Pipe Flow Pressure Drop Calculator (CFD)
Calculate pipe-flow Reynolds number, Colebrook-White friction factor, Darcy-Weisbach head loss and pressure drop for any liquid. Free, runs in your browser.
CFD Calculator
Simplified Navier-Stokes · Colebrook-White friction model
Fluid Properties
Radial Velocity Profile
A clear path from inputs to results.
Calculate the pressure drop and head loss for steady, fully developed flow of a liquid through a circular pipe. Despite the "computational fluid dynamics" label, this tool solves the classic internal-flow hydraulics problem: it finds the Reynolds number, selects the laminar or turbulent friction factor (via the Colebrook-White equation), and applies the Darcy-Weisbach equation. It is aimed at mechanical, civil, and chemical engineers sizing pipes, pumps, and plumbing runs.
How to use
- Enter the fluid density in kg/m^3 (default 998.2 for water at 20 C) and dynamic viscosity in Pa-s (default 0.001002 for the same water).
- Enter the internal pipe diameter in metres (default 0.1 m) and the pipe length in metres (default 50 m).
- Enter the mean flow velocity in m/s (default 1.5 m/s). The volumetric flow rate follows from velocity times cross-sectional area.
- Enter the absolute wall roughness in metres (default 0.000045 m, typical of commercial/drawn steel).
- Read the Reynolds number and flow regime (laminar below 2300, transitional 2300-4000, turbulent above 4000), the Darcy friction factor, the head loss in metres, and the pressure drop in pascals.
The formula
Reference: Colebrook, J. Inst. Civ. Eng. 11 (1939); Darcy-Weisbach equation as given in White, Fluid Mechanics, 7th ed., ch. 6; Moody, Trans. ASME 66 (1944).
Worked example
Water at 20 C through a 100 mm steel pipe
- Density 998.2 kg/m^3; viscosity 0.001002 Pa-s; diameter 0.1 m; length 50 m; velocity 1.5 m/s; wall roughness 0.000045 m; g = 9.81 m/s^2.
- 1
The Reynolds number is Re = rho V D / mu = (998.2 x 1.5 x 0.1) / 0.001002 = 149,431, which is well above 4000, so the flow is turbulent. The relative roughness is eps/D = 0.000045 / 0.1 = 0.000450. Solving the Colebrook-White equation iteratively for this Re and relative roughness gives a Darcy friction factor f = 0.019138. The Darcy-Weisbach head loss is h_f = f (L/D)(V^2 / 2g) = 0.019138 x (50/0.1) x (1.5^2 / (2 x 9.81)) = 1.0973 m. The pressure drop is deltaP = rho g h_f = 998.2 x 9.81 x 1.0973 = 10,745.5 Pa.
Reynolds number 149,431 (turbulent); friction factor f = 0.019138; head loss 1.0973 m of water; pressure drop 10,745.5 Pa (10.75 kPa) over the 50 m run.
Interpreting the result
The head loss is the energy per unit weight dissipated to friction, expressed as an equivalent column height of the flowing fluid; the pressure drop is that same loss expressed as pressure. A pump must supply at least this pressure (plus any elevation and fitting losses) to maintain the chosen flow rate. If the Reynolds number lands between 2300 and 4000 the flow is transitional and the friction factor is genuinely uncertain in the real world, so treat results in that band as indicative only.
Assumptions & limitations
- Flow is steady, fully developed, incompressible, and single-phase; entrance-length effects, pulsation, and two-phase or cavitating flow are not modeled.
- The pipe is straight, circular, and of constant cross-section; bends, valves, expansions, and other minor (fitting) losses are not included — only straight-run skin friction.
- Laminar flow (Re < 2300) uses f = 64/Re; turbulent flow uses the Colebrook-White correlation; the 2300-4000 transitional band has no reliable single friction law.
- Fluid properties (density and viscosity) are constant along the pipe, so large temperature changes or strongly non-Newtonian fluids fall outside the model.
- Elevation change and the resulting hydrostatic pressure difference are not added; the output is the friction loss only, consistent with a horizontal pipe.
Frequently asked questions
Is this a real CFD (Navier-Stokes field) solver?
No. The name reflects the broad topic, but the tool solves the one-dimensional pipe-flow problem analytically: Reynolds number, a friction factor from the Colebrook-White law, and the Darcy-Weisbach head loss. It does not discretize the Navier-Stokes equations or produce a velocity field. For straight-pipe pressure-drop estimates this one-dimensional approach is the standard engineering method and is far faster and more reliable than a full CFD run.
When is the flow laminar instead of turbulent?
The transition is governed by the Reynolds number Re = rho V D / mu. Below about 2300 the flow is laminar and the friction factor is simply f = 64/Re, independent of roughness. Above about 4000 it is turbulent and roughness matters. Between 2300 and 4000 the flow is transitional and inherently unpredictable, so any friction factor there should be treated as a rough estimate.
How do I get the pump pressure from the head loss?
Multiply head loss by rho x g to convert metres of fluid to pascals: in the example 1.0973 m becomes 10,745.5 Pa. A real pump sizing must also add elevation gain (rho g deltaz), the dynamic head, and minor losses from fittings and valves, which this straight-pipe tool does not include.
What is the Colebrook-White equation and why is it solved iteratively?
It is the implicit relation 1/sqrt(f) = -2 log10(eps/D/3.7 + 2.51/(Re sqrt(f))) that defines the turbulent Darcy friction factor as a function of relative roughness and Reynolds number — the equation underlying the Moody chart. Because f appears on both sides, there is no closed form, so the tool iterates (Newton-style) until f converges. The result matches explicit approximations such as Haaland to within a fraction of a percent.
Does wall roughness change the answer much?
In turbulent flow, yes. The relative roughness eps/D sets how far the friction factor sits above the smooth-pipe value. In the worked example eps/D = 0.00045 raises f noticeably above a hydraulically smooth pipe at the same Reynolds number. In laminar flow roughness has essentially no effect, because f = 64/Re does not depend on it.
What units does the calculator use?
SI throughout: density in kg/m^3, viscosity in Pa-s, diameter and length in metres, velocity in m/s, roughness in metres. Outputs are the dimensionless Reynolds number and friction factor, head loss in metres of fluid, and pressure drop in pascals. Convert to kPa or bar as needed (10,745.5 Pa is about 10.75 kPa or 0.107 bar).
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.