## 883

All tabulated values are in units of (ft3/s)/d5/2; d = diameter, ft; Dcrit = critical depth, ft. For SI units, multiply (m3/h)/m5/2 by 5.03 X 10-4 to obtain (ft3/s)/ft5/2. Examples 2, 3, and 4 illustrate the use of this table.

Source: Reference 13.

FIGURE 29 Area versus depth for a circular pipe pVD

In SI units: R =-(p in kg/m3, V in m/s, D in m, m in N-s/m2)

FIGURE 29 Area versus depth for a circular pipe pVD

In SI units: R =-(p in kg/m3, V in m/s, D in m, m in N-s/m2)

1 meter = 3.28 feet 1 VD (Vin m/s, D in m) = 129.2 VD" (Vin ft/s, D" in inches)

where Z = distance between suction and seal well levels (or discharge pool level if no seal well is used), ft (m)

hf(1_2) = frictional and minor losses from 1 to 2 (or 3 if no seal well is used), including exit velocity head loss at 2 (or 3), ft (m)

Use of Eq. 14 permits plotting of the normal system-head curve with a primed siphon, shown in Figure 28, for different flow rates. The normal pump flow is the intersection of the pump total head curve and the normal system-head curve.

If the pump cannot provide sufficient flow to prime the siphon, or if the driver does not have adequate power, the system must be primed externally by a vacuum or jet pump. An auxiliary priming pump can also be used to continuously vent the system because it is necessary that this be done to maintain full siphon recovery. In some systems, the water pumped is saturated with air, and as the liquid flows through the system, the pressure is reduced (and in cooling systems the temperature is increased). Both these conditions cause the release of some of the entrained air. Air will accumulate at the top of the siphon and in the upper parts of the down leg. The siphon works on the principle that an increase in elevation in the up leg produces a decrease in pressure and an equal decrease in elevation in the down leg resulting in recovery of this pressure. This cannot occur if the density of the liquid in the down leg is decreased as a result of the formation of air pockets. These air pockets also restrict the flow area. A release of entrained air and air leakage into the system through pipe joints and fittings will result in a centrifugal pump's delivering less than design flow, as the head will be higher than estimated. Also, high-specific-speed pumps with rising power curves toward shutoff can become overloaded. In order to maintain full head recovery, it is necessary to continuously vent the siphon at the top and at several points along the down leg, especially at the beginning of a change in slope.3 These venting points can be manifolded together and connected to a single downward venting system.

Some piping systems may contain several up and down legs; that is, several siphons in series. Each down leg, as in a single siphon, is vulnerable to air or vapor binding. The likelihood of flow reduction, and conceivably in some cases complete flow shutoff, is increased in a multiple siphon system.3 As shown in Figure 30, system static head is increased if

proper venting is not provided at the top of each siphon. Normally the static head is the difference between outlet and inlet elevations. If air pockets exist, head cannot be recovered and the normal static head is increased by the sum of the heights of all the intermediate liquidless pockets. Flow will stop when the total static head equals the pump shutoff head. The following examples illustrate the use of Eqs. 3,9,12,13, and 14, Table 1, and Figure 29.

example 2 A pump is required to produce a flow of 70,000 gpm (15,900 m3/h) through the system shown in Figure 27. Calculate the system total head from point 1 to point 3 (no seal well) under the following conditions:

Specific gravity = 0.998 for 80°F (26.7°C) water Barometric pressure = 29 in (73.7 cm) mercury abs (sp. gr. 13.6) Suction and discharge water levels are equal, Z = 0 Z1 = 40 ft (12.2 m)

Hf(1-s) = 3 ft (0.91 m) up-leg frictional head hf(S—3) = 3.3 ft (1 m) down-leg frictional head, including exit loss

Water vapor pressure = 0.507 lb/in2 (3.5 kPa) abs at 80°F (26.7°C) The maximum siphon height may be found from Eq. 12:

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