In this chapter you will find an in-depth analysis of the methods used by WCADI for solving irrigation queries. A discussion of techniques used by WCADI software to solve problems will enrich your understanding of the program and will enhance the efficiency with which you use it.

**Introduction**

Designing large-scale irrigation systems can be a time consuming procedure. This investment of time sometimes leads to either ambiguous or faulty results, despite the investment. Problem solving is eased by the use of the computer to generate an arithmetic model of the real-life problem and to efficiently solve the problem within the specifications requested.

WCADI adopts this approach to solving irrigation problems. A linear programming model is applied, provided the required parameters are supplied. Linear programming may best be described as the task of defining constraints to a model and obtaining the optimum points of the combined restraints.

If the requirements of a given system are entered into the WCADI software, along with all of the constraints and available resources, the most efficient solution, that achieves the requirements is constructed from the available resources.

Defining a model

A pipe network is constructed essentially of pipe lengths (or sections) and the intersection of those lengths (nodes). Pipe-sections are defined to be either main, sub-main or lateral sections of pipe

Htotal = Hph + Z + hloss

The pressure head Hph are computed for the inlets of the blocks. This makes computing the total head Htotal at a block’s inlet a matter of adding the surface elevation Z and the local head loss hloss in the take-off.

The total head for each take-off must be calculated separately. Once an optimum solution for the laterals is determined, the pressure heads Hph between and along the sub-mains and in all pipe-sections must be calculated.

Solution optimisation

Finding the most economically sound solution to the parameters, constraints, and requirements that define the system is dependant on efficient modelling of the costs of the system.

The cost per unit length of pipe C is dependant on the diameter of the pipe length. The cost of a pipe of length X is then C*X. The cost, along a certain section of pipe, is then the sum of the costs of all lengths of pipe.

C = åsection C*XZ

The total cost of all pipe lengths in the system is the summation of each section cost.

Ctotal = åOver Sections åsectionC*X

Determining the minimum solution to this equation is a primary objective of system optimisation.

Modelling constraints

Three primary constraints are defined before optimisation can be implemented:

1. Minimum pressure head at each node (see above).

2. The sum of the lengths of pipe that have a given diameter in a section is equal to the total length L.

3. Non-negativity of linear programming variables (i.e., pipe lengths are always positive values).

**Summary**

The WCADI Main pipe software has been designed to aid the irrigation specialist to develop optimal solutions to various system layouts. The software optimises the total cost of a given network, generates a detailed list of pipe material requirement (bill of quantities), calculates costs, determines pump requirements (including the use of booster pumps, if applicable), and displays network pressures and flows under various operating conditions. More than one operating condition can be analysed and optimised for different shifts of an irrigation system.

WCADI Main pipe can also be used to analyse existing networks. In this case, the equipment specific to that network must be specified.

Refer to the following example network while you read this chapter. Each of the functions of the Main pipe design menu is explained and displayed with an example table.

The Main Pipe Design consists of the following functions:

1 PARAMETERS FOR MAIN PIPE DESIGN

2 NODES

3 PIPE SECTIONS

4 OPERATING SYSTEM

5 DISCHARGE AND PRESSURE REQUIREMENTS

6 WATER SOURCE AND BOOSTER PUMPS

7 OPTIMISATION OF TOTAL COSTS

8 CHANGES IN THE DESIGNED NETWORK

9 PIPE NETWORK DIAMETERS AND COSTS

10 DESIGNED NETWORK HYDRAULICS

11 PUMP AND GENERAL EQUIPMENT

12 REDESIGN BLOCKS

13 ADDING TEXT TO THE MAIN PIPE DESIGN

14 CLEMENT FLOW CALCULATION

**Parameters for Main Pipe Design**

There are thirteen parameters for the Main pipe design which are described below. There is a default value for each of these parameters if the user does not enter this function or if he supplies only some of the 13 parameters. The parameters are stored in the Table of Main pipe parameters.

1. Number of nodes is entered here. When it is not filled in, the nodes entered with the aid of the Node function (see 9.2) are added up, to give the number of nodes.

2. Number of shifts is entered here or in the Operating System function as described in 9.3.

3. Velocity limits taken from sections table (0) pipe file (1). The user can either optimize his network using the velocity limits for a section of pipe or for each different diameter.

4. Shifts calculation flows from : 0-nodes 1-blocks?. If the user enters 1 in this parameter, all the flows and the pressures will be transferred automatically from the Block design to the Main pipe (from blocks to valves) ,0 from nodes .

5. To sort diameters in a branch? (N-0,Y-1). In order to eliminate having a design with large diameter pipes followed by small diameter pipes and again by large diameter pipes, the user can utilize this parameter to sort all the pipes in the network, according to ascending diameters. It is recommended that the optimization is first run with this parameter equal to 0.

6. Optimize according pressures (0) or energy cost (1,2). The user can select the type of optimization of the network either (0)-by giving the pressure of the pump. (1)-by giving the cost of pumping, the pump pressure will be part of the solution. (2)-by giving the cost of pumping, the pump pressure will not be part of the solution (no initialisation of pressures will be done).

7. The headloss for filtration (m). Here the user can enter the headloss for filtration which will then be added to the pressure of the pump.

8. The headloss for control valve (m). In this parameter the user can enter the headloss for the valves, which will be added to the minimum pressure needed at the valves.

9. The percentage of flow to be added during optimization (%). In order to have a safe design, the user can increase the flows of the different valves with the percentage that is entered here.

10. All valves of blocks as nodes? (N-0,Y-1). All the starting points of sub-mains, which have been defined in the Block design process, will automatically be defined as valves in the network.

11. Optimization including the class of pipe? (N-0,Y-1). This parameter offers the possibility to optimize the network and, simultaneously, determine the class of pipes to be used in each section. Make sure you have defined enough pipe files of different classes.

12. Pipe classes solving: pressures, add w. hammer, static head (0,1,2). In order to carry out parameter 11, the user must select the type of design pressures for the pipe classes analysis.

13. Design network using clement technique (0,1). If the user enters 1 in this parameter, all the flows and the pressures will be transferred automatically from clement.

1. Number of nodes 10

2. Number of shifts 2

3. Velocity limits from sections table (0) pipe file (1) 0

4. Shift calculation flows from : 0-nodes , 1-blocks 0

5. To sort diameters in a branch? (N-0,Y-1) 0

6. Optimize according pressures (0) or energy cost (1) 0

7. The head loss for filtration (m) 0.00

8. The head loss for control valve (m) 0.00

9. The percentage of flow to be added during optimization (%) 0.00

10. All valves of blocks as nodes? (N-0,Y-1) 1

11. Optimization including the class of pipe? (N-0,Y-1) 1

12. Pipe classes solving: pressures, add w hammer, static head (0,1,2) 0

13. Design network using clement technique (0,1) 0