PIPE FLOW (MOODY / BERNOULLI / REYNOLDS)

Internal pipe flow is laminar below Re=2300, turbulent above 4000. Friction factor f comes from f = 64/Re (laminar) or the Colebrook equation (turbulent), which Amni-Calc solves explicitly via Swamee-Jain or iteratively. The Moody diagram visualizes f as a function of Re and relative roughness ε/D. Bernoulli's equation accounts for pressure, velocity, and elevation head between two points, plus friction (Darcy-Weisbach) and minor losses (fittings, valves) summed via loss coefficients K.

• Re = ρ·v·D / μ
• f = 64/Re (laminar)
• 1/sqrt(f) = -2·log10(ε/(3.7D) + 2.51/(Re·sqrt(f))) (Colebrook)
• h_L = f·(L/D)·v²/(2g) + ΣK·v²/(2g)
• P₁ + ½ρv₁² + ρgz₁ = P₂ + ½ρv₂² + ρgz₂ + ΔP_loss

References & StandardsCrane TP-410, Moody (1944), White Fluid Mechanics

Size pipes for any liquid or gas system: water distribution, hydraulic lines, compressed air, process plumbing. Compute Re first to pick laminar or turbulent regime, then friction factor, then total head loss including minor losses. Pair with the pump module to find the operating point on a system curve. For long lines, iterate on diameter to balance capital cost vs pumping cost.