---
title: "Friction Factors in the hf Package"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Friction Factors in the hf Package}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
  
```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(hf)
```

## 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.

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