Chapter VII: Pumps and Pumping Stations (2)

“Fig. 70 attempts to represent graphically, the writer’s ideas
under general conditions, of the machines that should be selected
for certain capacities for both principal engine and alternate and
the station duty they may be expected to produce, but you must
realize that this intends the principal engine doing at least 90
per cent of the work and that the head, the cost of coal, the load
factor, the cost of real estate ... the boiler pressure, and the
space available, and finally ... the funds available, are factors
which may shift both the horizontal and curved lines. In the field
of low service pumps of 10,000,000 capacity or over, the
centrifugal pump reigns supreme, and for constant low heads of
20,000,000 capacity or over the turbine driven centrifugal usurps
the field.”

A reciprocating pump of any type would have to be specially built for pumping sewage not carefully screened or otherwise treated, as the valves, ordinarily used in such pumps for lifting water, would clog. The vertical triple-expansion pumping engine with special valves and for large installations, and the centrifugal pump for large or small installations are the only suitable types for pumping sewage. With steam turbine or electric drive the centrifugal has the field to itself.

FIG. 70.—Expectancy Curves for Pumping Engines Working against a
Pressure of 100 Pounds per Square Inch.

J. N. Chester, Journal Am. Water Works Ass’n, Vol. 3, 1916, p. 493.
]

=87. Costs of Pumping Machinery.=—The cost of pumping machinery can not be stated accurately as the many factors involved vary with the fluctuations in the prices of raw materials, transportation, labor, etc. The actual purchase price of machinery can be found accurately only from the seller. The costs given in this chapter are useful principally for comparative purposes and for exercise in the making of estimates. The costs of complete pumping stations are shown in Table 31.[48] These figures represent costs in 1911.

TABLE 31

COSTS OF COMPLETE PUMPING STATIONS

These costs include the best type of triple-expansion engines,
high-pressure boilers, brick or inexpensive stone building with slate
roof, chimney and intake. Cost of land is not included.
─────────────────┬─────────────────┬─────────────────┬─────────────────
Discharge │ Horse-power per │ │
Pressure, Lbs. │ Million Gals. │Cost, Dollars per│Cost, Dollars per
per Sq. In. │ Pumped │ Horse-power │ Million Gallons
─────────────────┼─────────────────┼─────────────────┼─────────────────
30│ 12│ 562│ 6,750
40│ 16│ 438│ 7,000
50│ 20│ 362│ 7,250
60│ 24│ 312│ 7,500
70│ 28│ 277│ 7,750
80│ 32│ 250│ 8,000
90│ 36│ 229│ 8,250
100│ 40│ 213│ 8,500
110│ 44│ 200│ 8,750
120│ 48│ 187│ 9,000
130│ 52│ 192│ 10,000
│ │ │
─────────────────┴─────────────────┴─────────────────┴─────────────────

=88. Cost Comparisons of Different Designs.=—In the design of a pumping station and its equipment the relative costs of different designs should be compared, and the least expensive design selected, due consideration being given to serviceability, reliability, and other factors without definite financial value. In comparing the costs of different types of machinery, all items in connection with the pumping station should be considered. For example, the cost of an electrically driven centrifugal pump and equipment may be less than the total cost of a steam driven reciprocating pump and equipment because of the saving in the cost of boilers, boiler house, etc., but a comparison of the capitalized cost of the two might show in favor of the reciprocating steam pump because of the lower cost of operation.

The total cost of a plant, or any portion thereof, may be considered as made up of three parts: (1) The first cost, (2) operation and maintenance and, (3) renewal. The total cost S can be expressed as

_S_ = _C_ + _O_⁄_r_ + _R_,

in which _C_ = the first cost;

_O_ = the annual expenditure for operation and maintenance;

_R_ = the amount set aside to cover renewal;

_r_ = the rate of interest.

_S_ is called the capitalized cost of a plant. The annual payment necessary to perpetuate a plant is

_A_ = _Sr_ = _Cr_ + _O_ + _Rr_.

The value of _R_ is useful when expressed in terms of the life of the plant or machine and the current rate of interest. It is sometimes called the depreciation factor or capitalized depreciation. If it is borne in mind that _R_ is the amount to be set aside at compound interest for the life of the plant, at the end of which time the accrued interest should be sufficient to renew the plant, it is evident that

_R_(1 + _R_)^n − _R_ = _C_

or _R_ = _C_⁄((1+_r_)^n − 1)

in which _n_ is the period of usefulness, or life of the plant, expressed in years, no allowance being made for scrap value.

A comparison of the annual expense of three different plants is shown in Table 32. It is evident from this comparison that the machinery with the least first cost is not always the least expensive when all items are considered.

A sinking fund is a sum of money to which additions are made annually for the purpose of renewing a plant at the expiration of its period of usefulness. The annual payment into the sinking fund is equivalent to the term _Rr_ in the expression for annual cost, or in terms of _C_, _r_, and _n_, the annual payment is

_Cr_⁄((1 + _r_)^n − 1).

It is the same as the capitalized depreciation multiplied by the rate of interest. The expression _r_⁄((1 + _r_)^n − 1) is sometimes called the rate of depreciation.

The present worth of a machine is the difference between its first cost and the present value of the sinking fund. If _m_ represents the present age of a plant in years, then the present worth is

_P_ = _C_(1 – ((1 + _r_)^n − 1)⁄((1 + _r_)^m − 1)).

TABLE 32

COMPARISON OF COSTS OF THREE DIFFERENT PUMPING STATIONS. NOMINAL
CAPACITY THIRTY MILLION GALLONS PER DAY RAISED THIRTY FEET

────────────────┬──────────────────────────────────
Equipment │ Plant A
────────────────┼──────────────────────────────────
│One Acre of Land. Brick Building,
│ Steel Trussed Roof, Slate
│ Covered. Cross Compound
│ Condensing Horizontal Pumping
│ Engine
────────────────┼───────┬──────────┬───────┬───────
│Annual │ Years of │Sinking│ Total
│Payment│Usefulness│ Fund │
│ on │ │Payment│
│ First │ │ │
│ Cost │ │ │
────────────────┼───────┼──────────┼───────┼───────
Land │ 100│ │ 0│ 100
Permanent │ 1188│ 50│ 1080│ 2,260
Structures[49]│ │ │ │
Pumps and │ 440│ 15│ 435│ 875
Machinery │ │ │ │
Boilers │ 280│ 10│ 446│ 726
Labor │ │ │ │ 14,000
Fuel │ │ │ │ 5,500
Repairs, etc. │ │ │ │ 480
────────────────┼───────┼──────────┼───────┼───────
Total │ │ │ │ 23,941
────────────────┴───────┴──────────┴───────┴───────

────────────────┬──────────────────────────────────
Equipment │ Plant B
────────────────┼──────────────────────────────────
│One Acre of Land. Brick Building.
│ Steel Trussed Roof, Slate
│ Covered. Compound Condensing Low
│ Duty Horizontal Pumping Engine
│
────────────────┼───────┬──────────┬───────┬───────
│Annual │ Years of │Sinking│ Total
│Payment│Usefulness│ Fund │
│ on │ │Payment│
│ First │ │ │
│ Cost │ │ │
────────────────┼───────┼──────────┼───────┼───────
Land │ 100│ │ 0│ 100
Permanent │ 1180│ 50│ 1080│ 2,260
Structures[49]│ │ │ │
Pumps and │ 390│ 15│ 395│ 785
Machinery │ │ │ │
Boilers │ 252│ 10│ 400│ 652
Labor │ │ │ │ 14,000
Fuel │ │ │ │ 7,200
Repairs, etc. │ │ │ │ 400
────────────────┼───────┼──────────┼───────┼───────
Total │ │ │ │ 25,497
────────────────┴───────┴──────────┴───────┴───────

────────────────┬──────────────────────────────────
Equipment │ Plant C
────────────────┼──────────────────────────────────
│One Acre of Land. Frame Building,
│ Shingle Roof. Compound Duplex
│ Non-Condensing Pumping Engine.
│
│
────────────────┼───────┬──────────┬───────┬───────
│Annual │ Years of │Sinking│ Total
│Payment│Usefulness│ Fund │
│ on │ │Payment│
│ First │ │ │
│ Cost │ │ │
────────────────┼───────┼──────────┼───────┼───────
Land │ 100│ │ 0│ 100
Permanent │ 810│ 50│ 775│ 1,585
Structures[49]│ │ │ │
Pumps and │ 360│ 15│ 352│ 712
Machinery │ │ │ │
Boilers │ 308│ 10│ 490│ 798
Labor │ │ │ │ 14,000
Fuel │ │ │ │ 8,200
Repairs, etc. │ │ │ │ 550
────────────────┼───────┼──────────┼───────┼───────
Total │ │ │ │ 25,945
────────────────┴───────┴──────────┴───────┴───────

Where straight-line depreciation is spoken of it is assumed that the worth of a machine depreciates an equal part of its first cost each year. For example, if the life of a plant is assumed to be 20 years, straight-line depreciation will assume that the plant loses 1/20 of its original value annually. The present worth of a plant under this assumption would be the product of its first cost and the ratio between its remaining life and its total life. This method of estimating depreciation and worth is frequently used, particularly for short-lived plants and for simplicity in bookkeeping, but it is less logical than the method given above.

=89. Number and Capacity of Pumping Units.=—In order to select the number and capacity of pumping units for the best economy, a comparison of the costs of different combinations of units should be made and the most economical combination determined by trial. The principles outlined in the preceding articles should be observed in making these comparisons. In a steam pumping station, when the number of units operating is less than the average daily maximum for the period, steam must nevertheless be kept on a sufficient number of boilers to operate the maximum number of pumps. This, and corresponding standby losses must not be overlooked, as they may show that a smaller number of larger units is ultimately more economical.

TABLE 33

SUMMARY OF FLUCTUATIONS OF SEWAGE FLOW AT A PROPOSED PUMPING STATION

─────────────────┬─────────────────┬─────────────────┬─────────────────
Number of Days │Flow in Thousand │ │
Loads Occurred in│ Gallons per │ │
One Year │ Minute │ Lift in Feet │ Horse-power
─────────────────┼─────────────────┼─────────────────┼─────────────────
1│ 293│ 6.0│ 450
8│ 163│ 8.6│ 354
15│ 119│ 10.0│ 300
18│ 106│ 10.6│ 284
23│ 88│ 11.2│ 249
31│ 69│ 12.2│ 211
32│ 65│ 12.4│ 204
45│ 51│ 13.4│ 173
41│ 50│ 13.5│ 169
30│ 45│ 13.8│ 158
28│ 44│ 13.9│ 154
23│ 40│ 14.2│ 143
21│ 38│ 14.4│ 137
18│ 35│ 14.6│ 129
12│ 29│ 15.0│ 111
8│ 24│ 15.6│ 95
5│ 20│ 16.0│ 79
3│ 16│ 16.5│ 65
2│ 14│ 16.8│ 58
1│ 6.5│ 18.0│ 29
─────────────────┴─────────────────┴─────────────────┴─────────────────
Total horse-power days for one year, 102,000.
Average load in horse-power, 280.

TABLE 34

POSSIBLE COMBINATIONS OF FIVE PUMPING UNITS TO CARE FOR THE LOADS SHOWN
IN TABLE 33[50]

──────────────────────────────────┬───────────────
40 Horse-power │ Load
Type 1[51] │
────────┬──────┬───────────┬──────┼───────┬───────
Per Cent│Pounds│ Load in │Pounds│Number │ Total
of Rated│Steam │Horse-power│Steam,│of Days│ Load
Capacity│ per │ │Units │Load is│Carried
│ H.P. │ │10,000│Carried│ on
│ Hour │ │Pounds│in Year│ these
│ │ │ │ │Days in
│ │ │ │ │ H.P.
────────┼──────┼───────────┼──────┼───────┼───────
151│ 45│ 60.4│ 6.5│ 1│ 681
120│ 44│ 48│ 40.5│ 8│ 542
102│ 45│ 40.8│ 66.1│ 15│ 458
96│ 45│ 38.4│ 74.8│ 18│ 434
98│ 45│ 39.2│ 97.5│ 23│ 381
│ │ │ │ 31│ 322
│ │ │ │ 32│ 312
│ │ │ │ 45│ 264
│ │ │ │ 41│ 258
101│ 45│ 40.4│ 131│ 30│ 242
98│ 45│ 39.2│ 119│ 28│ 235
│ │ │ │ 23│ 218
│ │ │ │ 21│ 210
│ │ │ │ 18│ 198
│ │ │ │ 12│ 170
104│ 45│ 41.6│ 20.9│ 8│ 145
│ │ │ │ 5│ 121
│ │ │ │ 3│ 100
99│ 45│ 39.6│ 8.5│ 2│ 89
113│ 44│ 45.2│ 4.8│ 1│ 45
│ │ │ ————│ │
Sub-total │ 596.6│ │
Grand total in pounds, 65,700,000
──────────────────────────────────────────────────

──────────────────────────────────┬───────────────
50 Horse-power │ Load
Type 1[51] │
────────┬──────┬───────────┬──────┼───────┬───────
Per Cent│Pounds│ Load in │Pounds│Number │ Total
of Rated│Steam │Horse-power│Steam,│of Days│ Load
Capacity│ per │ │Units │Load is│Carried
│ H.P. │ │10,000│Carried│ on
│ Hour │ │Pounds│in Year│ these
│ │ │ │ │Days in
│ │ │ │ │ H.P.
────────┼──────┼───────────┼──────┼───────┼───────
151│ 45│ 75.5│ 8.2│ 1│ 681
120│ 44│ 60.0│ 50.7│ 8│ 542
102│ 45│ 51.0│ 82.7│ 15│ 458
90│ 45│ 48.0│ 93.5│ 18│ 434
98│ 45│ 49.0│ 122.0│ 23│ 381
104│ 45│ 52.0│ 174.5│ 31│ 322
101│ 45│ 50.5│ 174.8│ 32│ 312
│ │ │ │ 45│ 264
103│ 45│ 51.5│ 228│ 41│ 258
│ │ │ │ 30│ 242
│ │ │ │ 28│ 235
│ │ │ │ 23│ 218
│ │ │ │ 21│ 210
│ │ │ │ 18│ 198
│ │ │ │ 12│ 170
│ │ │ │ 8│ 145
109│ 44│ 54.5│ 28.8│ 5│ 121
│ │ │ │ 3│ 100
99│ 45│ 49.5│ 10.7│ 2│ 89
│ │ │ │ 1│ 45
│ │ │ ————│ │
│ 973.9│ │

──────────────────────────────────────────────────

──────────────────────────────────┬───────────────
60 Horse-power │ Load
Type 1[51] │
────────┬──────┬───────────┬──────┼───────┬───────
Per Cent│Pounds│ Load in │Pounds│Number │ Total
of Rated│Steam │Horse-power│Steam,│of Days│ Load
Capacity│ per │ │Units │Load is│Carried
│ H.P. │ │10,000│Carried│ on
│ Hour │ │Pounds│in Year│ these
│ │ │ │ │Days in
│ │ │ │ │ H.P.
────────┼──────┼───────────┼──────┼───────┼───────
151│ 45│ 90.6│ 9.8│ 1│ 681
120│ 44│ 72.0│ 60.8│ 8│ 542
102│ 45│ 61.2│ 99.2│ 15│ 458
96│ 45│ 57.6│ 112│ 18│ 434
│ │ │ │ 23│ 381
104│ 45│ 62.4│ 209.0│ 31│ 322
101│ 45│ 60.6│ 210│ 32│ 312
102│ 45│ 61.2│ 325│ 45│ 264
│ │ │ │ 41│ 258
│ │ │ │ 30│ 242
│ │ │ │ 28│ 235
│ │ │ │ 23│ 218
│ │ │ │ 21│ 210
│ │ │ │ 18│ 198
106│ 45│ 63.6│ 137│ 12│ 170
│ │ │ │ 8│ 145
109│ 44│ 65.4│ 34.5│ 5│ 121
│ │ │ │ 3│ 100
│ │ │ │ 2│ 89
│ │ │ │ 1│ 45
│ │ │ ————│ │
│1197.3│ │

──────────────────────────────────────────────────

──────────────────────────────────┬───────────────
100 Horse-power │ Load
Type 4[51] │
────────┬──────┬───────────┬──────┼───────┬───────
Per Cent│Pounds│ Load in │Pounds│Number │ Total
of Rated│Steam │Horse-power│Steam,│of Days│ Load
Capacity│ per │ │Units │Load is│Carried
│ H.P. │ │10,000│Carried│ on
│ Hour │ │Pounds│in Year│ these
│ │ │ │ │Days in
│ │ │ │ │ H.P.
────────┼──────┼───────────┼──────┼───────┼───────
151│ 28│ 151│ 10.2│ 1│ 681
120│ 25│ 120│ 57.5│ 8│ 542
102│ 25│ 102│ 62.5│ 15│ 458
96│ 25│ 96│ 103.8│ 18│ 434
98│ 25│ 98│ 135.1│ 23│ 381
│ │ │ │ 31│ 322
│ │ │ │ 32│ 312
│ │ │ │ 45│ 264
│ │ │ │ 41│ 258
│ │ │ │ 30│ 242
│ │ │ │ 28│ 235
│ │ │ │ 23│ 218
│ │ │ │ 21│ 210
│ │ │ │ 18│ 198
106│ 25│ 106│ 76.5│ 12│ 170
104│ 25│ 104│ 29.1│ 8│ 145
│ │ │ │ 5│ 121
100│ 25│ 100│ 32.4│ 3│ 100
│ │ │ │ 2│ 89
│ │ │ │ 1│ 45
│ │ │ ————│ │
│ 507.1│ │

──────────────────────────────────────────────────

──────────────────────────────────┬───────────────
200 Horse-power │ Load
Type 5[51] │
────────┬──────┬───────────┬──────┼───────┬───────
Per Cent│Pounds│ Load in │Pounds│Number │ Total
of Rated│Steam │Horse-power│Steam,│of Days│ Load
Capacity│ per │ │Units │Load is│Carried
│ H.P. │ │10,000│Carried│ on
│ Hour │ │Pounds│in Year│ these
│ │ │ │ │Days in
│ │ │ │ │ H.P.
────────┼──────┼───────────┼──────┼───────┼───────
151│ 23│ 302│ 16.7│ 1│ 681
120│ 20│ 240│ 92.0│ 8│ 542
102│ 20│ 204│ 147│ 15│ 458
96│ 20│ 192│ 166│ 18│ 434
98│ 20│ 196│ 216│ 23│ 381
104│ 20│ 208│ 309.5│ 31│ 322
101│ 20│ 202│ 310│ 32│ 312
102│ 20│ 204│ 481│ 45│ 264
103│ 20│ 206│ 405│ 41│ 258
101│ 20│ 202│ 291│ 30│ 242
98│ 20│ 196│ 264│ 28│ 235
109│ 20│ 218│ 241│ 23│ 218
105│ 20│ 210│ 212│ 21│ 210
99│ 20│ 198│ 171│ 18│ 198
│ │ │ │ 12│ 170
│ │ │ │ 8│ 145
│ │ │ │ 5│ 121
│ │ │ │ 3│ 100
│ │ │ │ 2│ 89
│ │ │ │ 1│ 45
│ │ │ ————│ │
│3322.2│ │

──────────────────────────────────────────────────

TABLE 35

FINANCIAL COMPARISON OF PUMPING EQUIPMENTS

The loads to be cared for are shown in Table 34. An emergency unit is supplied to bring the overload capacity of the plant, less the largest unit, equal to the maximum load on the plant. No unit will be overloaded more than fifty per cent of its rated capacity.

───────────┬───────────┬───────────┬───────────┬───────────┬───────────
Number of │ │ │ │ │
Units │ │ │ │ │
Exclusive │ │ │ │ │
of │ │ │ │ │
Emergency │ │ │ │ │
Unit │ 5 │ 4 │ 3 │ 2 │ 1
───────────┼───────────┼───────────┼───────────┼───────────┼───────────
Capacity │ 40 h.p.,│ │ │ │
and Type of│ Type 1│ │ │ │
Units │ 50 h.p.,│ 50 h.p.,│ │ │
│ Type 1│ Type 1│ │ │
│ 60 h.p.,│ 100 h.p.,│ 50 h.p.,│ │
│ Type 1│ Type 4│ Type 1│ │
│ 100 h.p.,│ 125 h.p.,│ 150 h.p.,│ 200 h.p.,│
│ Type 4│ Type 4│ Type 5│ Type 5│
│ 200 h.p.,│ 175 h.p.,│ 250 h.p.,│ 250 h.p.,│ 450 h.p.,
│ Type 5│ Type 5│ Type 6│ Type 6│ Type 7
───────────┼───────────┼───────────┼───────────┼───────────┼───────────
Emergency │ │ │ │ │
Unit, │ │ │ │ │
Capacity │ 200 h.p.,│ 175 h.p.,│ 250 h.p.,│ 250 h.p.,│ 450 h.p.,
and Type │ Type 5│ Type 5│ Type 6│ Type 6│ Type 7
───────────┼───────────┼───────────┼───────────┼───────────┼───────────
Annual │ │ │ │ │
payments,│ │ │ │ │
Dollars │ │ │ │ │
First │ │ │ │ │
cost of│ │ │ │ │
pumps │ 1,560│ 1,660│ 1,480│ 1,440│ 1,500
Renewal │ │ │ │ │
of │ │ │ │ │
pumps │ 1,340│ 1,430│ 1,270│ 1,240│ 1,290
First │ │ │ │ │
cost, │ │ │ │ │
boilers│ 1,024│ 1,089│ 1,125│ 1,115│ 1,410
Renewal, │ │ │ │ │
boilers│ 800│ 935│ 966│ 958│ 1,210
Fuel │ 13,140│ 11,860│ 10,490│ 9,420│ 9,400
Repairs, │ │ │ │ │
oil, │ │ │ │ │
etc. │ 2,000│ 1,800│ 1,500│ 1,300│ 1,200
Labor │ 35,000│ 31,500│ 29,500│ 27,000│ 27,000
Emergency│ │ │ │ │
unit. │ │ │ │ │
First │ │ │ │ │
cost │ 640│ 560│ 800│ 800│ 1,500
Emergency│ │ │ │ │
unit. │ │ │ │ │
Renewal│ 550│ 480│ 690│ 690│ 1,290
───────────┼───────────┼───────────┼───────────┼───────────┼───────────
Total │ 56,134│ 51,314│ 47,821│ 43,963│ 45,800
───────────┴───────────┴───────────┴───────────┴───────────┴───────────

Type 1. Simple duplex, non-condensing, horizontal.

Type 4. Compound condensing low duty horizontal.

Type 5. Low duty, triple, condensing, horizontal.

Type 6. Cross compound, condensing, horizontal.

Type 7. High duty, triple, condensing, vertical.

For example, the sewage flow expected at a proposed pumping station is shown in Table 33. The steps involved in the selection of the number and capacity of pumping units to care for these quantities are as follows: (1) Determine the rated capacity of the equipment to be provided. In this case the capacity will be taken as 450 horse-power, which is the maximum load to be placed on the pumps. (2) Select any number of units of such different types and capacities as are available for comparison, and arrange them in different combinations so that each unit will operate as nearly as possible at its rated capacity. The work involved in such a study for 5 units is shown in Table 34. The weight of steam consumed per indicated horse-power hour corresponding to the per cent of the rated capacity at which the unit is operating is read from Fig. 64 or other data. (3) Repeat this step for other numbers and types of units. (4) Prepare a table showing the annual costs of combinations of different numbers and types of units as shown for this example in Table 35. The figures in Table 35 show that the least expensive of the combinations of the units studied is one 200 horse-power unit, and one 250 horse-power unit, with a 250 horse-power unit in reserve. It is to be noted that a reserve unit has been provided in each combination, the capacity of which is equal to that of the largest unit of the combination.