---
title: "Flamant Head Loss"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Flamant Head Loss}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(hf)
```

## Introduction

The Flamant equation is an empirical formula widely used in agricultural hydraulics, particularly for micro-irrigation systems (drip and micro-sprinkler irrigation). It is highly accurate for calculating friction head loss in **small-diameter pipes** (typically under 50 mm) made of smooth materials like PVC and Polyethylene (PE).

### The Roughness Coefficient ($b$)

The $b$ factor represents the internal roughness of the pipe according to Flamant's experiments. For smooth plastic pipes (PVC, PE), the standard value is **$0.000135$**.

### Equations

The base mathematical equation for head loss ($h_f$) in the metric system is:
$$h_f = 6.107 \cdot b \cdot \frac{L \cdot Q^{1.75}}{D^{4.75}}$$

Where:

* $h_f$: Friction head loss (m)
* $L$: Pipe length (m)
* $Q$: Volumetric flow rate ($m^3/s$)
* $b$: Flamant roughness coefficient (dimensionless)
* $D$: Internal diameter (m)

---

## 1. Calculating Head Loss

To calculate the friction head loss, use the `calc_head_loss_flamant()` function. Let's calculate the expected head loss for a 50-meter PE pipe ($b = 0.000135$) with an internal diameter of 0.015 meters (15 mm) carrying a flow of $0.0002\ m^3/s$ (0.2 L/s).

```{r head_loss}
library(hf)
calc_head_loss_flamant(length = 50, flow = 0.0002, diameter = 0.015)
```

## 2. Calculating Required Diameter

If you know the maximum allowable head loss for your lateral irrigation line, you can determine the required minimum pipe diameter using `calc_diameter_flamant()`. Suppose the system allows a maximum head loss of 1.5 meters for a 50m length and a $0.0002\ m^3/s$ flow rate.

```{r diameter}
library(hf)
calc_diameter_flamant(loss = 1.5, length = 50, flow = 0.0002)
```

## 3. Calculating Flow Rate

To find the maximum flow rate a small pipe can deliver given an available pressure head, use the `calc_flow_flamant()` function.

```{r flow}
library(hf)
calc_flow_flamant(loss = 1.5, length = 50, diameter = 0.015)
```