Velocity and Reynolds number
v = Q / A: 100 m3/h is 0.02778 m3/s; in 102.26 mm (0.008213 m2) that is 3.382 m/s. Re = v x D / nu = 3.382 x 0.10226 / 1.0034e-6 = 344687, turbulent flow.
Reference tool — arithmetic, not system design
Pressure drop in a pipe.
Velocity · Reynolds number · friction factor · pressure drop · head loss · K
Flow, pipe, friction.
Type a line (100 m3/h DN100 Sch 40 50 m water 20 C; or 400 l/min ID 52 mm 30 m 46 cSt 870 kg/m3, with K 2.5 for fittings) or fill in the fields: the line and the fields stay in step.
Examples:
All 130 engineering tools
Enter the flow rate, the pipe, the length and the liquid, and the calculator gives the mean velocity, the Reynolds number and the flow regime, the Darcy friction factor and the friction pressure drop by the Darcy-Weisbach equation, dp = f x (L / D) x rho x v²/2, in bar, kPa and psi, with the head loss in m of the liquid, over the length and per 100 m. The friction factor is 64 / Re for laminar flow and comes from the Colebrook-White equation, solved by iteration, for turbulent flow. For fresh water at 10 to 80 °C the viscosity and density are picks; for sea water the density is a typical pick and you enter the viscosity; for oil and fuel you enter both. Minor losses are added from the sum of the K values you enter. The working is shown with your numbers, and the result is a line you can copy.
Arithmetic only: no recommended velocities, no pressure drop limits and no pump sizing, which the system designer and the class rules set. No K tables either: the K values come from the makers of the valves and fittings.
How it is worked out
Velocity, friction, drop.
Friction factor
eps / D = 0.045 / 102.26 = 0.00044. Colebrook-White by iteration: f = 0.01768 (Swamee-Jain check 0.01779). For laminar flow, below Re 2000: f = 64 / Re.
Pressure drop and head loss
dp = f x (L / D) x rho x v²/2 = 0.01768 x (50 / 0.10226) x 998.2 x 3.382²/2 = 49358 Pa = 0.494 bar = 7.16 psi; h = dp / (rho x g) = 5.04 m; per 100 m, 0.987 bar.
| Re | Smooth (eps/D 0) | eps/D 0.0001 | eps/D 0.001 | eps/D 0.01 |
|---|---|---|---|---|
| 1e4 | 0.0309 | 0.0310 | 0.0324 | 0.0431 |
| 1e5 | 0.0180 | 0.0185 | 0.0222 | 0.0385 |
| 1e6 | 0.0116 | 0.0134 | 0.0199 | 0.0380 |
| 1e7 | 0.0081 | 0.0122 | 0.0197 | 0.0379 |
The figures are the same Colebrook-White solution the calculator uses: the Moody chart in figures. Below Re 2000 the friction factor is 64 / Re (0.064 at Re 1000); between 2000 and 4000 it is uncertain.
Sources
The working is the Darcy-Weisbach equation with the Darcy friction factor: 64 / Re for laminar flow and the Colebrook-White equation for turbulent flow, as the references on pipe flow give them; the Swamee-Jain approximation is shown as a check, as two references also give it. The laminar limit of Re 2000 and the band up to Re 4000 in which the friction factor is uncertain follow one reference; others start the band at Re 2300. The Colebrook solution is checked against two published worked solutions (Re 6000 with eps/D 0.002, f 0.0378; Re 1e6 with eps/D 0.001, f 0.0199). The roughness picks, the fresh water densities and viscosities at 10 to 80 °C and the typical sea water density are each checked against two independent references. The ASME B36.10 outside diameters and schedule walls are those of the pipe size identifier. 1 psi = 6894.757 Pa, standard gravity 9.80665 m/s2, 1 cSt = 1 mm2/s and 1 cP = 1 mPa s are exact. The data of the pipe maker, the data sheet of the liquid and the system design always come first.
Before you work it out
Questions about pipe pressure drop
How is the pressure drop in a straight pipe worked out?
By the Darcy-Weisbach equation, dp = f x (L / D) x rho x v²/2, with the friction factor f, the length L and the inside diameter D in m, the density rho in kg/m3 and the mean velocity v in m/s. 100 m3/h in a DN100 Sch 40 pipe (inside diameter 102.26 mm) runs at 3.382 m/s; with fresh water at 20 °C (998.2 kg/m3) and f 0.01768, 50 m of pipe loses 0.01768 x (50 / 0.10226) x 998.2 x 3.382²/2 = 49358 Pa, that is 0.494 bar, or 5.04 m of head (dp / (rho x g)).
What is the Reynolds number, and what does it show?
Re = v x D / nu, with nu the kinematic viscosity in m2/s (1 cSt = 1 mm2/s). Fresh water at 20 °C has 1.0016 mPa s and 998.2 kg/m3, so nu = 1.0034 cSt, and 3.382 m/s in 102.26 mm gives Re = 344687, about 3.4e5: turbulent flow. Below Re 2000 the flow is laminar. Up to Re 4000 lies a transitional band, which the references start at 2000 or 2300 and in which they agree that the friction factor is uncertain; from 4000 the flow is turbulent.
How is the friction factor found?
For laminar flow, f = 64 / Re. For turbulent flow, the Colebrook-White equation, 1/sqrt(f) = -2 log10(eps / (3.7 D) + 2.51 / (Re sqrt(f))), which has f on both sides and is solved here by iteration until it no longer changes. For Re 344687 and eps/D 0.00044 it gives f = 0.01768; the explicit Swamee-Jain approximation, shown as a check, gives 0.01779. The Moody chart is the same equation drawn as curves; the small chart on this page shows where the result sits on it.
Which roughness does the calculator take?
The absolute roughness eps of new pipe, from two tables that agree: commercial steel 0.045 mm, drawn tubing 0.0015 mm, galvanised iron 0.15 mm, uncoated cast iron 0.26 mm. With no material given, new commercial steel is taken. For stainless steel, copper-nickel and plastics the tables differ, so there is no pick: enter the roughness. Pipe that has corroded or scaled in service is rougher than new pipe; the calculator does not guess by how much.
Which viscosity and density are used?
Fresh water has picks at 10, 20, 30, 40, 50, 60, 70 and 80 °C: at 20 °C, 1.0016 mPa s and 998.2 kg/m3; at 60 °C, 0.4660 mPa s and 983.2 kg/m3. Sea water takes a typical density of 1025 kg/m3, but its viscosity is entered. Oil, fuel and other liquids are entered from their data sheet, in cSt (kinematic) or in cP (dynamic, with the density: nu = mu / rho). An ISO VG grade is a viscosity at 40 °C; at the working temperature the oil has another viscosity, which the data sheet gives.
Are minor losses, velocity limits or a pump size given?
Minor losses only from the K values you enter: their sum times rho x v²/2, so K 2.5 at 3.382 m/s of fresh water at 20 °C adds 14273 Pa, 0.143 bar. This page has no K tables, no recommended velocities, no pressure drop limits and no pump sizing: those come from the valve and fitting makers, the system designer and the class rules.
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The calculator works out the pressure drop from the figures you enter. When pipe, valves, fittings or gaskets for the line are needed, send the line with the size, the material and a photograph of any nameplate, and Vessel Core checks the details before an offer goes back.
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