Pipe Pressure Drop Calculator
Friction, fittings, valves and lift — the head your pump has to deliver, with the working.
Fittings and valves
K values from Crane TP-410 (K = n × fT, fT for clean steel of the same bore). Control valves by their Cv (US gpm at 1 psi) or Kv (m³/h at 1 bar).
Where the pressure goes
| Part | Δp | Head | Share |
|---|
Resistance coefficients
| Item | Qty | K each | K total |
|---|
How it was calculated
Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Pipe Pressure Drop Calculator
Find the pressure lost to friction in a pipe, plus its fittings and valves, and the head a pump must deliver to lift the fluid and overcome those losses. Use Darcy–Weisbach for any liquid or gas — the friction factor comes from 64/Re in laminar flow and from the Colebrook–White equation (or the explicit Swamee–Jain formula) in turbulent flow — or Hazen–Williams for water, in the general SI form or the NFPA 13 form used for sprinkler systems.
Pick a steel pipe by nominal size and schedule (ASME B36.10M) or type the bore; choose the material’s roughness or C factor; add elbows, tees, entrances, exits and isolation valves from the Crane TP-410 resistance coefficients, and control valves by their Cv or Kv. The fluid can be water or steam at any temperature (IAPWS), air, a preset oil or seawater, or anything you describe. The result shows velocity, Reynolds number, friction factor, where every pascal goes, the pump head and power, and each step of the calculation.
How to use it
- Choose the pipe: a steel pipe size and schedule, or the inside diameter. Enter the length of straight pipe, how far the outlet is above the inlet, and any extra pressure needed at the outlet (a pressurised tank, a nozzle).
- Enter the flow as a volume flow, a velocity or a mass flow, and pick the fluid with its temperature (and pressure for air).
- Choose the method: Darcy–Weisbach with a material roughness, or Hazen–Williams with a C factor for water.
- Add the fittings and valves with how many of each. Their K values follow the pipe size; choose “Other” to type your own K, or add a control valve by Cv or Kv.
- Read the pressure loss, the pump head and power, and the table of where the pressure goes. Download it as CSV or copy the summary.
Examples
Bore 52.50 mm, ε = 0.045 mm
V = 1.28 m/s, Re = 67,100, f = 0.0227 (Colebrook) → 35.5 kPa (3.63 m) of friction loss
f_T = 0.0189, ΣK = 4.25
Fittings add 3.50 kPa (the loss of 9.8 m of pipe): 39.0 kPa in all. Lifting 20 m as well needs a 24.0 m pump head — 652 W into the water, 1.0 kW at the shaft at 65 % efficiency
Hazen–Williams with C = 120: 19.4 kPa. Darcy–Weisbach with clean steel (ε = 0.045 mm): 14.1 kPa — C = 120 describes pipe that has been in service a while
0.0098 psi per foot, 0.98 psi per 100 ft
Common uses
- Sizing a pump for a cooling-water, irrigation or transfer line
- Checking a sprinkler or fire-main branch with NFPA 13 Hazen–Williams
- Seeing whether a bigger pipe or fewer fittings would save pump power
- Estimating the drop across a control valve from its Cv or Kv
Formulas
- Darcy–Weisbach: Δp = f (L ÷ D) ρV² ÷ 2, head loss h = Δp ÷ (ρg)
- Laminar (Re < 2,300): f = 64 ÷ Re
- Colebrook–White: 1 ÷ √f = −2 log₁₀(ε ÷ 3.7D + 2.51 ÷ (Re √f)), solved by iteration
- Swamee–Jain: f = 0.25 ÷ [log₁₀(ε ÷ 3.7D + 5.74 ÷ Re^0.9)]², within about 1 % of Colebrook for 5,000 < Re < 10⁸
- Hazen–Williams (SI): h_f = 10.67 L Q^1.852 ÷ (C^1.852 D^4.8704); NFPA 13: p = 4.52 Q^1.85 ÷ (C^1.85 d^4.87) psi/ft with Q in gpm and d in inches
- Fittings: Δp = K ρV² ÷ 2 with K = n f_T (Crane), f_T = 0.25 ÷ [log₁₀(ε_steel ÷ 3.7D)]²
- Control valves: Δp = (ρ ÷ 1000) (Q ÷ Kv)² bar with Q in m³/h, or (Q ÷ Cv)² psi with Q in US gpm; Kv = 0.865 Cv
- Pump head: H = Δz + h_loss + Δp_outlet ÷ (ρg); hydraulic power P = ρ g Q H
Fittings and the Crane method
Crane Technical Paper 410 gives each fitting a resistance coefficient as a multiple of f_T, the friction factor of clean commercial steel pipe of the same size in fully turbulent flow — for example 30 f_T for a standard threaded 90° elbow, 14 f_T for a long-radius elbow, 20 f_T for flow through a tee’s run and 60 f_T through its branch, 8 f_T for an open gate valve, 340 f_T for a globe valve and 100 f_T for a swing check valve. Entrances and exits have fixed values (0.5 for a sharp entrance, 1.0 for discharge into a tank). This calculator works out f_T from the bore; Crane also tabulates it by nominal size (0.019 for 2″, 0.015 for 6″).
Choosing roughness and C
Roughness values are Moody’s for clean new pipe: 0.045 mm for commercial steel, 0.15 mm galvanised iron, 0.26 mm cast iron, 0.0015 mm drawn tubing and plastics. Pipes roughen with age, scale and corrosion, which raises the friction loss — enter a larger ε for old pipe. The C factors listed are those NFPA 13 sets for sprinkler pipe (120 for black or galvanised steel in wet systems, 100 in dry systems, 150 for plastic and copper, 140 for cement-lined iron). The 2022 edition also lets a dry system kept under nitrogen from a listed, permanently installed nitrogen generator use 120, under the conditions it sets — enter 120 as your own C if that applies.
Sources
- Colebrook, C. F. (1939), Turbulent flow in pipes, J. Inst. Civil Eng. 11: 133–156
- Swamee, P. K. & Jain, A. K. (1976), J. Hydraulics Div. ASCE 102(5): 657–664
- Moody, L. F. (1944), Friction factors for pipe flow, Trans. ASME 66: 671–684
- Crane Co., Flow of Fluids through Valves, Fittings and Pipe, Technical Paper No. 410
- ANSI/ISA-75.01.01 / IEC 60534-2-1 (valve flow coefficients Cv and Kv)
- Williams & Hazen, Hydraulic Tables; NFPA 13 (2022), chapter 28 (hydraulic calculations)
- ASME B36.10M (steel pipe dimensions)
Limitations
- Incompressible flow: for gases and steam the result is only reliable while the loss is under about 10 % of the inlet pressure (the page warns above that), and it does not handle choked flow.
- One pipe size at a time. Networks, parallel branches and multi-segment runs with different diameters are not solved here.
- K values are representative; real fittings vary by make and size, and fittings close together interact. Valve-maker data should be used where it is available.
- Two-phase flow, slurries and non-Newtonian fluids are outside these methods. Results are estimates, not a design — have a qualified engineer check pumping and pressure systems.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I calculate the pressure drop in a pipe?
With Darcy–Weisbach: Δp = f (L/D) ρV²/2. Find the velocity from the flow, the Reynolds number Re = VD/ν (see the Reynolds number calculator), the friction factor from Re and the relative roughness ε/D (64/Re if laminar, Colebrook–White if turbulent), then add K × ρV²/2 for the fittings. The calculator does each step and shows the numbers.
Darcy–Weisbach or Hazen–Williams?
Darcy–Weisbach is physically based and works for any fluid, temperature and flow regime. Hazen–Williams is an empirical formula for cold water in turbulent flow; it is quick and is required by NFPA 13 for sprinkler calculations, but it should not be used for hot water, oils or gases.
What is the friction factor of a pipe?
The Darcy friction factor f is the dimensionless number in Δp = f (L/D) ρV²/2. It is 64/Re for laminar flow; in turbulent flow it depends on Re and ε/D and typically lies between 0.01 and 0.05. Note that some texts use the Fanning factor, which is a quarter of the Darcy value.
How do I include elbows and valves?
Each fitting adds K velocity heads: Δp = K ρV²/2. Add them in the fittings list — the K values follow Crane TP-410 and change with the pipe size through f_T. The table also gives the equivalent length of straight pipe that would lose the same.
What pump head do I need?
The height the fluid is lifted, plus all the friction and fitting losses expressed as head, plus any extra pressure needed at the outlet: H = Δz + h_loss + Δp ÷ (ρg). Add a margin and check the pump curve; the shaft power is ρgQH divided by the pump efficiency.
How do Cv and Kv work?
Kv is the flow in m³/h of water that gives a 1 bar drop across the valve; Cv is the flow in US gpm that gives 1 psi. The drop at another flow is (Q ÷ Kv)² bar (or (Q ÷ Cv)² psi) times the fluid’s relative density. Kv = 0.865 Cv.