Pipe pressure drop per Darcy-Weisbach
Compute the pressure drop of a pipe from medium, inner diameter, length, roughness and flow: Reynolds number and flow regime, friction factor λ per Colebrook-White, straight-run loss, minor losses via ζ values and the static head add up to the total pressure drop in bar, mbar, Pa and metres of head.
Pipe pressure drop calculator (Darcy-Weisbach)
Roughness, ζ values and velocity recommendations are guide values with real scatter; manufacturer data takes precedence.
Flow and λ
- Velocity v̄
- 2 m/s
- Volume flow V̇
- 15.88 m³/h
- Reynolds number Re
- 105,578
- Relative roughness k/d
- 0.00094
- Friction factor λ
- 0.0219
- Method
- Colebrook
λ method comparison
- Colebrook
- 0.0219
- Haaland
- 0.0217
- Swamee-Jain
- 0.022
- Dynamic pressure p_dyn
- 1,996 Pa
Pressure drop
- Friction Δp_friction
- 0.8234 bar
- Minor losses Δp_minor
- 0 bar
- Static Δp_stat
- 0 bar
- Total Δp_total
- 0.8234 bar
- Total Δp_total
- 823 mbar
- Head h
- 8.41 m
System curve: pressure drop over volume flow with operating point
Formulas and fundamentals
Continuity and velocity: Volume flow V̇, mean velocity v̄ and inner diameter d are linked through the circular area A = π/4·d²: v̄ = V̇/A. The calculator takes two of the three quantities (switch between volume flow and velocity) and derives the third. What matters is the inner diameter, not the nominal size: a DN50 threaded pipe has an inner diameter of about 53 mm.
Reynolds number and flow regime: The Reynolds number Re = v̄·d/ν sets the flow state. Below Re ≈ 2300 the flow is laminar, above roughly 4000 it is turbulent, and in between lies an unstable transition range where λ cannot be given reliably. The kinematic viscosity ν is strongly temperature dependent; for water it falls from about 1.79 mm²/s at 0 °C to about 0.29 mm²/s at 100 °C, which is why the calculator tracks the fluid temperature.
Friction factor λ: In the laminar range λ = 64/Re is exact (Hagen-Poiseuille). In the turbulent range the calculator solves the implicit Colebrook-White equation 1/√λ = −2·log₁₀(2.51/(Re·√λ) + (k/d)/3.71) iteratively as a fixed point in x = 1/√λ, seeded from the Haaland approximation and stopped when the change falls below 1e-10. The explicit Haaland and Swamee-Jain formulas are shown for comparison; their deviation from Colebrook is typically below 1 to 2 percent, well within the scatter of the roughness.
Straight-run loss and minor losses: The friction loss of the straight run follows from the Darcy-Weisbach equation Δp = λ·(L/d)·(ρ/2)·v̄². Fittings such as bends, tees, valves and inlets/outlets are captured through the ζ method Δp = Σζ·(ρ/2)·v̄²; the calculator sums n·ζ over all minor losses. As an intuitive alternative the equivalent length L_eq = Σζ·d/λ can be stated, i.e. the length of straight pipe that produces the same loss.
Total pressure drop and head: The static share of a height difference Δz is Δp_stat = ρ·g·Δz. The total pressure drop Δp_total = Δp_friction + Δp_minor + Δp_stat is reported in bar, mbar, Pa and as head h = Δp_total/(ρ·g). A traffic light compares the velocity with the recommended range of the chosen application (for example suction, pressure or return line) to surface cavitation and noise risks early.
Worked example
Water example: For water at 20 °C (ρ = 998.2 kg/m³, ν = 1.004 mm²/s) in a new steel pipe DN50 (d = 53 mm, k = 0.045 mm) at v̄ = 2 m/s the Reynolds number is Re = 2·0.05/1.004e-6 ≈ 99600, hence turbulent. Colebrook yields λ = 0.0218 (Haaland 0.0216, Swamee-Jain 0.0220 as a cross-check). Over L = 100 m the straight-run loss is Δp = 0.0218·(100/0.05)·(998.2/2)·2² ≈ 87200 Pa, about 0.87 bar at a gradient of roughly 872 Pa per metre.
Example with minor losses: The same line over just 20 m with a sharp-edged inlet (ζ = 0.5), four 90° bends at R/d = 1.5 (ζ = 0.3), two open gate valves (ζ = 0.2) and an outlet (ζ = 1.0) gives Σζ = 3.1. At p_dyn = 1996 Pa the friction loss is about 17400 Pa and the minor loss Δp_minor = 3.1·1996 ≈ 6190 Pa, together roughly 23600 Pa or 0.236 bar. The fittings act like L_eq = 3.1·0.05/0.0218 ≈ 7.1 m of extra pipe.
Frequently asked questions
Which diameter goes into the calculator, DN or inner diameter?
The inner diameter d. The nominal size DN is only a size class and differs from the clear inner diameter. A threaded pipe DN50 per EN 10255-M measures 53.0 mm inside, not 50 mm. You can either enter the inner diameter directly or preset it via the DN selection; for precision or pressure pipes of other series, enter the inner diameter directly.
Why do Colebrook, Haaland and Swamee-Jain differ?
All three describe the same friction factor in the turbulent range. Colebrook-White is the implicit reference equation and must be solved iteratively; Haaland and Swamee-Jain are explicit approximations that need no iteration. Their deviation from Colebrook is usually below 1 to 2 percent, far below the uncertainty of the roughness k. The calculator uses Colebrook by default and shows the other two as a check.
How accurate are the roughness and ζ values?
They are guide values with real scatter. Roughness depends on manufacturing, ageing, scaling and corrosion and can change by a large factor in service; ζ values scatter by ±30 to 50 percent depending on design and approach flow. For hydraulically smooth pipes such as copper or plastic the result is nearly independent of roughness, whereas for rusty steel or cast-iron pipes the uncertain roughness dominates. Manufacturer data and measured Kv values take precedence.
What does the transition range between Re 2300 and 4000 mean?
There the flow switches between laminar and turbulent and is physically unstable. A friction factor cannot be given reliably in this range. The calculator flags this state as uncertain and continues conservatively with the turbulent formula. For a robust design the operating point should ideally not sit in the transition range.
Does the calculator also apply to air and other gases?
Yes, as long as the pressure change stays small. The calculation assumes incompressible flow, which holds for gases only at small relative pressure change (rule of thumb Δp below about 10 percent of the absolute pressure). For larger pressure drops or high Mach numbers a compressible calculation is required. The air properties in the calculator apply to about 20 °C and 1 bar.
Why is a velocity traffic light useful?
Excessive velocities drive the pressure drop up quadratically and cause noise and erosion, while too low velocities lead to oversized pipes and, in suction lines, to deposits. In suction lines an excessive velocity can also drop the pressure below the vapour pressure and trigger cavitation. The traffic light compares the computed velocity with the experience ranges of the chosen application and warns early.