# Design rule purpose

The purpose of this design rule is to calculate all parameters related to gravity flow in water pipelines. The hydraulic profile is calculated (and validated) based on pipe parameters, required flow parameters, elevation changes. Gravity-fed pipelines are cost effective as they don't require (costly) pumping, especially when whole lifetime of the asset is taken into account. Optioneer takes flow requirements when generating and evaluating options and returns a lot of useful data on feasibility to the user.

# How to configure

This is a complex design rule that involves multiple steps and a large number of various parameters.

Step 1 - calculate the pipe loss parameters

There is a number of standard calculations this design rule is carrying out to find friction factors of the pipe based on its flow. The following steps are done:

1. Calculation of internal diameter based on outer diameter and standard dimensional ratio

2. Calculation of flow velocity based on internal area of the pipe and the required flow rate.

3. Calculation of the Reynolds number based on the velocity, pipe dimensions and water viscosity.

4. Calculation of the Swamee-Jain factor, a special case of Darcy’s equation, to calculate the friction factor of the pipe (formula for Swamee-Jain factor is provided below). Epsilon stands for pipe roughness, D stands for pipe internal diameter and Re is the Reynolds number.

Swamee-Jain factor:

Step 2 - calculate head loss along the pipe

Due to friction present during the flow, the pipe will exhibit an increasing head loss along its length. This head loss is the function of distance, pipe dimensions and the friction factor calculated in the previous step (Swamee-Jain factor). This factor is expressed ‘per unit length’.

Hydraulic slope factor:

Where ‘S' is the hydraulic slope factor, ‘f_D’ is the friction head loss, ‘g’ indicates the gravitational constant, ‘V’ is flow speed and 'D’ describes the diameter of the pipe.

Head loss at distance is then obtained by multiplying the hydraulic slope by the distance (chainage) of the pipe. The further away from the pump (starting point) the higher the total head loss is.

Step 3 - calculate the head loss due to potential energy change

Gravity flow assumes a head profile based on:

• difference in elevation between end point and start point,

• friction head loss along the length

Based on parameters outlined above, the profile of available head can be derived.

Required head is derived based on:

• elevation profile of the route

• minimum head requirement at each point

• friction loss along the length

An example of feasible gravity flow profile can be found below (observe all of required head is UNDER the available head):

An example of infeasible gravity flow profile can be found below (observe sections where required head is ABOVE the available head.

Sections where the profile is feasible are highlighted in green. Red sections indicate constraint violations that render the profile infeasible.

User can also specify starting head if there is any reason for that (like an elevated storage tank).

# Important notes

• This design rule might yield incorrect results if no feasible gravity-fed path can be found.

# Input / output summary

## Input parameters

This design rule doesn't require a dedicated dataset and draws terrain data from the 'elevation' dataset.

Pipe parameters:

 Name Default value Unit Pipe OD 0.355 meters Pipe ID 0.335 meters SDR 17 number Pipe roughness 0.05 coefficient

Flow parameters:

 Name Default value Unit Minimum static head required 2 meters Start head available 2 meters Flow rate 0.3 m3/s

## Output parameters

 Name Example value Unit Friction head 27.5 meters Static head 22 meters Total head 49.5 meters Hydraulic profile (head) plot Plot on Vertical Profile Chart Pressure profile plot Plot on Vertical Profile Chart