Darcy-Weisbach Equation

The Darcy-Weisbach equation is the fundamental formula for calculating pressure drop in pipe flow. It relates head loss to pipe geometry, flow velocity, and friction:

h_f = f * (L/D) * (V^2 / 2g)

Where h_f = head loss (m), f = Darcy friction factor, L = pipe length (m), D = pipe diameter (m), V = flow velocity (m/s), g = gravitational acceleration (9.81 m/s^2).

Reynolds Number and Flow Regimes

The Reynolds number determines whether flow is laminar, transitional, or turbulent:

Re = V * D / v

Where v = kinematic viscosity (m^2/s).

• Laminar (Re < 2,300): Smooth, orderly flow in parallel layers. Friction factor f = 64/Re.
• Transitional (2,300 < Re < 4,000): Unstable flow regime, may alternate between laminar and turbulent.
• Turbulent (Re > 4,000): Chaotic flow with eddies and mixing. Most industrial applications operate here.

Friction Factor (Colebrook-White Equation)

For turbulent flow, the Darcy friction factor is calculated using the Colebrook-White equation:

1/sqrt(f) = -2 * log10(e/3.7D + 2.51/(Re*sqrt(f)))

This is an implicit equation solved iteratively. The calculator uses the Swamee-Jain approximation for initial estimate, then refines with Newton-Raphson iteration.

Head Loss vs Pressure Drop

Head loss (h_f) represents energy loss as height of fluid column. Pressure drop relates to head loss by:

dP = rho * g * h_f

Where rho = fluid density (kg/m^3). Use head loss when comparing systems with different fluids; use pressure drop for pump/system sizing.