Pipe Pressure Drop & Reynolds Number Calculator

Reynolds number and pipe pressure drop

UnitsSIUS customary

Flow rate Q (L/s)Volumetric flow.

Inside diameter D (mm)Actual bore, not nominal size.

Pipe length L (m)Straight pipe only.

Absolute roughness ε (mm)0 for a smooth tube.

Density ρ (kg/m³)At operating temperature.

Dynamic viscosity μ (mPa·s (cP))Water near 20 °C is about 1.0 mPa·s.

Pressure drop Δp

7.358 kPa

Head loss hf

0.7519 m

Reynolds number

50830 (turbulent)

Darcy friction factor f

0.02369

Mean velocity V

1.019 m/s

Relative roughness ε/D

0.0009

Friction factor from the Colebrook–White equation, solved iteratively. Swamee–Jain gives 0.02383 as a check.

Intermediate steps
Step	Formula	Value
Mean velocity	V = Q / (π·D² / 4)	1.019 m/s
Reynolds number	Re = ρ·V·D / μ	50830
Relative roughness	ε / D = 0.045 / 50	0.0009
Friction factor (Colebrook)	1/√f = −2·log10(ε/(3.7D) + 2.51/(Re·√f)), 10 iterations	0.02369
Friction factor (Swamee–Jain check)	f = 0.25 / [log10(ε/(3.7D) + 5.74/Re^0.9)]²	0.02383
Pressure drop	Δp = f·(L/D)·ρV²/2	7.358 kPa
Head loss	hf = Δp / (ρ·g)	0.7519 m

Inputs

Flow rate Q (L/s or US gpm) — Volumetric flow through the pipe.
Inside diameter D (mm or in) — The bore, not the nominal pipe size. Check the wall schedule.
Length L (m or ft) — Straight length of pipe.
Absolute roughness ε (mm or in) — Average wall roughness height. Use 0 for a hydraulically smooth tube.
Density ρ (kg/m³ or lb/ft³) — At the operating temperature.
Dynamic viscosity μ (mPa·s (= cP)) — At the operating temperature. Viscosity changes strongly with temperature for liquids.

Key formulas

Formulas used on this page, with the textbook each is cited from
Formula	Expression	Where	Cited from
Mean velocity	`V = Q / (π·D² / 4)`	full circular pipe	White, Fluid Mechanics
Reynolds number	`Re = ρ·V·D / μ`	laminar below about 2300, turbulent above about 4000	Munson et al., Fundamentals of Fluid Mechanics
Laminar friction factor	`f = 64 / Re`	Re < 2300 (Hagen–Poiseuille flow)	White, Fluid Mechanics
Colebrook–White equation	`1/√f = −2·log10(ε/(3.7·D) + 2.51/(Re·√f))`	implicit in f; solved by fixed-point iteration to 10⁻¹² relative change	Colebrook (1939), Journal of the Institution of Civil Engineers
Swamee–Jain approximation	`f = 0.25 / [log10(ε/(3.7·D) + 5.74/Re^0.9)]²`	explicit; used as the starting value and shown as a check	Swamee & Jain (1976), Journal of the Hydraulics Division, ASCE
Darcy–Weisbach equation	`Δp = f·(L/D)·ρ·V²/2, hf = Δp / (ρ·g)`	f = Darcy (Moody) friction factor, g = 9.80665 m/s²	White, Fluid Mechanics

Assumptions

Steady, incompressible, fully developed flow in a straight, full, circular pipe of constant bore. For gases, keep the pressure drop small compared with the absolute pressure, or split the line into segments.
Major (friction) losses only. Fittings, valves, entrances and exits add minor losses that are not included, and neither is any change in elevation.
The friction factor is the Darcy factor, four times the Fanning factor.
Between Re ≈ 2300 and 4000 the flow can be laminar or turbulent and f is uncertain. The calculator uses Colebrook there and flags the result.
Colebrook was fitted to commercial pipe data and is the basis of the Moody chart. Computed against it, Swamee–Jain stays within 3% over 5000 ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 10⁻², the range its authors give for it.

Worked example

Example: Cooling water through a steel line

Given

Water at about 20 °C, taken as ρ = 998 kg/m³ and μ = 1.0 mPa·s (typical handbook values).
Flow Q = 2 L/s through 30 m of pipe with a 50 mm bore.
Absolute roughness ε = 0.045 mm, a value commonly used for new commercial steel pipe.

Find

The Reynolds number and flow regime.
The Darcy friction factor.
The pressure drop and head loss.

Solution

Find the flow area and mean velocity.A = π × 0.05² / 4 = 1.963 × 10⁻³ m², V = 0.002 / 1.963 × 10⁻³ = 1.019 m/s
Find the Reynolds number. It is well above 4000, so the flow is turbulent.Re = 998 × 1.019 × 0.05 / 0.0010 = 50 830
Find the relative roughness and a starting friction factor from Swamee–Jain.ε/D = 0.045 / 50 = 0.0009, f₀ = 0.25 / [log10(0.0009/3.7 + 5.74/50 830^0.9)]² = 0.02383
Iterate Colebrook from f₀ until f stops changing.1/√f = −2·log10(0.0009/3.7 + 2.51/(50 830·√f)) → f = 0.02369
Apply Darcy–Weisbach.Δp = 0.02369 × (30 / 0.05) × 998 × 1.019² / 2 = 7358 Pa = 7.358 kPa
Convert to head of the flowing water.hf = 7358 / (998 × 9.80665) = 0.7519 m

Answer: Re = 50 830 (turbulent), f = 0.02369 (Colebrook; Swamee–Jain gives 0.02383), Δp = 7.358 kPa and hf = 0.7519 m over the 30 m run.

Common mistakes

Using the nominal pipe size as the diameter. Pressure drop scales roughly with 1/D⁵ at a fixed flow, so a small error in bore is a large error in Δp. Use the actual inside diameter.
Mixing up the Darcy and Fanning friction factors. Darcy f is four times Fanning f. The Moody chart, Colebrook and Darcy–Weisbach here all use Darcy.
Using kinematic viscosity where dynamic is asked for. Dynamic viscosity μ (Pa·s, cP) = kinematic viscosity ν (m²/s, cSt) × density.
Ignoring temperature. Liquid viscosity can change several-fold between cold and hot service. Use properties at the operating temperature.
Leaving out fittings. Elbows, tees and valves often add as much loss as the straight pipe in short plant runs. Add them as minor losses on top of this result.

Frequently asked questions

Which friction factor equation does this calculator use?

Colebrook–White, solved iteratively, for any Reynolds number of 2300 and above, and 64/Re below that. The explicit Swamee–Jain equation is shown alongside so you can see how close the approximation is.

What Reynolds number is turbulent?

Pipe flow is usually laminar below about 2300 and fully turbulent above about 4000. In between, the flow can switch between the two, so friction is uncertain.

What roughness should I use?

Use a value for your pipe material and condition from a fluid mechanics reference or the pipe manufacturer. Drawn tubing is close to smooth; old or corroded pipe can be many times rougher than new.

Can I use this for air or other gases?

Yes, if the pressure drop is small compared with the absolute pressure, so density barely changes along the pipe. Enter the gas density at the line pressure and temperature.

How do I convert the pressure drop to pump head?

Head loss hf = Δp/(ρg) is shown in metres or feet of the flowing fluid. Add elevation change and minor losses to get the total head the pump must supply.

More engineering calculators

Darcy–Weisbach equation lesson · All engineering calculators

Sources

C. F. Colebrook, Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws (1939), Journal of the Institution of Civil Engineers
P. K. Swamee, A. K. Jain, Explicit equations for pipe-flow problems (1976), Journal of the Hydraulics Division, ASCE
L. F. Moody, Friction factors for pipe flow (1944), Transactions of the ASME
F. M. White, Fluid Mechanics, McGraw Hill
B. R. Munson, T. H. Okiishi, W. W. Huebsch, A. P. Rothmayer, Fundamentals of Fluid Mechanics, Wiley
NIST Special Publication 811, Guide for the Use of the International System of Units (conversion factors), NIST

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Pipe Pressure Drop Calculator