Pipe-Flow Pressure-Drop Calculator

Content

Estimate straight-pipe liquid friction loss or screen compressed-air line pressure loss.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Liquid operating point

Major loss in a straight circular pipe; fittings and elevation are excluded.

Liquid pressure drop

Major pressure loss, Δp

67.91Pa
Head loss hf0.0069 m
Flow regimeLaminar
Area A0.79 ×10⁻⁴ m²
Mean velocity v0.21 m/s
Reynolds number Re2122
Relative roughness ε/d0.000000
Darcy factor fD0.030159
Distributed coefficient Kf3.015929

This result covers wall-friction loss over the entered straight length only.

Straight length Ldp₁p₂Q

How to use

  1. Select Liquid pipe for incompressible straight-pipe major loss or Compressed air for the empirical air-line estimate.
  2. For liquid, enter positive Q, d, L, ρ, and μ; enter nonnegative ε; then select the flow unit. Use properties from one operating condition.
  3. For compressed air, enter positive normal flow Qn, supply pressure p₁, straight length L, and diameter d; select both units. The nominal diameter basis is approximately 3.2–150 mm.
  4. Select Calculate. Select Reset to restore that mode’s worked example and recalculate.
  5. Interpret the large pressure-loss result first. Liquid diagnostics identify velocity, Re, regime, roughness, and Darcy factor; air diagnostics show converted SI inputs. Resolve any red warning before use.
  6. Do not use either mode for fittings, elevation, leakage, transients, two-phase or non-Newtonian flow, certification, or safety-critical sizing. Do not use the air mode as a compressible-flow/choking solver.

Worked example

  1. Liquid: Q=1 L/min, d=10 mm, L=1 m, ε=0 µm, ρ=1000 kg/m³, and μ=1 mPa·s gives A=0.79×10⁻⁴ m², v=0.21 m/s, Re=2122, fD=0.030159, Δp=67.91 Pa, and hf=0.0069 m. The flow is laminar.
  2. Compressed air: Qn=25 L/s, p₁=7 bar, L=40 m, and d=25 mm gives Δpair=10175.85 Pa, displayed as 0.10 bar. Confirm the normal-flow and pressure basis independently.

Equations used

Liquid pipe

A = πd²/4; v = Q/ARe = ρvd/μ; r = ε/dRe ≤ 2300: fD = 64/ReRe > 2300: fC = [−2 log₁₀(r/3.7 + 2.51/(Re√fg))]⁻²Kf = fDL/dΔp = Kfρv²/2; hf = Δp/(ρg)

Compressed air

Qn = QinputcQ; p₁ = pinputcpΔpair = 1600 Qn1.85L/(d⁵p₁)

For the empirical air equation, Qn is in m³/s; p₁ and Δpair are in Pa; and L and d are in m. The coefficient 1600 carries the required units.

Definitions: Q is actual liquid flow; Qn is normal-condition air flow; cQ and cp are unit factors; d is inside diameter; L is straight length; ε is absolute roughness; ρ is density; μ is dynamic viscosity; A is area; v is mean velocity; Re is Reynolds number; r=ε/d; fg is a retained trial Darcy factor; fC is its Colebrook value; fD is the accepted Darcy factor; Kf is the distributed-loss coefficient; Δp and Δpair are positive loss magnitudes; hf is liquid head loss; g=9.807 m/s²; and p₁ is the positive upstream pressure magnitude. The turbulent scan checks fg=i/10000 for i=1…800 and accepts the first point with (fC−fg)/fg<0.005.

Theory and method

Liquid mode applies the Darcy–Weisbach major-loss model to steady, one-dimensional flow in a constant circular pipe. It retains the discrete Re=2300 branch: fD=64/Re below or at the threshold and a Colebrook scan above it. The friction factor is the Darcy convention. Constant density and Newtonian viscosity are assumed.

FunctionalProduct

Compressed-air mode is a separate empirical screening correlation based on normal-condition flow and supply pressure. It is strongly sensitive to diameter through d⁵ and is not a full compressible-flow calculation. It excludes pressure-dependent density integration, sonic limits, temperature change, and downstream pressure constraints.

Neither mode includes minor losses from fittings, valves, entrances, or exits; elevation; leakage; transients; heat transfer; two-phase behavior; or safety factors. Add those effects independently and check results against applicable codes and supplier data.

References: Darcy–Weisbach major-loss relation; C. F. Colebrook, “Turbulent Flow in Pipes, with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws,” 1939, doi:10.1680/ijoti.1939.13150.

Continue in TriboSolver to refine a coupled fluid-system model or independently check pressure-loss assumptions where an appropriate workflow is available.