## Rate Of Flow

FIGURE 5 System-head curves for pump and branch lines shown in Figure 4

The total head at the junction is the head ZD in the suction tank measured above point 1 plus the pump total head less the frictional head loss hjD in line D, and it varies with flow, as illustrated by curve F.

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 frictional resistance plus the elevation head measured relative junction 1 for each branch is identical and (c) the flow divides to produce these identical total branch heads. Therefore, at several head points, add together the flow of each branch to obtain curve A + B + C. Supply line D is in series with branches A, B, and C, and their system heads are added algebraically for several flow conditions to obtain curve (A + B + C) + D. If curve E is 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 Y1 represents the total head at junction 1, and this head determines the flow through each branch; consequently points a, b, and c give individual branch flows.

In this example the pump discharges to all tanks, but this should not be assumed. There is a limiting liquid level elevation for each tank, and, if this level is exceeded, flow will be from the tank into the junction. Therefore it is possible for the lower-level tanks to be fed by the higher-level tank and the pump. The limit for the liquid elevation in tank B is Z'B, and it is found from the intersection of curve A + C with curve F, point Y "1.The flow in branches A and C is at rates a and c when there is no flow in branch B. This is also a condition similar to closing a valve in branch B.

If elevation ZB is greater than previously found limiting height ZB flow in branches A and C is determined in the following manner. Construct a curve for junction head versus flow by adding heads and flows that result when the pump and suction tank are in a series with each other and tank B (less line losses) is in parallel with the pump and suction tank. The intersection of this curve with curve A + C will give the junction head required to determine the individual flows from the pump and tank and the flows to tanks A and C (not illustrated).

If flow to branches B and C is shut off, Figure 5 illustrates the construction of the curves required to determine the pump flow point X and junction head point Y 1.

Bypass orifices around centrifugal pumps are often used to maintain a minimum flow recommended by the pump manufacturer because of one or more of the following reasons:

• To limit the temperature rise to prevent seizing and cavitation

• To reduce shaft and bearing loads

• To prevent excessive recirculation in the impeller and casing

• To prevent overloading of driver if pump power increases with decrease in flow

Figure 6 illustrates a system that under certain conditions reduces pump flow below the recommended minimum. The pump delivers its flow to either tank A or tank B. Figure 7 shows the separate system-head curves for flow to tank A and for flow to tank B. Curve E is the head-capacity characteristics of the centrifugal pump. Individual flow rates to each tank are shown as QA and QB. The recommended minimum flow is QR, which is greater than QB by the amount shown. In order to maintain the minimum flow, a bypass orifice with necessary pipe, valves, and fittings is required to pass flow Qc at total head HR is when the pump discharges to tank B only.

Figure 8, (curve C) shows the construction necessary to determine the required bypass head versus flow characteristics of the orifice and pipe. The bypass system-head curve C includes the pipe, valve, and fitting losses from the pump connection between the suction tank and the end of the bypass piping below the suction water level. These losses must be deducted from the total bypass losses to determine the required orifice head.

Figure 9 illustrates the resultant pump flow with the bypass in operation. Curve C is added to curve B to obtain curve B + C by combining flows through each system at the same heads. Note that flow through the piping from the suction tank to junction 1 is the

## Survival Treasure

This is a collection of 3 guides all about survival. Within this collection you find the following titles: Outdoor Survival Skills, Survival Basics and The Wilderness Survival Guide.

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