Friction Factors in the hf Package

Introduction

The Darcy friction factor ($f$) is a key parameter for calculating head loss. The hf package uses a functional programming approach, allowing users to “inject” different calculation methods into the Darcy-Weisbach functions.

Available Equations

Colebrook-White (calc_friction_cw)

The industry standard for turbulent flow in rough pipes. Being an implicit equation, hf solves it using numerical root-finding (uniroot).

$$\frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\epsilon}{3.7D} + \frac{2.51}{Re\sqrt{f}} \right)$$

Swamee-Jain (calc_friction_sj)

A highly accurate explicit approximation of the Colebrook-White equation. Recommended for high-performance calculations where numerical iteration is too slow.

$$f = \frac{0.25}{\left[ \log_{10} \left( \frac{\epsilon}{3.7D} + \frac{5.74}{Re^{0.9}} \right) \right]^2}$$

Haaland (calc_friction_haaland)

The Haaland equation is an excellent explicit alternative to the Colebrook-White equation. It provides highly accurate results for turbulent flows without the need for numerical iteration.

$$\frac{1}{\sqrt{f}} = -1.8 \log_{10} \left[ \left( \frac{\epsilon}{3.7D} \right)^{1.11} + \frac{6.9}{Re} \right]$$

Blasius (calc_friction_blasius)

An empirical formula for smooth pipes and Reynolds numbers up to $10^5$. It provides a simpler alternative when relative roughness is negligible.

$$f = \frac{0.3164}{Re^{0.25}}$$