# Small Problems

## TRN

TRN has eight undetermined pipes and nine prefixed pipes, two reservoirs fixed at 365.76 m (left) and 371.86 m (right) and nine demand nodes. New and cleaned pipes have the same Hazen-Williams roughness coefficient of 120. The minimum pressure of all the nodes under three demand patterns is specified in Table TRN.1. The decision variables are the pipe diameters for five new pipes and alternative options (duplication or cleaning or leaving alone) for three existing pipes. Each pipe has eight diameter options to choose from. Table TRN.2 shows available options for pipe diameter and the corresponding unit costs. Figure TRN.1 depicts the layout of TRN.

 Table TRN.1. Minimum pressure requirement of each node under three demand patterns of TRN
 Table TRN.2. Diameter options and associated unit costs of TRN
 Figure TRN.1. Layout of Two Reservoir Network (Undetermined pipes are shown in red lines.)

## TLN

Two loop network (TLN) consists of one reservoir, six demand nodes and eight pipes organised in two loops. The reservoir has a constant head fixed at 210 m. As a hypothetical network, all pipes have the same length (1000 m) and the Hazen-Williams coefficient of 130. The pressure is set to be at least 30.0 m at all demand nodes. Table TLN.1 shows commercially available diameters and the corresponding unit costs (1 in.=0.0254 m). Figure TLN.1 depicts the layout of TLN.

 Table TLN.1 Diameter options and associated unit costs of TLN
 Figure TLN.1. Layout of Two Loop Network

## BAK

BakRyan Network (BAK) has fifty-eight pipes including nine new pipes to be sized, thirty-five demand nodes, one reservoir with a fixed head of 58 m. The Hazen-Williams roughness coefficient for each new pipe is 100. The minimum pressure head above the ground elevation of each node is 15 m. Among the new pipes, six of them are parallel. Table BAK.1 shows commercially available diameters and the corresponding unit costs. Figure BAK.1 depicts the layout of BAK.

 Table BAK.1 Diameter options and associated unit costs of BAK
 Figure BAK.1 Layout of BakRyan Network (Undetermined pipes are shown in red lines.)