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Pipe pressure-loss calculator

Calculate Darcy–Weisbach friction and local losses in one circular pipe segment; inspect Reynolds number and flow-regime limits.

Trace the loss through a pipe

Convert flow and geometry to SI, identify the flow regime, then separate pipe-wall friction from fittings. The model solves one full circular pipe at a prescribed steady flow.

hL = [fD(L/D) + ΣK] v²/(2g) Δploss = ρg hL

Inputs and assumptions

Use a decimal dot or comma, with no thousands separators. Scientific notation is accepted. Values are not inferred from a fluid name.

Volumetric flow Qm³/h0–100000 m³/h; nonzero minimum 0.000001. Forward-flow magnitude only.

Internal diameter Dmm1–10000 mm. Use actual bore, not nominal pipe size or outside diameter.

Straight-pipe length Lm0–100000 m; nonzero minimum 0.000001. Do not include fitting equivalent lengths if also counted in ΣK.

Absolute roughness εmm0–100 mm; ε/D ≤ 0.05. Zero is ideal hydraulically smooth. Nonzero minimum 0.000001.

Sum of local-loss coefficients ΣKdimensionless0–10000; all coefficients must use this pipe velocity. Nonzero minimum 0.000001.

Liquid density ρkg/m³100–20000 kg/m³. Initial 1000 is an illustrative value; enter relevant properties.

Dynamic viscosity μmPa·s0.001–100000 mPa·s. This is dynamic viscosity, not kinematic viscosity in cSt.

Gravitational acceleration gm/s²0.1–30 m/s². Initial 9.80665 is conventional standard gravity, not a local measurement.

Derived limits: velocity ≤ 50 m/s; for nonzero flow, 0.001 ≤ Re ≤ 100000000; ε/D ≤ 0.05. These are tool bounds, not acceptable operating limits.

Calculated result

Illustrative starting example. Edit the inputs to explore the model.

Quantity	Value	Unit
Flow regime	Turbulent
Frictional pressure loss	10.42418	kPa
Δp	0.1042418	bar
Total loss head	1.06297	m
Pipe-wall loss	0.8138412	m
Fitting / local loss	0.2491292	m
Mean velocity	1.105243	m/s
Re	88419.41	1
Darcy friction factor	0.02090716	1
ε/D	0.0005625	1
L/D	625	1
Cross-sectional area	0.005026548	m²
Velocity head	0.0622823	m
Hydraulic dissipation	57.9121	W

This is dissipative pressure loss. The actual pressure difference between two points also depends on elevation, changes in velocity and any pumps or turbines.

Bars compare straight-pipe and local losses using the same velocity reference. Values are also listed in the result table.

Calculation trace

Q = 20 ÷ 3600 = 0.005555556 m³/s; D = 80 ÷ 1000 = 0.08 m
ε = 0.045 ÷ 1000 = 0.000045 m; μ = 1 ÷ 1000 = 0.001 Pa·s
A = π × 0.08² ÷ 4 = 0.005026548 m²
v = 0.005555556 ÷ 0.005026548 = 1.105243 m/s
Re = 1000 × 1.105243 × 0.08 ÷ 0.001 = 88419.41
ε/D = 0.000045 ÷ 0.08 = 0.0005625
x + 2 log₁₀[0.0005625/3.7 + 2.51x/88419.41] = 0; x = 6.91596; fD = 1/x² = 0.02090716
v²/(2g) = 1.105243² ÷ (2 × 9.80665) = 0.0622823 m
hm = 4 × 0.0622823 = 0.2491292 m
hf = 0.02090716 × (50/0.08) × 0.0622823 = 0.8138412 m
hL = 0.8138412 + 0.2491292 = 1.06297 m
Δp = 1000 × 9.80665 × 1.06297 = 10424.18 Pa
QΔp = 0.005555556 × 10424.18 = 57.9121 W

Numerical checks

Colebrook solver
Quantity	Value	Unit
Converged	Yes
Iterations	45
Equation residual	-0.0000000000003836931	1
Residual tolerance	1e-12	1

Pressure-form consistency

Δp − [fD(L/D) + ΣK]ρv²/2 = 0 Pa

Displayed values are rounded; computation and CSV use unrounded values. A small arithmetic residual checks implementation consistency, not physical accuracy.

Sensitivity: change one assumption

Recalculate at 0.5× to 1.5× the current flow, with bore, length, roughness, ΣK and liquid properties fixed. The friction factor is solved again for each row. A transition or out-of-envelope row has no total loss; no power-law extrapolation is used.
Q ×	Q · m³/h	Re	fD	hL · m	Δp · kPa	Flow regime
0.5	10	44209.71	0.02323404	0.2883869	2.828109	Turbulent
0.75	15	66314.56	0.02177013	0.6168165	6.048904	Turbulent
1	20	88419.41	0.02090716	1.06297	10.42418	Turbulent
1.25	25	110524.3	0.02032895	1.625723	15.9429	Turbulent
1.5	30	132629.1	0.01991114	2.304448	22.59891	Turbulent

The calculation and CSV are created in this page in your browser. This calculator does not transmit or store the inputs.

How the calculation works

1. Convert Q from m³/h to m³/s by dividing by 3600. Divide D and ε in mm by 1000 to obtain metres. Divide μ in mPa·s by 1000 to obtain Pa·s. Density and gravity are already in SI.

2. For a full circular bore, A = πD²/4 and v = Q/A. Reynolds number is Re = ρvD/μ. Relative roughness is ε/D. The tool assumes incompressible, single-phase, Newtonian flow with fully developed wall friction.

3. For 0 < Re < 2000, the Darcy factor is 64/Re. For 2000 ≤ Re ≤ 4000, this tool withholds the friction factor and total loss rather than presenting an unqualified transition estimate. Regime boundaries are a modelling convention, not a guarantee about actual disturbances.

4. For Re > 4000, solve 1/√fD = −2 log₁₀[ε/(3.7D) + 2.51/(Re√fD)]. The factor is Darcy, four times the Fanning factor. The solver uses x = 1/√fD and bisection on [1, 100], stopping at absolute equation residual ≤ 10⁻¹² within at most 100 iterations. No result is accepted after non-convergence.

5. Compute velocity head v²/(2g), major loss fD(L/D)v²/(2g), and local loss ΣK v²/(2g). Add the losses and convert with Δploss = ρg hL. The reported ρgQhL is hydraulic dissipation, not motor input power.

6. Check Δploss against [fD(L/D) + ΣK]ρv²/2. In laminar flow, compare the major-loss pressure with Hagen–Poiseuille: 128μLQ/(πD⁴). These algebraically independent evaluations help expose conversion mistakes, but cannot validate the fluid or installation.

Worked examples and interpretation

The starting example uses Q = 20 m³/h, D = 80 mm, L = 50 m, ε = 0.045 mm, ΣK = 4, ρ = 1000 kg/m³, μ = 1 mPa·s and g = 9.80665 m/s². It is an illustrative liquid and pipe combination, not a material or temperature property lookup. The live trace below substitutes every input.

Laminar cross-check: Q = 0.18 m³/h, D = 20 mm, L = 10 m, μ = 10 mPa·s, ρ = 1000 kg/m³ and ΣK = 0. Then Q = 0.00005 m³/s, v ≈ 0.159155 m/s, Re ≈ 318.310 and fD ≈ 0.201062. Hagen–Poiseuille gives Δp ≈ 1273.239545 Pa. Load the example to compare both routes.

A change in flow changes Reynolds number and usually the friction factor. In laminar flow, straight-pipe pressure loss is proportional to Q; the fixed-K term is proportional to Q². In turbulent flow, recompute fD instead of assuming it is constant.

Changing gravity changes the head measured in metres, but it does not change the calculated frictional pressure loss for the same flow, geometry and properties. This follows because g cancels between the head and pressure formulas.

Model boundaries

One full, constant-bore circular pipe with one prescribed steady flow. No branched-network solution, pump operating point, free-surface flow, compressible gas, two-phase mixture, slurry, yield-stress or non-Newtonian fluid model.
Density, viscosity, roughness and ΣK must represent the actual condition. Temperature, salinity, corrosion, deposits, fouling, valve opening and ageing are not inferred. A numerical result is not evidence that these inputs are correct.
Fully developed wall friction is assumed. Entrance, swirl, closely spaced fittings and developing flow are not resolved. Generic high-Re fitting K values may be unsuitable at low Re; verify the component data.
The result excludes static elevation and pressure boundaries, water hammer, cavitation, vapor pressure, NPSH, erosion, vibration, pipe stress, heat transfer and class or regulatory acceptance.
Head in metres is metres of the entered liquid. Do not read it as metres of water unless the density actually represents water. No result approves an operating velocity, pump, valve, line size or safety margin.

Method sources

Primary technical references for the equations. The input envelope, transition hold and solver tolerances are conservative implementation choices, not certification criteria.

fluids-1.0.0

Read the method and its limits

Related project: ShipExact

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