 Sewer

Rising main

Section A-A

Sewer

Sectional plan

Rising main

FIGURE 4.1 Plan and section of a pumping station showing parallel connections.

### FIGURE 4.2 Pumps connected in series.

unit through the eye of the impeller. This is indicated in Figure 4.2 where the "Q in" line meets the "eye." In positive-displacement pumps, no eye exists.

The left-hand side of Figure 4.3 shows an example of a positive-displacement pump. Note that the screw pump literally pushes the wastewater in order to move it. The right-hand side shows a cutaway view of a deep-well pump. This pump is a centrifugal pump having two impellers connected in series through a single shaft forming a two-stage arrangement. Thus, the head developed by the first stage is added to that of the second stage producing a much larger head developed for the whole assembly. As discussed later in this chapter, this series type of connection is necessary for deep wells, because there is a limit to the depth that a single pump can handle.

Figure 4.4 shows various types of impellers that are used in centrifugal pumps. The one in a is used for axial-flow pump. Axial-flow pumps are pumps that transmit the fluid pumped in the axial direction. They are also called propeller pumps, because the impeller simply propels the fluid forward like the movement of a ship with propellers. The impeller in d has a shroud or cover over it. This kind of design can develop more

FIGURE 4.1 Plan and section of a pumping station showing parallel connections.

Q out Q out

Impeller eye

FIGURE 4.2 Pumps connected in series. FIGURE 4.3 A screw pump, an example of a positive-displacement pump (left); cutaway view of a deep-well pump (right). FIGURE 4.4 Various types of pump impellers: (a) axial flow; (b) open type; (c) mix-flow type; and (d) shrouded impeller.

head as compared to the one without a shroud. The disadvantage, however, is that it is not suited for pumping liquids containing solids in it, such as rugs, stone, and the like, because these materials may easily clog the impeller.

In general, a centrifugal impeller can discharge its flow in three ways: by directly throwing the flow radially into the side of the chamber circumscribing it, by conveying the flow forward by proper design of the impeller, and by a mix of forward and radial throw of the flow. The pump that uses the first impeller is called a radial-flow pump; the second, as mentioned previously, is called the axial-flow pump; and the third pump that uses the third type of impeller is called a mixed-flow pump. The impeller in c is used for mixed-flow pumps.

Figure 4.5 shows various impellers used for positive-displacement pumps and for centrifugal pumps. The figures in d and e are used for centrifugal pumps. The figure in e shows the impeller throwing its flow into a discharge chamber that circumscribes a circular geometry as a result of the impeller rotating. This chamber is shaped like a spiral and is expanding in cross section as the flow moves into the outlet of the pump. Because it is shaped into a spiral, this expanding chamber is called a volute—another word for spiral. In centrifugal pumps, the kinetic energy that the flow possesses while in the confines of the impeller is transformed into pressure energy when discharged into the volute. This progressive expansion of the cross section of the volute helps in transforming the kinetic energy into pressure energy without much loss of energy. Using diffusers to guide the flow as it exits

FIGURE 4.5 Various types of pump impellers, continued: (a) lobe type; (b) internal gear type; (c) vane type; (d) impeller with stationary guiding diffuser vanes; (e) impeller with volute discharge; and (f) external gear type impeller.

Outlet

Internal seal here Outlet

Internal seal here FIGURE 4.5 Various types of pump impellers, continued: (a) lobe type; (b) internal gear type; (c) vane type; (d) impeller with stationary guiding diffuser vanes; (e) impeller with volute discharge; and (f) external gear type impeller.

from the tip of the impeller into the volute is another way of avoiding loss of energy. This type of design is indicated in d, showing stationary diffusers as the guide.

The figure in a is a lobe pump, which uses the lobe impeller. A lobe pump is a positive-displacement pump. As indicated, there is a pair of lobes, each one having three lobes; thus, this is a three-lobe pump. The turning of the pair is synchronized using external gearings. The clearance between lobes is only a few thousandths of a centimeter, thus only a small amount of leakage passes the lobes. As the pair turns, the water is trapped in the "concavity" between two adjacent lobes and along with the side of the casing is positively moved forward into the outlet. The figures in b and f are gear pumps. They basically operate on the same principle as the lobe pumps, except that the "lobes" are many, which, actually, are now called gears. Adjacent gear teeth traps the water which, then, along with the side of the casing, moves the water to the outlet. The gear pump in b is an internal gear pump, so called because a smaller gear rolls around the inside of a larger gear. (The smaller gear is internal and inside the larger gear.) As the smaller gear rolls, the larger gear also rolls dragging with it the water trapped between its teeth. The smaller gear also traps water between its teeth and carries it over to the crescent. The smaller and the larger gears eventually throw their trapped waters into the discharge outlet. The gear pump in f is an external gear pump, because the two gears are contacting each other at their peripheries (external). The pump in c is called a vane pump, so called because a vane pushes the water forward as it is being trapped between the vane and the side of the casing. The vane pushes firmly against the casing side, preventing leakage back into the inlet. A rotor, as indicated in the figure, turns the vane.

Fluid machines that turn or tend to turn about an axis are called turbomachines. Thus, centrifugal pumps are turbomachines. Other examples of turbomachines are turbines, lawn sprinklers, ceiling fans, lawn mower blades, and turbine engines. The blower used to exhaust contaminated air in waste-air works is a turbomachine.

In the design of pumping stations, the engineer must ensure that the pumping system can deliver the fluid to the desired height. For this reason, energies are conveniently expressed in terms of heights or heads. The various terminologies of heads are defined in Figure 4.6. Note that two pumping systems are portrayed in the figure: pumps connected in series and pumps connected in parallel. Also, two sources of the water are pumped: the first is the source tank above the elevation of the eye of the impeller or centerline of the pump system; the second is the source tank below the eye of the impeller or centerline of the pump system. The flow in flow pipes for the first case is shown by dashed lines. In addition, the pumps used in this pumping station are of the centrifugal type.

The terms suction and discharge in the context of heads refer to portions of the system before and after the pumping station, respectively. Static suction lift h( is the vertical distance from the elevation of the inflow liquid level below the pump inlet to the elevation of the pump centerline or eye of the impeller. A lift is a negative head. Static suction head hs is the vertical distance from the elevation of the inflow liquid level above the pump inlet to the elevation of the pump centerline. Static discharge head hd is the vertical distance from the centerline elevation of the pump to the elevation of the discharge liquid level. Total static head hst is the vertical distance from the elevation of the inflow liquid level to the elevation of the discharge liquid level. Suction velocity head hvs is the entering velocity head at the suction side of the pump hydraulic system. This is not the velocity head at the inlet to a pump such as points a, c, e, etc. in the figure. In the figure, because the velocity in the wet well is practically zero, hvs will also be practically zero. Discharge velocity head hvd is the outgoing velocity head at the discharge side of the pump hydraulic system. Again, this is not the velocity head at the discharge end of any particular pump. In the figure, it is the velocity head at the water level in the discharge tank, which is also practically zero.

The literature has used two names for this subject: total dynamic head or total developed head (H or TDH). Let us derive TDH first by considering the system connected in parallel between points 1 and 2. Since the connection is parallel, the head losses across each of the pumps are equal and the head given to the fluid in each of the pumps are also equal. Thus, for our analysis, let us choose any pump such as the one with inlet g. From fluid mechanics, the energy equation between the points is

where P, V, and z are the pressure, velocity, and elevation head at the indicated points; g is the acceleration due to gravity; hf is the head equivalent of the resistance loss (friction) between the points; hq is the head equivalent of the heat added to the flow;

and hp is the head given to the fluid by the pump impeller. Using the level at point 1 as the reference datum, z1 equals zero and z2 equals hst. It is practically certain that there will be no hq in the physical-chemical treatment of water and wastewater, and will therefore be neglected. Let hf be composed of the head loss inside the pump hlp, plus the head loss in the suction side of the pumping system hfs and the head loss in the discharge side of the pumping system hfd. Thus, the energy equation becomes

The equation may now be solved for -hp + hp. This term is composed of the head added to the fluid by the pump impeller, hp, and the losses expended by the fluid inside the pump, hlp. As soon as the fluid gets the hp, part of this will have to be expended to overcome frictional resistance inside the pump casing. The fluid that is actually receiving the energy will drag along those that are not. This dragging along is brought about because of the inherent viscosity that any fluid possesses. The process causes slippage among fluid planes, resulting in friction and turbulent mixing. This friction and turbulent mixing is the hlp. The net result is that between the inlet and the outlet of the pump is a head that has been developed. This head is called the total developed head or total dynamic head (TDH) and is equal to -hlp + hp.

Solving Equation (4.2) for -hlp + hp, considering that the tanks are open to the atmosphere and that the velocities at points 1 and 2 at the surfaces are practically zero, produces

When the two tanks are open to the atmosphere, P1 and P2 are equal; they, therefore, cancel out of the equation. Thus, as shown in the equation, TDH is referred to as TDHOsd. In this designation, O stands for the fact that the pressures cancel out. The s and d signify that the suction and discharge losses are used in calculating TDH.

The sum hfs + hfd may be computed as the loss due to friction in straight runs of pipe, hfr , and the minor losses of transitions and fittings, hfm. Thus, calling the corresponding TDH as TDHOrm (rm for run and minor, respectively),

where f is Fanning's friction factor, l is the length of the pipe, D is the diameter of the pipe, V is the velocity through the pipe, g is the acceleration due to gravity 2 2 (equals 9.81 m/s ) and K is the head loss coefficient. V /2g is called the velocity head, hv. That is,

If the points of application of the energy equation is between points 1 and B, instead of between points 1 and 2, the pressure terms and the velocity heads will remain intact at point B. In this situation, refering to the TDH as TDHfullsd (full because velocities and pressure are not zeroed out), p _ p v 2

TDH = TDHfullsd = -hlp + hp = B atm + 2g + z2 + f + hfd (4.8)

where z2 is the elevational head of point B, referred to the chosen datum at point 1. Note that Patm is the pressure at point 1, the atmospheric pressure. When the friction losses are expressed in terms of hfr + hfm and calling the TDH as TDH fullrm, the equation is

TDH = TDHfullrm = -hlp + hp = B atm + 2g + z2 + hfr + hfm (4.9)

If the energy equation is applied using the source tank at the upper elevation as point 1, the same respective previous equations will also be obtained. In addition, if the energy equation is applied to the system of pumps that are connected in series, the same equations will be produced except that TDH will be the sum of the TDHs of the pumps in series. Also the subscripts denoted by B will be changed to A. See Figure 4.6.

Applying the energy equation between an inlet i and outlet o of any pump produces

(P V 2'\ (P V \ TDHmano = -hp + hp = (-o + ^J - + ^ J (4T0)

where TDHmano (mano for manometric) is the name given to this TDH. hfs + hfd is equal to zero. P/ y = ht is called either the inlet manometric head or the inlet manometric height absolute; Po Y = ho is also called either the outlet manometric head or the outlet manometric height absolute. The subscripts i and o denote "inlet" and "outlet," respectively.

Manometric head or level is the height to which the liquid will rise when subjected to the value of the gage pressure; on the other hand, manometric height absolute is the height to which the liquid will rise when subjected to the true or absolute pressure in a vacuum environment. The liquid rising that results in the manometric head is under a gage pressure environment, which means that the liquid is exposed to the atmosphere. The liquid rising, on the other hand, that results in the manometric height absolute is not exposed to the atmosphere but under a complete vacuum. Retain h as the symbol for manometric head and, for specificity, use habs as the symbol for manometric height absolute. Thus, the respective formulas are h = P (4.11) 