Fluid Mechanics

Pipe Flow Calculator

Full-range pipe flow analysis — Hagen-Poiseuille for laminar flow and Darcy-Weisbach with Colebrook-White friction factor for turbulent flow. Both regimes shown simultaneously.

Inputs

Fluid

ISO Oil — viscosity at temperature

Pipe

Pressure drop

Reynolds number (Re)

—

Results — both regimes

Hagen-Poiseuille (Laminar) Re < 2,300
Flow rate (Q) — gpm
Velocity (V)— ft/s
Hydraulic power— kW
Darcy-Weisbach (Turbulent) Re > 4,000
Flow rate (Q) — gpm
Velocity (V)— ft/s
Friction factor (f)—
Hydraulic power— kW

Moody diagram — operating point shown

Governing equations

Laminar (Re < 2,300): Q = π·d⁴·ΔP / (128·µ·L)   [Hagen-Poiseuille] Turbulent: ΔP = f·(L/d)·(ρV²/2)   [Darcy-Weisbach] Colebrook-White: 1/√f = −2·log(ε/(3.7d) + 2.51/(Re·√f))   [iterated] Swamee-Jain (explicit): f ≈ 0.25 / [log(ε/(3.7d) + 5.74/Re⁰·⁹)]² Re = ρ·V·d / µ   |   V = Q / A   |   P = Q·ΔP
ε = absolute pipe roughness ε/d = relative roughness f = Darcy friction factor (4× Fanning) Transitional 2,300 < Re < 4,000 — neither equation is reliable For ΔP→Q turbulent: iterative solution using Colebrook-White