## Pressure At Pool Datum

It is instructive to derive Equation (4.44) by applying the energy equation between the wet well pool surface (point 1 of the lower tank) and the inlet to the pump (a or g). The equation is:

Y fs 2g e y where V1 = velocity at the wet pool level, z1 = elevation of the pool level with reference to a datum (the pool level, itself, in this case), P1 = pressure at pool level, hfs = friction loss from pool level to inlet of pump (the suction side friction loss), Va = velocity at inlet to the pump, za = elevation of the inlet to the pump with reference to the datum (the pool level), and Pa = pressure at the inlet to the pump. Pa is the absolute pressure at the pump inlet, i.e., not a gage pressure but an absolute pressure corrected for the vapor pressure of water. This type of absolute pressure is not the same as the normal absolute pressure where the prevailing barometric pressure is simply added to the gage reading. This is an absolute pressure where the vapor pressure is first subtracted from the gage reading Pgage and then the result added to the prevailing atmospheric pressure. In other words, Pa = Pgage - Pv + Patm. This produces the true pressure acting on the liquid at the inlet to the pump. By also considering the source tank above the center line of the impeller, the final equation after rearranging is:

V- + _a = V- + -J-M-v-^ = Patm P- _ he(or + hs) - hfs (4.45)

Therefore, NPSH is also

NPSH = -- + gage v ' - am = ----- +1 hi + am - (4.46)

Note that Pa/y is equal to Pgage - Pv + Patm/y = h + Patm - Pv /y, where the vapor pressure Pv has been subtracted to obtain the true pressure acting on the fluid as mentioned.

In simple words, the NPSH is the amount of energy that the fluid possesses at the inlet to the pump. It is the inlet dynamic head that pushes the fluid into the pump impeller blades. Finally, NPSH and cavitation effects must be related. If NPSH does not exist at the suction side, cavitation will, obviously, occur.

The next point to be considered is the influence of the NPSH on deep-well pumps. It should be clear that the depth of water that can be pumped is limited by the net positive suction head. We have learned, however, that when pumps are connected in series, the heads are added. Thus, it is possible to pump groundwater from any depth, if impellers of the pump are laid out in series. This is the principle used in the design of deep-well pumps.

Refer to the deep-well pump of Figure 4.3. This pump is shown to have two stages. The water lifted by the first stage is introduced to the second stage. And, since the stages are in series, the head developed in the first stage is added to that of the second stage. Thus, this pump is capable of pumping water from deeper wells. Deep-well pumps can be designed for any number of stages, within practical limits. Because of the limitation of the NPSH, these pumps must obviously be lowered toward the bottom at a distance sufficient to have a positive NPSH on the first impeller, with an ample margin of safety. Provide a margin of safety in the neighborhood of 90% of the calculated NPSH. In other words, if the computed NPSH is in the neighborhood of 7 m, for example, assume it to be 0.9(7) « 6 m.

Example 4.7 A wastewater is to be pumped to an elevation of 30 m above a sump. Overall friction losses of the system and the velocity at the discharge side are estimated to be 20 m and 1.30 m/s, respectively. The operating drive is to be 1,200 rpm. Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 mm and 225 mm, respectively. The vertical distance from the sump pool level to the pump centerline is 2 m. What is the NPSH?

Solution: The formula to be used is Equation 4.44.

Not all of these variables are given; therefore, some assumptions are necessary. In an actual design, this is what is actually done; the resulting design, of course, must be shown to work. Assume standard atmosphere and 20°C.

Patm = 101,325 N/m2 Pv = 2340 N/m2 y = 997 (9.81) N/m3 h( = 2 m hfs = 1.03 m

Therefore, NPSH = -/-i n 07; - 2 - 1.03 = 7.09 m of water Ans

### 4.7 pumping station head analysis

The pumping station (containing the pumps and station appurtenances) and the system piping constitute the pumping system. In this system, there are two types of characteristics: the pump characteristics and the system characteristic. The term system characteristic refers to the characteristic of the system comprising everything that contains the flow except the pump casing and the impeller inside it.

Specifically, system characteristic is the relation of discharge Q and the associated head requirements of this system which, again, does not include the pump arrangement. The pump arrangement may be called the pump assembly. In the design of a pumping station, both the pump characteristics and the system characteristic must be considered simultaneously.

For convenience, reproduce the formulas for TDH as follows:

TDH = TDHfullsd = B atm + + z2 + hfs + hfd (c) P — P V2

TDH is the "total developed head" developed inside the pump casing, that is, developed by the pump assembly. This TDH is equal to any of the right-hand-side expressions of the above equations. If the TDH on the left refers to the pump assembly, then the right-hand-side expressions must refer to the system piping. By assuming different values of discharge Q, corresponding values of the right-hand-side expressions can be calculated. These values are head loss equivalents corresponding to the Q assumed. This is the relationship of the various Qs and head losses in the system characteristic mentioned above. As can be seen, these head losses are head loss requirements for the associated Q. It is head loss requirements that the TDH of the pump assembly must satisfy. Call head loss requirements TDHR. TDHR, therefore, requires the TDH of the pump.

It should be obvious that, if the TDH of the pump assembly is less than the TDHR of the system piping, no fluid will flow. To ensure that the proper size of pumps are chosen for a given desired pumping rate, the TDH of the pumps must be equal to the TDHR of the system piping. This is easily done by plotting the pump head-discharge-characteristic curve and the system-characteristic curve on the same graph. The point of intersection of the two curves is the desired operating point. The principle of series or parallel connections of pumps must be used to arrive at the proper pump combination to suit the desired system characteristic requirement. The specific speed should be checked to ensure that the pump assembly selected operates at the best operating efficiency.

The system piping is composed of the suction piping and the discharge piping system. Both the suction and the discharge piping systems would include the piping

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