Friction

Overview

Friction in fluid flow refers to the resistance encountered as fluid moves through pipes, ducts, and equipment. This resistance manifests as pressure drop, which must be overcome by pumps or compressors. Understanding and accurately predicting friction is essential for designing piping systems, sizing equipment, and optimizing energy consumption in industrial processes.

The fundamental relationship governing friction in pipe flow is the Darcy-Weisbach equation, which relates pressure drop to the Darcy friction factor (also called the Darcy-Weisbach friction factor or Moody friction factor). This dimensionless parameter depends on the Reynolds number (which characterizes the flow regime) and the relative roughness of the pipe wall (the ratio of surface roughness height to pipe diameter).

Figure 1: Friction factor behavior: (Left) Transition from Laminar to Turbulent flow for relative roughness e/D = 0.001; (Right) Relative error of explicit approximations (Haaland, Swamee-Jain) compared to the implicit Colebrook equation.

Flow Regimes and Friction Behavior

Fluid flow in pipes exhibits distinctly different friction characteristics depending on the flow regime:

  • Laminar flow (Re < 2,300): Flow occurs in smooth, parallel layers with minimal mixing. The friction factor depends only on Reynolds number and follows the exact theoretical relation f_D = 64/\text{Re}, implemented in FRICTION_LAMINAR.

  • Turbulent flow (Re > 4,000): Flow is chaotic with significant mixing and eddy formation. The friction factor depends on both Reynolds number and relative roughness. No exact analytical solution exists; friction factors are determined from the implicit Colebrook equation or various approximations.

  • Transition regime (2,300 < Re < 4,000): Flow is unstable and difficult to characterize. The CHURCHILL correlation provides continuous coverage across all regimes.

Friction Factor Correlations

The friction category provides multiple correlations for calculating the Darcy friction factor, each with different characteristics:

Exact and High-Precision Solutions: - COLEBROOK: The implicit Colebrook-White equation is the reference standard for turbulent flow in commercial pipes. Requires iterative solution but is highly accurate. - CLAMOND: Clamond’s analytical solution achieves nearly machine precision without iteration, making it ideal for applications requiring maximum accuracy.

Explicit Approximations: Explicit approximations avoid iteration by providing direct formulas that approximate the Colebrook equation with varying accuracy: - SWAMEE_JAIN: Popular explicit approximation with ±1% accuracy over a wide range of practical conditions. - HAALAND: Simpler explicit formula with good accuracy for most engineering applications. - MOODY: Historical correlation developed alongside the famous Moody diagram. - CHURCHILL: Universal correlation valid for all flow regimes (laminar, transition, and turbulent).

Specialized Correlations: - BLASIUS: For smooth pipes in turbulent flow (Re < 100,000), provides a simple power-law relation f_D = 0.316/\text{Re}^{0.25}. - FT_CRANE: Fully turbulent approximation from the Crane Technical Paper 410, widely used in the process industries. - VON_KARMAN: Limiting case for rough pipes at infinite Reynolds number.

General-Purpose Function: - FRICTION_FACTOR: Automatically selects the appropriate correlation based on flow regime and pipe roughness, simplifying implementation.

Specialized Geometries

Standard correlations assume straight, circular pipes. Specialized functions handle more complex geometries:

  • Curved and helical pipes: Flow in curved pipes experiences secondary flows due to centrifugal effects, increasing friction. FF_CURVED accounts for both curvature ratio and flow regime, while HELICAL_RE_CRIT determines the transition Reynolds number for curved pipes.

  • Plate heat exchangers: Chevron-style plate heat exchangers have complex flow channels with corrugated surfaces. FP_MARTIN and FP_MULEY_MANGLIK provide correlations specific to this geometry, accounting for chevron angle and surface enlargement.

Pressure Drop Calculations

Beyond calculating friction factors, several functions compute actual pressure drops:

  • ONE_PHASE_DP: Implements the complete Darcy-Weisbach equation to calculate frictional pressure drop in horizontal or vertical pipes.
  • DP_GRAV: Calculates the gravitational (hydrostatic) component of pressure drop in inclined pipes, which must be combined with frictional losses for total pressure drop.

Gas Pipeline Applications

For natural gas pipelines, a different parameter called the transmission factor is commonly used:

Native Excel capabilities

Excel has no built-in functions for calculating friction factors or pressure drops. Users typically: - Manually implement explicit correlations (Swamee-Jain, Haaland) in formulas - Use iterative techniques (Goal Seek) to solve the implicit Colebrook equation - Reference pre-calculated Moody diagram values or lookup tables

These manual approaches are time-consuming, error-prone, and lack the specialized correlations for curved pipes or plate heat exchangers. Python functions provide immediate access to industry-standard correlations with validated implementations.

Third-party Excel add-ins

  • CheCalc Add-in: Provides various chemical engineering calculations including friction factors, though with limited correlation options.
  • LMNO Engineering Add-ins: Offers pipe flow calculations with basic friction factor correlations.
  • Engineering libraries: Most third-party add-ins focus on general pipe sizing rather than providing comprehensive friction factor correlation libraries like those in Python’s fluids package, which underlies these functions.

Tools

Tool Description
BLASIUS Calculates Darcy friction factor for turbulent flow in smooth pipes using the Blasius correlation.
CHURCHILL Calculate Darcy friction factor using the Churchill (1977) universal equation for all flow regimes.
CLAMOND Calculate Darcy friction factor using Clamond’s high-precision solution accurate to nearly machine precision.
COLEBROOK Calculate Darcy friction factor using exact solution to the Colebrook equation.
DP_GRAV Calculate gravitational pressure drop component for single-phase flow in inclined pipes.
FF_CURVED Calculate friction factor for fluid flowing in a curved pipe or helical coil, supporting both laminar and turbulent regimes.
FP_MARTIN Calculate Darcy friction factor for single-phase flow in Chevron-style plate heat exchangers using Martin (1999) correlation.
FP_MULEY_MANGLIK Calculate Darcy friction factor for single-phase flow in Chevron-style plate heat exchangers using Muley-Manglik correlation.
FRICTION_FACTOR Calculate the Darcy friction factor for fluid flow in a pipe using various correlations, automatically selecting appropriate method based on Reynolds number and relative roughness.
FRICTION_LAMINAR Calculate the Darcy friction factor for laminar flow using the theoretical solution fd = 64/Re.
FT_CRANE Calculate the Crane fully turbulent Darcy friction factor for flow in commercial pipe.
HAALAND Calculate Darcy friction factor using the Haaland (1983) approximation.
HELICAL_RE_CRIT Calculate the transition Reynolds number for fluid flowing in a curved or helical pipe between laminar and turbulent flow.
MOODY Calculate Darcy friction factor using the Moody (1947) correlation.
ONE_PHASE_DP Calculate single-phase pressure drop in a pipe using the Darcy-Weisbach equation.
SWAMEE_JAIN Calculate Darcy friction factor using the Swamee-Jain (1976) equation.
TRANS_FACTOR Convert between Darcy friction factor and transmission factor for compressible gas pipeline flow.
VON_KARMAN Calculate Darcy friction factor for rough pipes at infinite Reynolds number from the von Karman equation.