in your code or specification.
What is the formula for fire pipe friction loss?
In metric units, p = 6.05 x 10^5 x Q^1.85 / (C^1.85 x d^4.87) in bar per metre, with Q in L/min and d in mm. In imperial units, p = 4.52 x Q^1.85 / (C^1.85 x d^4.87) in psi per foot, with Q in gpm and d in inches.
What is the maximum velocity in fire water pipes?
Many designers keep velocity below about 6 m/s (20 ft/s) for sprinkler pipes. Underground fire mains are often kept lower, around 3 m/s (10 ft/s). Check your project specification, because the limit is not the same in every code.
How do I include fittings in the calculation?
Each fitting has an equivalent length of straight pipe. Add these lengths to the pipe length. This calculator also lets you add a simple percentage of the pipe length, which is a good early estimate.
Why does elevation matter?
Water needs about 0.0981 bar of pressure to rise one metre (0.433 psi per foot). If the pipe goes up, this pressure is lost. If it goes down, the pressure is gained.
What is the difference between Schedule 40 and Schedule 10 pipe?
Schedule 10 has a thinner wall, so for the same nominal size it has a larger internal diameter and lower friction loss. Schedule 40 is thicker and stronger.
Can I use this calculator for fire pump sizing?
It gives the pipe friction loss, which is one part of the pump head. The pump also needs the sprinkler or hydrant pressure, elevation, losses in valves and fittings, and the suction side.
Can I use it for copper or plastic pipe?
Yes. Select copper or plastic as the material for the C-factor, then choose Custom as the pipe schedule and type the internal diameter from the manufacturer data.
What if the required pipe size is larger than DN 300?
The calculator shows a red message. In that case, consider a higher allowable loss, a shorter route or splitting the flow into more than one pipe, and size larger pipe from the supplier data.
Is this a replacement for a hydraulic calculation?
No. It gives a quick estimate for one pipe section. The final design needs a full hydraulic calculation along the whole route and the approval of the authority having jurisdiction.