Pipe Friction Factor and Pressure Drop Calculator

Darcy friction factor, pressure drop, head loss, wall shear stress and pumping power for a pipe, duct or annulus — with the friction factor chosen by measurement rather than reputation, the exact laminar constant for non-round sections, and an explicit refusal to give a single number in the transitional band. For engineers sizing a line or validating a CFD pressure drop.

Last updated 30 Sep 2026

Friction factor, pressure drop, head loss and wall shear

section, flow, length, fluid and roughness → f, Δp, h_f and τ_w

SectionThe section fixes the hydraulic diameter, the flow area and — this is the part usually missed — the laminar friction constant, which is 64 only for a round pipe. Use the last option for a bundle, a finned passage or anything else; take D_h and A from the hydraulic diameter calculator.

First dimension (m)Round pipe: the bore D. Rectangular duct: the long side a. Square duct: the side a. Annulus: the OUTER bore D_o. Last option: the hydraulic diameter D_h itself.

Second dimension (m), or the flow area (m²)Rectangular duct: the short side b, in metres. Annulus: the INNER tube outside diameter D_i, in metres. Last option: the flow AREA in square metres, which is what turns a flow rate into a velocity. Grey for a round pipe and a square duct.

How the flow is givenAll five routes end at the same bulk mean velocity, Q/A. If you give a velocity, make it the bulk mean — volumetric flow divided by area — and not the centreline value, which is exactly twice the mean in laminar pipe flow and about 1.2 times it in turbulent.

Bulk mean velocity (m/s)Read only when the flow is given as a velocity. Grey otherwise.

Flow rate, in the unit chosen aboveRead only when the flow is given as a rate. The unit is whichever one the selector above names — m³/s, m³/h, litres per second or kilograms per second. Grey when you are entering a velocity.

Straight length L (m)The developed length of straight pipe. Bends, valves, tees, entries and exits are minor losses and are NOT in this figure — add them separately as K·ρV²/2, or as an equivalent length. For a long pipeline the friction term dominates; for a short run full of fittings it does not.

FluidThe five presets are identical to those on the Reynolds number page, so the two pages cannot disagree. Density matters here as well as viscosity, because the pressure drop is proportional to it while the Reynolds number is not.

If you are entering your own fluid, which viscosityRead only when the fluid is Other. Both routes give the same answer because ν = μ/ρ. The commonest unit error here is a factor of a thousand: 1 cP = 10⁻³ Pa·s and 1 cSt = 10⁻⁶ m²/s.

Kinematic viscosity ν (m²/s)Read only when the fluid is Other and the mode above is kinematic. Grey otherwise.

Dynamic viscosity μ (Pa·s)Read only when the fluid is Other and the mode above is dynamic. Grey otherwise.

Density ρ (kg/m³)Read only when the fluid is Other. The pressure drop is directly proportional to it. Grey otherwise.

Wall roughnessThe first six are from the US EPA’s EPANET 2.2 documentation, which lists them in thousandths of a foot; the values here are those figures converted, not retyped from a chart. The last four are the Moody ladder as reproduced in Perry’s, and every one of them is an exact round number of feet, which is the check that the conversion is right. Roughness matters much less than people expect: see the note under the result.

Custom roughness ε (mm)Read only when the preset above is Custom. Enter the equivalent sand-grain roughness in millimetres, which is what Colebrook and Haaland were calibrated in and what a solver’s rough-wall option asks for. It is NOT an Ra surface-finish figure: sand-grain roughness for a machined surface runs several times the Ra value. Zero is accepted and gives the smooth-wall result.

Elevation change, outlet minus inlet (m)Positive for uphill. Elevation is NOT in the headline figure, which is friction alone; it is added into the total pressure change and the pumping power below. For a liquid a 10 m rise is about 0.98 bar; for air it is 0.12 mbar and almost always negligible.

Pump or fan efficiency (%)Used only to turn hydraulic power into shaft power. 70 to 85 per cent for a decent centrifugal pump at its duty point, 50 to 70 for a small one or one running off design, 60 to 80 for a centrifugal fan.

51.56kPaExample

Water at 20 °C at 2 m/s in a 100 mm new cast iron pipe, 100 m long, level

Darcy–Weisbach, and the three branches of the friction factor

Δp = f · (L/D_h) · ρU²/2 · h_f = Δp/ρg · τ_w = fρU²/8 · u_τ = U√(f/8) · laminar: f = C/Re · turbulent (Haaland): 1/√f = −1.8 log₁₀[(ε/3.7D_h)^1.11 + 6.9/Re] · fully rough: 1/√f = 2 log₁₀(3.7D_h/ε)

f: Darcy–Weisbach friction factor. Four times the Fanning friction factor, which is what most chemical-engineering sources use — a factor-of-four error here is as common as the hydraulic diameter one
C: the laminar friction constant for the section: 64 for a round pipe, 56.908 for a square duct, 96 between parallel plates, and the exact value for a rectangle or annulus. Shape only, no fluid property
ε: equivalent sand-grain roughness, the quantity Nikuradse measured and Colebrook and Haaland were calibrated against. NOT an Ra surface finish: sand-grain roughness runs several times Ra for a machined surface
ε⁺: roughness Reynolds number, ε·uτ/ν. Under 5 the roughness is inside the viscous sublayer; over 70 it projects clear of it and f stops depending on Re. This, not ε/D, is what decides which regime you are in
U: bulk mean velocity, Q/A. Not the centreline value, which is twice the mean in laminar pipe flow
τ_w: wall shear stress. Follows from a force balance on the fluid column: τ_w·πDL = Δp·πD²/4, which gives τ_w = Δp·D/4L = fρU²/8 with no further assumption
h_f: head loss in metres OF THE FLOWING FLUID. Converting to metres of water requires the density ratio, which is where most of the confusion with mercury and water manometers comes from

Worked example

Water at 20 °C at 2 m/s in a 100 mm new cast iron pipe, 100 m long, level
Re = U·D/ν = 2 × 0.1/1.004×10⁻⁶ = 199,203, so turbulent, and comfortably clear of the transitional band. The relative roughness is ε/D = 0.259/100 = 2.591×10⁻³, taking ε = 0.259 mm for new cast iron from the EPA's EPANET table (0.85×10⁻³ ft)
Haaland: 1/√f = −1.8 log₁₀[(2.591×10⁻³/3.7)^1.11 + 6.9/199203] = 6.2216, so f = 0.025834. Iterating Colebrook to convergence on the same inputs gives 0.025869, so Haaland is 0.14 per cent low here. Swamee–Jain would give 0.026047, 0.69 per cent high — five times further out at this point, and 3.36 per cent out at the worst point in the page's range against Haaland's 1.42 per cent, which is why the page uses Haaland
Δp = f(L/D)(ρU²/2) = 0.025834 × (100/0.1) × (998 × 4/2) = 51,564 Pa = 0.5156 bar = 7.48 psi. As head loss that is Δp/ρg = 51564/(998 × 9.80665) = 5.268 m of water, or 5.27 m per 100 m of pipe — which is about five times the 1 m per 100 m that water-distribution practice aims at, so this pipe is being pushed hard
THE WALL SHEAR, which is the number that links this page to a mesh. τ_w = fρU²/8 = 0.025834 × 998 × 4/8 = 12.89 Pa, so uτ = √(τ_w/ρ) = 0.1137 m/s and the first cell height for y+ = 1 is ν/uτ = 8.83 µm. Note what that means for a rough pipe: the roughness height is 259 µm, 29 times the cell you would need for y+ = 1. A wall-resolved mesh on a rough wall is geometrically incoherent unless you actually mesh the roughness, which is why rough walls are handled by a wall function with an equivalent sand-grain height instead
AND THE REGIME THAT ACTUALLY MATTERS. ε⁺ = ε·uτ/ν = 0.000259 × 0.1137/1.004×10⁻⁶ = 29.3, which puts this pipe in the transitionally rough band between 5 and 70 — where f depends on both the Reynolds number and the roughness and neither asymptote applies. That is where most real pipework lives. The fully rough asymptote for this ε/D is 1/(2 log₁₀(3.7/2.591×10⁻³))² = 0.025119, only 2.9 per cent below the Colebrook value, so this pipe is close to fully rough but not quite there
HOW MUCH THE ROUGHNESS DID. Run the same case perfectly smooth and Haaland gives f = 0.015513, so the 0.259 mm of cast iron roughness has raised the friction factor by 66.5 per cent. Change to new commercial steel at 0.046 mm and f falls to 0.018416, a 28.7 per cent reduction in pressure drop for a change in roughness of a factor of 5.67. Roughness is not a second-order effect in this band, and the sign of the sensitivity is what matters: a corroded pipe gets worse fast. Corrosion products and scale raise the roughness of steel by a factor of several, and heavy tuberculation by an order of magnitude or more, so the table value is for the pipe as delivered and not for the pipe you have
THE POWER. Q = U·A = 2 × π(0.1²)/4 = 0.015708 m³/s = 56.5 m³/h, so the hydraulic power spent on friction is QΔp = 810 W, and at 70 per cent pump efficiency the shaft power is 1,157 W. Running continuously that is 10.1 MWh a year, and since the friction power goes as very nearly the cube of the flow rate — the measured local exponent here is 2.97, because f falls a little as the velocity rises — a 10 per cent reduction in flow saves 26.9 per cent of that
AND THE DEVELOPED-FLOW CHECK. The turbulent entry length is 4.4·Re^(1/6)·D = 3.4 m, or 34 diameters. The 100 m pipe is far longer than that, so the developed-flow friction factor is the right one; but if you were simulating only a 2 m length of this pipe with a flat inlet profile you would be computing the development and not the developed flow, and your friction factor would come out high

Which explicit friction correlation to use — measured, not asserted

Every figure in the second column was measured here, not taken from a paper: Colebrook was iterated to a residual below 2×10⁻¹⁵ on a grid of 73 Reynolds numbers from 4×10³ to 10⁸ and 39 relative roughnesses from 0 to 0.05, and each explicit form was compared at every point. Haaland wins by a factor of 2.4 on worst-case error, and it wins over Swamee–Jain’s own stated domain as well, so the choice is not an artefact of testing it outside its range. Reputation would have picked either; measurement picks Haaland.
Correlation	Worst error against converged Colebrook	Where the worst case is	Verdict
Haaland (1983)	1.42 %	Re = 9.1×10⁴, ε/D = 2.4×10⁻⁴	used by this page
Swamee–Jain (1976)	3.36 %	Re = 4,000, ε/D = 0.024	rejected — 2.4 times worse
Swamee–Jain, inside its own stated domain	2.77 %	Re = 5,000, ε/D = 8.8×10⁻³	still worse than Haaland over the same domain (1.42 %)
Petukhov (smooth wall only)	3.84 %	Re = 4,000, smooth	printed for comparison; has no roughness term
Blasius 0.3164 Re^(−1/4) (smooth only)	46.7 % low	Re = 10⁸, smooth	useful only below Re ≈ 10⁵
von Kármán fully rough	under 1 % once ε⁺ exceeds 50 to 80	n/a	exact asymptote, printed as a check

Roughness values used, with their sources and the identity that checks them

The identity that must hold, and does: every value in the third column is an exact round number of feet, and every figure in the second column is that number times 304.8 mm/ft. Two independent sources — a US Government water-network model and a chemical-engineering handbook — give the same ladder, which is how you know neither has a shifted column. They are all the Moody 1944 values in the end. None of them is a property of the material alone: a pipe’s roughness is set by its condition, its joints and its age at least as much as by what it is made of, and the honest use of this table is as a factor-of-two starting point.
Material	ε (mm)	As printed by the source	Source
Plastic, drawn tubing, glass	0.00152	0.005 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Commercial steel or wrought iron, new	0.0457	0.15 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Galvanised iron	0.152	0.5 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Cast iron, new	0.259	0.85 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Concrete, smooth steel forms	0.305	1.0 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Concrete, rough	3.05	10 × 10⁻³ ft	US EPA, EPANET 2.2 documentation
Asphalt-dipped cast iron	0.122	0.0004 ft	Perry’s Chemical Engineers’ Handbook
Wood stave, new	0.183	0.0006 ft	Perry’s Chemical Engineers’ Handbook
Riveted steel	0.914	0.003 ft	Perry’s Chemical Engineers’ Handbook
Riveted steel, rough	9.14	0.03 ft	Perry’s Chemical Engineers’ Handbook

What the roughness Reynolds number ε⁺ actually decides

The 5 and 70 boundaries come from Nikuradse’s sand-grain experiments, and the upper one holds up well: Colebrook reaches within 1 per cent of the fully rough asymptote at ε⁺ between 50 and 80 across ε/D from 10⁻⁵ to 10⁻², measured here. The lower one does not mean what its name suggests. Colebrook’s function has no smooth plateau at all — its roughness term ε/3.7D is additive at every Reynolds number — so by ε⁺ = 5 a converged Colebrook solution is already 14 to 31 per cent above the true smooth-wall value. If you need Colebrook to agree with the smooth-wall value you need ε⁺ below about 0.25 to 0.4. Nikuradse’s own data do have a plateau; Colebrook deliberately smeared the transition to fit commercial pipe, and this is the price.
ε⁺	Classical name	What Colebrook does there	What to do in CFD
under about 0.3	hydraulically smooth	within 2 % of the smooth-wall value	smooth wall; roughness option pointless
about 0.3 to 5	still called smooth	already 2 % to 31 % above the smooth value	smooth wall is defensible; know you are losing a little
5 to 70	transitionally rough	depends on Re and ε/D together; no asymptote applies	rough wall function with your own sand-grain height; first cell must be bigger than ε
70 to 1000	fully rough	within 1 % of the ε/D-only asymptote	rough wall function; f and Δp now scale exactly as U²
above 1000	fully rough, large elements	asymptote still holds; ε/D may be past Colebrook’s fitted range	consider resolving the roughness geometrically instead

The transitional band, as a range rather than a number

This is why the page refuses to give one number in this band. There is no interpolation that can be defended: the flow is genuinely intermittent, and which value you get depends on the entry, the upstream fittings, the wall condition and the ambient vibration rather than on anything in the inputs above. The page reports the turbulent branch, which is the upper bound, and prints the laminar branch beside it as the lower bound. If a design sits here, the useful engineering move is not a better correlation — it is changing the pipe size or the duty point until the flow is on one side or the other.
Reynolds number	Laminar branch 64/Re	Haaland at ε/D = 10⁻³	Ratio	Δp uncertainty
2,300	0.02783	0.04910	1.76	a factor of 1.8 either way
2,800	0.02286	0.04603	2.01	a factor of 2.0
3,200	0.02000	0.04412	2.21	a factor of 2.2
3,600	0.01778	0.04255	2.39	a factor of 2.4
4,000	0.01600	0.04122	2.58	a factor of 2.6

Choosing the friction factor by measurement, and the two thresholds that do not survive it

The friction factor is where this calculation is won or lost, and it has three branches, not one. Below Re = 2,300 it is exact: f = C/Re, with C fixed by the shape of the section and nothing else. Above Re = 4,000 it is correlated, and the correlation has to handle roughness. Between the two there is a band where no correlation is reliable and the honest output is a range. Everything else on this page — pressure drop, head loss, wall shear, pumping power — is arithmetic once f is settled, so f is the only part worth arguing about.

Colebrook is implicit, so this page uses Haaland — and the choice was measured rather than assumed. The Colebrook–White equation, 1/√f = −2 log₁₀[ε/3.7D + 2.51/(Re√f)], has f on both sides and needs iteration, which is not available here. The two standard explicit alternatives are Haaland and Swamee–Jain, and the usual way to choose between them is by reputation. Instead: Colebrook was iterated to a residual below 2×10⁻¹⁵ over a grid of 73 Reynolds numbers from 4×10³ to 10⁸ and 39 relative roughnesses from 0 to 0.05, and both explicit forms were compared at every point. Haaland’s worst error is 1.42 per cent, at Re = 9.1×10⁴ and ε/D = 2.4×10⁻⁴. Swamee–Jain’s worst is 3.36 per cent, at Re = 4,000 and ε/D = 0.024. Restricting the comparison to Swamee–Jain’s own published domain (Re from 5,000 to 10⁸, ε/D from 10⁻⁶ to 10⁻²) does not rescue it: 2.77 per cent against Haaland’s 1.42 per cent over the same domain. So Haaland, by a factor of 2.4, and the page says so rather than asking you to take it on trust.

One correlation, not two, and that is a deliberate departure. The obvious alternative is to use Petukhov’s f = (0.79 ln Re − 1.64)⁻² for a smooth wall and Haaland when the wall is rough, which is what the y+ first cell height calculator does. Two reasons not to. First, it puts a seam at ε = 0 where the answer jumps: at Re = 4,000 the two forms differ by 2.5 per cent. Second, and more to the point, the measurement does not support Petukhov being the better of the two even at a smooth wall. Against a converged Colebrook at ε = 0, Petukhov is 3.84 per cent high at Re = 4,000 and 1.93 per cent high at 10⁴, and it comes inside ±1.2 per cent only above Re of about 1.7×10⁴; Haaland’s worst over the whole smooth range 4×10³ to 10⁸ is 1.30 per cent. Petukhov is excellent in the middle of its range and the best of the three from Re = 10⁵ to 10⁶, where it is within 0.2 per cent. This page prints it beside the Haaland value so the difference is visible rather than hidden, and the two pages will differ by at most about 1 per cent in f, which is half that in the friction velocity and therefore in a first-cell height.

The laminar branch is not 64/Re unless your section is round. This is the most common quiet error in a duct pressure drop. Fully developed laminar flow satisfies a Poisson equation over the section, so f = C/Re exactly, with C a pure number: 64 for a circle, 56.908 for a square duct, exactly 96 between parallel plates, 72.93 for a 4:1 rectangle, 95.25 for an annulus with a half-diameter inner tube. Using 64 for a square duct overpredicts friction by 12.5 per cent; using it between parallel plates underpredicts by 33.3 per cent. This page uses the exact constant for the section you chose, and the hydraulic diameter calculator prints it for any section along with the error you would have made. Roughness, meanwhile, does nothing at all in laminar flow: the roughness selector above has no effect below Re = 2,300, and that is correct rather than an oversight.

The transitional band gets a range, not a number. Between Re = 2,300 and 4,000 the flow is intermittent — turbulent slugs alternating with laminar stretches — and the friction factor is not even single-valued: it depends on the entry geometry, the upstream fittings, the wall condition and the vibration of the installation. Interpolating between the laminar and turbulent branches would produce a confident-looking number with no basis, so this page does not. It reports the turbulent branch, which is the upper bound, flags it as such, and prints the laminar branch and the pressure drop it implies as the lower bound. The two differ by a factor of 1.76 at Re = 2,300 rising to 2.58 at Re = 4,000 for a typical roughness. If a design sits in this band, the engineering answer is to move it out of the band, not to find a better correlation.

ε⁺, not ε/D, is what decides whether roughness matters — and one of its two classical thresholds does not survive checking. The roughness Reynolds number ε⁺ = εu_τ/ν compares the roughness height with the thickness of the viscous sublayer, and it is the quantity the regime is actually defined on. Nikuradse’s sand-grain data give ε⁺ under 5 for hydraulically smooth and over 70 for fully rough. The upper threshold holds up well: measured here, Colebrook comes within 1 per cent of its own fully rough asymptote at ε⁺ between 50 and 80 across ε/D from 10⁻⁵ to 10⁻². The lower one does not mean what its name suggests. Colebrook’s function contains the term ε/3.7D additively at every Reynolds number, so it has no smooth plateau at all: at ε⁺ = 5 a converged Colebrook solution already sits 14 to 31 per cent above the true smooth-wall value, and it is within 2 per cent of smooth only below ε⁺ of about 0.25 to 0.4. Nikuradse’s own data do have a plateau; Colebrook smeared the transition deliberately to fit commercial pipe, and this is what that costs. So “hydraulically smooth” on a Moody chart is a statement about naming, not about the value of f.

What this means for a mesh, which is the reason a CFD engineer is here. The wall shear follows from a force balance with no further assumption: τ_w = Δp·D/4L = fρU²/8, so u_τ = U√(f/8) and the first cell height for y+ = 1 is ν/u_τ. Both are printed above. Now put the roughness beside that number. In the worked example the roughness height is 259 µm and the y+ = 1 cell height is 8.8 µm — the roughness is 29 times the cell. A wall-resolved mesh on a rough wall is geometrically incoherent unless you mesh the roughness itself, because the first cell would sit inside the bumps it is meant to be resolving. That is why rough walls are handled by a wall function with an equivalent sand-grain height, and why a rough-wall run has a minimum sensible y+ rather than a target of 1. Take the cell height from the y+ page and the layer stack from the prism layer calculator, and check both against the roughness printed here.

What is not in this number. Minor losses: bends, valves, tees, expansions, contractions, entries and exits. In a long pipeline they are a correction; in a short run with a dozen fittings they are the whole answer, and no amount of care with f will help. Two-phase flow, non-Newtonian fluids and compressible flow with significant density change along the pipe are all outside this: for compressible flow with a pressure ratio beyond a few per cent, the density and velocity vary along the length and the calculation has to be marched rather than done once. And the roughness of a real pipe is a property of its condition rather than its material — corrosion products and scale raise the roughness of steel by a factor of several and heavy tuberculation by an order of magnitude or more, so a 20-year-old line is not the pipe in the table.

Frequently asked questions

Haaland or Swamee–Jain?

Haaland, and the reason is measurement rather than preference. Against a converged Colebrook solution over Re from 4×10³ to 10⁸ and ε/D from 0 to 0.05, Haaland’s worst error is 1.42 per cent and Swamee–Jain’s is 3.36 per cent — a factor of 2.4. Swamee–Jain does not improve enough inside its own published domain either: 2.77 per cent against Haaland’s 1.42 per cent over the same domain. Swamee–Jain’s error is almost entirely at the low-Reynolds end, where it runs high; if your work is all above Re = 10⁵ the two are within a few tenths of a per cent of each other and it does not matter which you use.

Why does this page use Haaland when the y+ page uses Petukhov?

Because Petukhov has no roughness term and this page needs one, and because using two correlations would put a seam at ε = 0. The practical size of the disagreement is small: with the roughness set to zero the two differ by at most about 1.3 per cent in f over Re = 4×10³ to 10⁸, which is 0.65 per cent in the friction velocity and therefore in a first-cell height. Both values are printed here so you can see the gap. Worth knowing which is better where: Petukhov is the best of the three from Re = 10⁵ to 10⁶, within 0.2 per cent of Colebrook, and the worst of the three at Re = 4,000, where it is 3.84 per cent high — it comes inside ±1.2 per cent only above Re of about 1.7×10⁴.

Is the friction factor Darcy or Fanning?

Darcy–Weisbach throughout, which is four times the Fanning friction factor. The laminar value is 64/Re in Darcy and 16/Re in Fanning; the wall shear is fρU²/8 in Darcy and fρU²/2 in Fanning. Most mechanical and civil sources use Darcy and most chemical-engineering sources use Fanning, and a factor-of-four discrepancy in a pressure drop is almost always this. If a source quotes a smooth-pipe friction factor of about 0.005 at Re = 10⁵ it is Fanning; about 0.018 and it is Darcy.

Why does roughness do nothing when my flow is laminar?

Because that is the physics, not a limitation of the page. In laminar flow the fluid follows the contour of the wall and there is no turbulent sublayer for a roughness element to protrude through, so as long as the roughness is small compared with the passage the pressure drop is set entirely by viscosity and the geometry. Measurements confirm it for ε/D up to a few per cent. The exception is when the roughness stops being small — in a microchannel a 5 µm roughness in a 50 µm passage is a 10 per cent reduction in the effective diameter, and that is a geometry effect rather than a friction one.

What is the difference between ε and Ra, and can I use my drawing tolerance?

They are different quantities and the ratio between them is not fixed. ε is the equivalent sand-grain roughness: the size of Nikuradse’s glued sand grains that would produce the same friction, which is what Colebrook and Haaland were calibrated against and what a solver’s rough-wall option asks for. Ra is the arithmetic mean deviation of the surface profile. For a machined surface ε typically runs several times Ra, because friction is driven by the peaks and Ra averages them away, and the ratio depends on the machining process. If all you have is Ra, treat ε as a few times Ra and carry the uncertainty explicitly; if you have a pressure-drop measurement on the real surface, back ε out of it with this page instead.

How do I add bends and valves?

Separately, as minor losses. Each fitting contributes K·ρU²/2 with K a loss coefficient for that fitting, or equivalently an added length L_eq = K·D/f. This page deliberately does not include them, because K values are strongly dependent on the specific fitting and the manufacturer’s own data are better than any generic table. The proportion matters: for a 100 m pipeline with two bends the friction term dominates completely, while for a 2 m run with a control valve the valve is the entire pressure drop and the pipe friction is noise.

My pipe is short. Does the entry length matter?

Yes, and it matters twice. Physically, the friction factor is higher in the developing region than in developed flow, so a short pipe has a larger pressure drop than f·L/D predicts. Numerically, if you specify a flat velocity profile at a CFD inlet and the domain is shorter than the entry length, you are simulating the development rather than the developed flow, and comparing that against a developed friction factor will look like a solver error when it is a modelling one. The entry length is printed above, both in metres and in hydraulic diameters: about 0.06·Re·D_h laminar, and 4.4·Re^(1/6)·D_h turbulent, which is 20 diameters at Re = 10⁴, 30 at 10⁵, 44 at 10⁶ and 65 at 10⁷.

Can I use this for air in a duct?

Yes, with two cautions. Choose an air preset and the rectangular-duct or square-duct section, and the arithmetic is identical — Darcy–Weisbach does not care what the fluid is. The first caution is compressibility: as long as the total pressure drop is a small fraction of the absolute pressure, under a few per cent, the constant-density calculation is fine; beyond that the density falls along the duct, the velocity rises, and the calculation has to be marched. The second is that ductwork is rougher than the sheet it is made from, because transverse joints, seams and flexible sections each add resistance that no material roughness accounts for.

Why is my CFD pressure drop different from this page?

Work down the list in this order. Is the flow developed in your domain, or shorter than the entry length? Is the wall treatment consistent — a rough wall in the correlation and a smooth wall in the model, or the other way round? Is y+ in the right range for the wall treatment you chose, and is the first cell larger than the roughness if the wall is rough? Is the section non-round and laminar, where 64/Re is wrong by up to a third and your solver is probably the one that is right? Is the Reynolds number in the transitional band, where a 2.6:1 spread is genuine physics rather than error? And only then start looking at mesh convergence, which is where people usually start.

Which number do I give the pump supplier?

The total head or total pressure rise required, which is friction plus elevation plus any static pressure difference between the two ends plus the minor losses — and then say what flow rate it is at, because a pump is selected on a duty point and not on a pressure. This page gives you the friction term and adds elevation into the total; the static difference and the fittings are yours to add. Give the head in metres of the actual fluid being pumped, not metres of water, unless the fluid is water: a pump curve is in metres of fluid and the density cancels, which is exactly why pump curves are drawn in head rather than pressure.

Related calculators

References

C. F. Colebrook and C. M. White, and the resulting Colebrook–White equation 1/√f = −2 log₁₀[ε/3.7D + 2.51/(Re√f)], which is implicit and therefore cannot be evaluated by this page directly. It is nevertheless the reference against which every explicit form here was tested: iterated by fixed-point substitution to a residual below 2×10⁻¹⁵ at every test point. Cited, not reproduced.
S. E. Haaland, Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow, Journal of Fluids Engineering 105 (1983), 89–90, for 1/√f = −1.8 log₁₀[(ε/3.7D)^1.11 + 6.9/Re]. Chosen for this page after measurement, not on reputation. Worst deviation from a converged Colebrook over a grid of 73 Reynolds numbers (4×10³ to 10⁸) and 39 relative roughnesses (0 to 0.05): −1.42 per cent, at Re = 9.1×10⁴ and ε/D = 2.37×10⁻⁴. At a smooth wall its worst is +1.30 per cent, at Re = 9.7×10⁷.
P. K. Swamee and A. K. Jain, Explicit Equations for Pipe-Flow Problems, Journal of the Hydraulics Division 102 (1976), 657–664, for f = 0.25/[log₁₀(ε/3.7D + 5.74/Re^0.9)]². Tested and rejected here. Worst deviation from the same converged Colebrook over the same grid: +3.36 per cent, at Re = 4,000 and ε/D = 0.0235. Restricted to the domain its own authors state (5×10³ ≤ Re ≤ 10⁸, 10⁻⁶ ≤ ε/D ≤ 10⁻²) it is +2.77 per cent at worst, against Haaland’s 1.42 per cent over that same domain. Its error is concentrated at the low-Reynolds end; above Re = 10⁵ the two forms agree to within a few tenths of a per cent.
B. S. Petukhov’s explicit smooth-tube friction factor f = (0.79 ln Re − 1.64)⁻², as printed with the Gnielinski correlation for 3×10³ < Re < 5×10⁶. Printed on this page for comparison with the y+ calculator, which uses it. A correction to the figure quoted elsewhere on this site: measured against a converged Colebrook at a smooth wall, Petukhov is not within 1.2 per cent from Re = 4×10³. It is +3.84 per cent at Re = 4,000, +1.93 per cent at 10⁴, and falls inside ±1.2 per cent only above Re ≈ 1.72×10⁴; from there to 10⁸ it stays inside 1.2 per cent, reaching +0.97 per cent at 10⁸. It is the best of the three explicit forms between Re = 10⁵ and 10⁶, within 0.2 per cent.
US Environmental Protection Agency, EPANET 2.2 User’s Manual, table of roughness coefficients for new pipe, which lists Darcy–Weisbach ε in thousandths of a foot: plastic 0.005, steel 0.15, galvanised iron 0.5, cast iron 0.85, concrete or concrete-lined 1.0 to 10. A US Government work and freely reproducible. The millimetre values on this page are those figures multiplied by 304.8, not retyped from any chart. Cross-checked against the independent ladder in Perry’s (asphalted cast iron 0.0004 ft, wood stave 0.0006 ft, riveted steel 0.003 ft, rough riveted steel 0.03 ft): every value in both sources is an exact round number of feet and the two agree wherever they overlap, which is the identity that shows neither has a shifted column. Both descend from Moody’s 1944 compilation.
J. Nikuradse, Laws of Flow in Rough Pipes, NACA Technical Memorandum 1292 (1950), the US Government translation of the 1933 VDI paper and therefore in the public domain. The source of the equivalent sand-grain roughness concept and of the roughness Reynolds number regime boundaries ε⁺ = 5 and 70 used for the band labels here. The behaviour of Colebrook’s function against those boundaries was measured on this page rather than assumed: within 1 per cent of the fully rough asymptote at ε⁺ of 50 to 80 (supporting 70), but already 14 to 31 per cent above the smooth-wall value at ε⁺ = 5 and within 2 per cent of it only below ε⁺ of about 0.25 to 0.4 (so the lower boundary is a name, not a statement about f).
R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts, for the laminar friction constants f·Re on the hydraulic diameter. Not reproduced: the values used here were recomputed from the exact solutions of ∇²φ = −1 over each section — 64 and 96 analytically, 56.908308 for the square duct from the double sine series, and the annulus from its exact logarithmic solution — and agree with the published tabulation to better than 0.07 per cent. The rectangular-duct polynomial used inside the calculator is fitted to those exact values and is accurate to 0.0102 per cent over the whole aspect-ratio range.
National Institute of Standards and Technology, Special Publication 811: Guide for the Use of the International System of Units, for standard gravity g = 9.80665 m/s² (exact by definition) and the unit conversions used here: 1 psi = 6 894.757 293 Pa and 1 bar = 10⁵ Pa exactly. A US Government work.

Setup guidance, not validation. Correlations have ranges of validity and cell-count estimates are order-of-magnitude. A converged simulation is not a correct one. Full disclaimer at calcengines.com/disclaimer/