## Branches In Closedloop Systems

Figure 1 illustrates a pump and network of piping consisting of three parallel branches in series with common supply and return headers. Junction points 1 and 2 need not be at the same elevation (provided the liquid density remains constant and the pipes flow full and free of vapor) because, in a closed-loop system, the net change in elevation is zero. Figure

POSITIVE DISPLACEMENT"

POSITIVE DISPLACEMENT"

0 RATE OF FLOW

FIGURE 2 System-head curves for pump and branch lines shown in Figure 1 with all valves open

0 RATE OF FLOW

FIGURE 2 System-head curves for pump and branch lines shown in Figure 1 with all valves open

2 shows the system total-head curves for each branch line and header considered independent of the others. These curves are constructed for several flow rates by adding the frictional resistances of the pipes, fittings, and head losses through the equipment serviced from point 1 to point 2. Curves A, B, C, and D therefore represent the variation in system resistance in feet (meters) versus flow through each branch and header.

If the valves are open in all branches, the total system resistance, total pump flow, and individual branch flows are found by the following method. First observe that (a) the total flow must be equal to the sum of the branch flows, (b) the head loss or pressure drop across each branch from junction 1 to junction 2 is identical, and (c) the flow divides to produce these identical head losses. Therefore, at several head points, add together the flow through each branch and obtain curve A + B + C. Header D is in series with branches A, B, and C, and their system heads are added together for several flow conditions to obtain curve (A + B + C) + D. On curve E, the head-capacity characteristics of a centrifugal pump, point X represents the pump flow because at this point the system total head and pump total head are equal. Point Y'1_2 represents the total head across points 1 and 2, and this head determines the flow through each branch; consequently points a, b, and c give individual branch flows. Curve F represents the head-capacity characteristics of a positive displacement pump (constant capacity) that would produce the same flow conditions.

If valve A is open and valves B and C are closed, Figure 3 shows the construction of the curves required to determine pump flow point X'. Obviously the pump flow and branch A flow are the same. Note that the total flow of point X is less than when all valves are open as a result of an increase in system head. If all valves were open and the total flow was obtained by a positive displacement pump having a constant capacity curve F, closing valves B and C would not change the flow. The system head would, however, increase to point X" and the head would be greater than for a centrifugal pump having curve E.

Also shown in Figure 3 are the system total-head curves for different combinations of open valves A, B, and C and the resulting flow caused by a pump having characteristic curve E. For these various valve combinations, the head differential across the junction points is found by subtracting the head of the curve D from the system total head for the condition investigated, for example, point Y\_2 for only valve A open. The intersection of a horizontal line through point Y'1_2 and the individual branch curves gives the branch flow, as illustrated in Figure 2.

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