Introduction

Pipe flow calculations are fundamental to process engineering, determining the pressure drop and head loss in piping systems. Understanding these principles is essential for pump sizing, system design, and energy optimization.

The primary equation for calculating frictional pressure drop in pipes is the Darcy-Weisbach equation, which relates pressure loss to fluid velocity, pipe dimensions, and the friction factor.

Darcy-Weisbach Equation

The Darcy-Weisbach equation calculates the pressure drop due to friction:

Where:

• ΔP = Pressure drop (Pa)
• f = Darcy friction factor (dimensionless)
• L = Pipe length (m)
• D = Pipe inner diameter (m)
• ρ = Fluid density (kg/m³)
• V = Average flow velocity (m/s)

The head loss form is often more convenient:

Reynolds Number

The Reynolds number determines the flow regime and is essential for friction factor calculation:

Friction Factor

Laminar Flow (Re < 2300)

For laminar flow, the friction factor depends only on Reynolds number:

Turbulent Flow (Re > 4000)

For turbulent flow, the Colebrook-White equation is the most accurate:

This implicit equation requires iterative solution. The Swamee-Jain approximation provides a direct explicit solution accurate to within 1%:

Moody Diagram

The Moody diagram is a graphical representation of the friction factor as a function of Reynolds number and relative roughness (ε/D). Key features include:

• Laminar region - Single line where f = 64/Re
• Transitional region - Shaded area (2300 < Re < 4000)
• Turbulent region - Multiple curves for different roughness values
• Fully rough zone - Friction factor independent of Re at high Reynolds numbers

Pipe Roughness Values

Surface roughness (ε) varies by pipe material and condition:

Minor Losses (Fittings)

Fittings, valves, and other components cause additional pressure losses calculated using K-factors:

Common K-values:

Design Guidelines