CHAPTER VII
PUMPS AND PUMPING STATIONS
=68. Need.=—In the design of a sewerage system it is occasionally necessary to concentrate the sewage of a low-lying district at some convenient point from which it must be lifted by pumps. In the construction of sewers in flat topography the grade required to cause proper velocity of sewage flow necessitates deep excavation. It is sometimes less expensive to raise the sewage by pumping than to continue the construction of the sewers with deep excavation.
In the operation of a sewage-treatment plant a certain amount of head is necessary. If the sewage is delivered to the plant at a depth too great to make possible the utilization of gravity for the required head, pumps must be installed to lift the sewage. In the construction of large office buildings, business blocks, etc., the sub-basements are frequently constructed below the sewer level. The sewage and other drainage from the low portion of the building must therefore be removed by pumping. Because pumps are often an essential part of a sewerage system, their details should be understood by the engineer who must write the specifications under which they are purchased and installed.
=69. Reliability.=—If the only outlet from a sewerage system is through a pumping station, the inability of the pumps to handle all of the sewage delivered to them may so back up the sewage as to flood streets and basements, endangering lives and health and destroying property. Such an occurrence should be guarded against by providing sufficient pumping capacity and machinery of the greatest reliability.
=70. Equipment.=—The equipment of a sewage pumping station, in addition to pumping machinery, may include a grit chamber, a screen, and a receiving well. The grit chamber and screen are necessary to protect the pumps from wear and clogging. Grit chambers are not necessary in sewage devoid of gritty matter, such as the average domestic sewage, unless reciprocating pumps are used. Sufficient gritty matter is found in average domestic sewage to have an undesirable effect on reciprocating pumps. Receiving wells are used in small pumping stations where the capacity of the pumps is greater than the average rate of sewage flow. The pumps are then operated intermittently, the pumps standing idle during the time that the receiving well is filling.
Except for a few types of pumps of which the valve openings are unsuitable, any machine capable of pumping water is capable of pumping sewage which has been properly screened. The principles of sewage pumps are then similar to principles of water pumps. The conditions under which these principles are applied differ but slightly in the character of the liquid, and a smaller range of discharge pressures. Pumps with large passages, discharging under low heads are more commonly found among sewage pumps.
=71. The Building.=—The pumping station should, if possible, be of pleasing design and should be surrounded by attractive grounds. The Calumet Sewage Pumping Station in Chicago is shown in Fig. 49. Its architecture is pleasing particularly in contrast with its location and immediate surroundings. Such structures tend to remove the popular prejudice from sewerage and to arouse interest in sewerage questions. Service to the public is of value. It can be rendered more easily by arousing public interest and cooperation by the erection of attractive structures, than by feeding popular prejudice by the construction of miserable eyesores.
=72. Capacity of Pumps.=—The capacity of the pumping equipment should be sufficient to care for the maximum quantity of sewage delivered to it, with the largest pumping unit shut down, and the provision of such additional capacity as, in the opinion of the designer, will provide the necessary factor of safety.
Pumps can usually be operated under more or less overload. Power pumps and centrifugal pumps driven by constant speed electric motors have no overload capacity. A power pump or a centrifugal pump may be overloaded up to the maximum horse-power of any variable speed motor or steam engine driving it, provided the pump has been designed to permit it. Direct-acting steam pumps which are designed for proper piston speed and valve action at normal loads, can carry a 50 per cent overload for short periods, although the strain on the pump is great. They will carry a 20 to 25 per cent overload for about eight hours with less vibration and strain. The use of pumps capable of working at an appreciable overload is somewhat of an additional factor of safety, but the overload factor should not be taken into consideration in determining the capacity of the pumping equipment.
The load on a pumping station consists of the quantity of sewage to be pumped and the height it must be lifted. Variations in the quantity are discussed in Chapter III. The head against which the pumps must operate fluctuates with the level in the tributary sewer or pump well, and in the discharge conduit. For a free discharge or discharge into a short force main the greater the rate of sewage flow the smaller the lift, as the depth of flow in the tributary sewer increases more rapidly than that in the discharge conduit. If the discharge is into a large body of water or under other conditions where the discharge head is approximately constant, the fluctuations in total head should not exceed the diameter of the tributary sewer. Such fluctuations are of minor importance in the operation of direct-acting steam pumps, but may be of great importance in the operation of centrifugal pumps, as is brought out in Art. 78.
=73. Capacity of Receiving Well.=—The use of receiving wells is restricted to small installations which require, in addition to the standby unit, only one pump, the capacity of which is equal to the maximum rate of sewage flow. When the receiving well has been pumped dry the pump stops, allowing the well to fill again. Although the use of a large receiving well, or an equalizing reservoir, for a large pumping station would permit the operation of the pumps under more economical conditions, the storage of sewage for the length of time required would not be feasible. The sewage would probably become septic, creating odors and corroding the pumps. The extra cost of the reservoir might not compensate for the saving in the capacity and operation of the pumps.
The capacity of the receiving well should be so designed that the pump when operating will be working at its maximum capacity, and the period of rest during conditions of average rate of flow should be in the neighborhood of 15 to 20 minutes. For example, assume an average rate of flow of 2 cubic feet per second, with a maximum rate of double this amount. The pump should have a capacity of 4 cubic feet per second, and if the receiving well is to be filled in 15 minutes by the average rate of sewage flow its capacity should be 15 × 5 × 60 × 7.5 or 14,000 gallons. Under these circumstances the pump will operate 15 minutes and rest 15 minutes, during average conditions of flow.
=74. Types of Pumping Machinery.=—The two principal types of pumping machines for lifting sewage are centrifugal pumps and reciprocating pumps. A centrifugal pump is, in general, any pump which raises a liquid by the centrifugal force created by a wheel, called the impeller, revolving in a tight casing, as shown in Fig. 50. A reciprocating pump is one in which there is a periodic reversal of motion of the parts of the pump.
Centrifugal pumps are sometimes classified as volute pumps and turbine pumps. A volute pump is a centrifugal pump with a spiral casing into which the water is discharged from the impeller with the same velocity at all points around the circumference, as shown in Fig. 51. A turbine pump is a centrifugal pump in which the water is discharged from the impeller through guide passages into a collecting chamber, in such a manner as to prevent loss of energy in changing from kinetic head to pressure head. A turbine pump is shown in section in Fig. 51. Centrifugal pumps are sometimes classified as single stage and multi-stage. A centrifugal pump from which the water is discharged at the pressure created by a single impeller is called a single-stage pump. If the water in the pump is discharged from one impeller into the suction of another impeller the pump is known as a multi-stage pump. The number of impellers operating at different pressures determines the number of stages of the pump. A three-stage pump is shown in Fig. 52.
375 Lubricating ring.
380 Oil hole cap.
383 Oil drain tube.
404 Shaft sleeve lock nut.
440 Driving coupling.
441 Driven coupling.
443 Coupling check nut.
450 Coupling bolt.
451 Coupling bolt nut.
452 Coupling rubber.
453 Coupling rubber steel tube.
500 Pump case.
550 Bearing bracket cap.
551 Bearing.
552 Shaft.
553 Shaft sleeve, right hand thread.
PW Impeller.
554 Shaft sleeve, left hand thread.
555 Shaft stop collar, inner.
555–1 Shaft stop collar, outer.
556 Guide ring.
560 Packing gland.
563 Bearing.
567R Impeller protecting ring, right hand thread.
567L Impeller protecting ring, left hand thread.
583 Pump case protecting ring.
567 Labyrinth packing.
583 Labyrinth packing.
600 Pump case cover.
692 Impeller key.
815 Bearing bracket, outer.
815–1 Bearing bracket, inner.
Reciprocating pumps are generally driven by steam and are either direct-acting, or of the crank-and-fly-wheel type. Power pumps are reciprocating machines which may be driven by any form of motor, to which they are connected by belt, chain or shaft. A Deming triplex power pump is shown in Fig. 53. Power pumps can be used only where the character of the sewage will not clog the valves nor corrode the pump. A direct-acting steam pump is one in which the steam and water cylinders are in the same straight line and the steam is used at full boiler pressure throughout the full length of the stroke. The crank-and-fly-wheel type of pumping engine permits the use of steam expansively during a part of the stroke, the energy stored in the flywheel carrying the machine through the remainder of the stroke. Reciprocating pumps are sometimes classified as plunger pumps and piston pumps. In the action of a plunger pump the water is expelled from the water cylinder, by the action of a plunger which only partly fills the water cylinder, as shown in Figs. 54 and 55. In a piston pump the water is expelled from the water cylinder by the action of a piston which completely fills the water cylinder, as shown in Fig. 63, which illustrates a direct-acting piston pump.
Plungers are better than pistons for pumping sewage as the wear between the pistons and the inside face of the cylinder soon reduces the efficiency of the pump. Outside packed plungers are better than the inside packed type because the packing can be taken up without stopping the pump and the leakage from the pump is visible at all times. Outside packed pumps are more expensive in first cost, but are easier to maintain and have a longer life than piston pumps.
In selecting a pump to perform certain work the size of the water cylinder and the speed of the travel of the piston should be investigated to insure proper capacity. The average linear travel of the piston for slow speed pumps is estimated at about 100 feet per minute, dependent on the length of stroke and the valve area. For short strokes and small valve areas the speed may be as low as 40 feet per minute, and for long stroke fire pumps with large valves the piston can be operated at a speed of 200 feet per minute.[45] Vertical, triple-expansion, crank-and-fly-wheel, outside packed plunger pumps with flap valves can be operated at speeds of 200 feet per minute when lifting sewage, and when equipped with mechanically operated valves and lifting water they can be run at speeds of 400 to 500 feet per minute. The speed of travel multiplied by the volume of piston or plunger displacement, with proper allowance for slippage, will give the capacity of the pump. The slippage allowance may be from 3 to 8 per cent for the best pumps, and for pumps in poor conditions it may be a high as 30 to 40 per cent.
There are two types of ejector pumps used for lifting sewage. One of these depends on the vacuum created by the velocity of a stream of water or steam passing through a small nozzle. The operation of this pump is described in Art. 139 and it is illustrated in Fig. 97. The other type of ejector pump is known as the compressed-air ejector. It is operated by means of compressed air which is turned into a receptacle containing sewage. The details of this type are explained in Art. 83 and are illustrated in Fig. 68.
=75. Sizes and Description of Pumps.=—The size of a centrifugal pump is expressed as the diameter of the discharge pipe in inches. It has nothing to do with the head for which the pump is suited. On the assumption of a velocity of flow of 10 feet per second through the discharge pipe the capacity of the pump can be approximated.
The size of a reciprocating pump involves the expression of the diameters of the steam cylinders, the water cylinder, and the length of the stroke in inches, in the order named, beginning with the steam cylinder with the highest pressure. A complete description of a steam pumping engine might be; compound, duplex, horizontal, condensing, crank-and-fly-wheel, outside-center-packed, 12″ × 24″ × 18″ × 24″ pump. The word compound means that there are a high-pressure and a low-pressure steam cylinder; the word duplex means that there are two of each of these cylinders; the word horizontal means that the axes of these cylinders are in a horizontal plane; the word condensing means that the steam is discharged from the low-pressure cylinders into a condenser; the name crank-and-fly-wheel is self-explanatory; the name outside-center-packed means that the water cylinder is divided into two portions between which the plunger is exposed to the atmosphere, and that the packing rings are on the outside of the two portions of the cylinder as shown in Fig. 55; the figures shown mean that the high-pressure steam cylinder is 12 inches in diameter, the low-pressure 24 inches in diameter, the water cylinder is 18 inches in diameter, and the stroke of the pump is 24 inches.
=76. Definitions of Duty and Efficiency.=—The duty of a pump is the number of foot-pounds of work done by the pump per million B.T.U., per thousand pounds of steam, or per hundred pounds of coal, consumed in performing the work. These units are only approximately equal as 100 pounds of coal or 1,000 pounds of steam do not always contain the same number of B.T.U. and may only approximately equal 1,000,000 B.T.U.
Since 1,000,000 B.T.U. are equal to 778,000,000 foot-pounds of work, a pump with a duty of 778,000,000 will have an efficiency of 100 per cent. The efficiency of a pump is therefore its duty based on B.T.U. divided by 778,000,000. The efficiencies or duties of various types of pumps are given in Table 26.[46]
TABLE 26
APPROXIMATE DUTIES OF STEAM PUMPS
Small duplex, non-condensing 10,000,000 Large duplex, non-condensing 25,000,000 Small simple, flywheel, condensing 50,000,000 Large simple, flywheel, condensing 65,000,000 Small compound, flywheel, condensing 65,000,000 Large compound, flywheel, condensing 120,000,000 Small triple, flywheel, condensing 150,000,000 Large triple, flywheel, condensing 165,000,000
=77. Details of Centrifugal Pumps.=—A section of a centrifugal pump with the names of the parts marked thereon is shown in Fig. 50. Among the important parts which require the attention of the purchaser are: the impeller (_PW_), the impeller packing rings (567 _R_ & _L_), the bearings (551, 563), the thrust bearings (555–1), the shaft (552), and the shaft coupling (440).
The impeller should be of bronze, gun metal, or other alloy, because there is no rusting or roughening of the surface, and the efficiency does not fall with age. Normal fresh sewage is not corrosive, but septic sewage and sludge are usually so corrosive that iron parts cannot be used with success in contact with them. The impeller should be machined and polished to reduce the friction with the liquid. Impellers are made either closed or open, i.e., either with or without plates on the sides connecting the blades to avoid the friction of the liquid against the side of the casing. The closed type of impeller is shown in Fig. 50. Closed impellers are slightly more expensive, but generally give better service and higher efficiencies than the open type. Single impeller pumps should have an inlet on each side of the impeller to aid in balancing the machine, unless the plane of the impeller is to be horizontal when operating. Multi-impeller pumps usually have single inlet openings for each impeller. Vibration in the pump is sometimes caused by an unbalanced impeller. The moving parts may be balanced at one speed and unbalanced at another. To determine if the moving parts are balanced the pump should be run free at different speeds and the amount of vibration observed. If the impeller is removed from the pump its balance when at rest can be studied by resting it on horizontal knife edges. If there is a tendency to rotate in any direction from any position the impeller is not perfectly balanced.
Packing rings are used to prevent the escape of water from the discharge chamber back into the suction chamber. These rings should be made of the same material as the impeller. Labyrinth type rings, as shown in Fig. 50, are sometimes used as the long tortuous passages are efficient in preventing leakage.
The bearings must be carefully made because of the high speed of the pump. They are usually made of cast iron with babbitt lining. They should be placed on the ends of the shaft on the outside of the pump casing, as shown in Fig. 50, and should be split horizontally so as to be easily renewed. Exterior bearings are oil lubricated by means of ring or chain oilers with deep oil wells. Where interior bearings are necessary, because of the length of the shaft, they should be made of hard brass and should be water lubricated.
Thrust bearings or thrust balancing devices are used to take up the end thrust which occurs in even the best designed pumps. To overcome this pumps are designed with double suction, opposed impellers, or two pumps with their impellers opposed may be placed on the same shaft. Due to inequalities in wear, workmanship or other conditions, end thrust will occur and must be cared for. Various types of thrust bearings are in successful use, such as: the piston, ball, roller or marine types. The marine type thrust bearing is shown in Fig. 56. The piston type of hydraulic balancing device is shown in Fig. 57. In the figure _A_ represents the impeller, and _B_ a piston fixed to the shaft and revolving with it. There is a passage for water through the openings (1), (2), and (3) leading from the impeller chamber to the atmosphere or to the suction of the pump. If the impeller tends to move to the right opening (1) is closed resulting in pressure on the right of the impeller forcing it to the left. If the impeller moves to the left (1) is opened thus transmitting pressure to the piston _B_ forcing the impeller to the right. The flange _C_ is not essential, but is advantageous in pumps handling gritty matter. As the channel (2) wears larger the pressure against the piston decreases allowing it to move to the left. This partially closes (3) building up the pressure again.
Flexible shaft couplings should be used if the shaft of the driving motor and the pump are in the same line, as direct alignment is difficult to obtain or to maintain. Where connected to steam turbines, reduction gearing and rigid couplings are usually used on sewage pumps to obtain slow speed and permit large passages. Flexible couplings are of various types, one of which is shown in Fig. 50. A rigid coupling would be formed by bolting the flanges firmly together. Shaft couplings are usually not necessary where the pump is driven by belt connection to the engine or motor, or where the pump and pulley rest on only two bearings.
The stuffing box shown in Fig. 50 is packed loosely with two layers of hemp between which is a lantern gland, in order to permit a small amount of leakage. A drip box is placed below this gland to catch the leakage and return it to the pump. The leakage is permitted as it aids in lubrication and the tightening of the gland will cause binding of the shaft. The gland on the suction side of the pump should be connected by a small pipe to the discharge chamber in order to keep a constant supply of water for lubrication and to prevent the entrance of air to the suction end of the pump.
=78. Centrifugal Pump Characteristics.=—The capacity of a centrifugal pump is fixed by the size and type of its impeller and by the speed of revolution. Roughly, the capacity of a pump, for maximum efficiency, varies directly as the speed of revolution, the discharge pressure varies as the square of the speed, and the power varies as the cube of the speed. These relations are found not to hold exactly in tests because of internal hydraulic friction in the pump.
The characteristic curves for a centrifugal pump, or the so-called pump characteristics, are represented graphically by the relation between quantity and efficiency, quantity and power necessary to drive, and quantity and head, all at the same speed. The quantities are plotted as abscissas in every case. The curve whose ordinates are head and whose abscissas are quantities is known as “the characteristic.” The curve showing the relation between quantities and speeds is sometimes included among the characteristics. Characteristics of pumps with different styles of impellers are shown in Fig. 58. Fig. 59 shows the characteristics of a pump run at different speeds, the efficiencies at these speeds when pumping at different rates, and the maximum efficiency at different speeds. It is to be noted that the information given in this figure is more extensive than that in Fig. 58. The operating conditions under any head, rate of discharge, and speed are given. The curves of constant speed are parallel, and their distances apart vary as the square of the speed. The line of maximum efficiency is approximately a parabola.
A study of the characteristics of any particular pump should be made with a view to its selection for the load and conditions under which it is to be used. Among the important things to be considered in the selection of a centrifugal pump for the expected conditions of load are: the capacity required, the maximum and minimum total head to be pumped against, the maximum variations in suction and discharge heads, and the nature of the drive. For example, the pump, whose characteristics are shown in Fig. 59, should be operated at about 800 revolutions per minute. Under total heads between 40 and 50 feet, the discharge for the best efficiency will vary between 600 and 670 gallons per minute.
The efficiencies of centrifugal pumps increase with their capacities as is shown approximately in Fig. 60.
=79. Setting of Centrifugal Pumps.=—In setting a centrifugal pump, care should be taken to provide a firm foundation to hold the shafts of the pump and the electric motor or the reduction gearing in good alignment, or to prevent the pump from being displaced by the pull of a belt. It is desirable that the foundation be level. Centrifugal pumps should be set submerged for small pumping stations automatically controlled. Sludge pumps must be set submerged as otherwise they will not prime successfully. Provision should be made by which the pump can be lifted from the sewage, or sludge, for inspection and repair. In many cases the pump can be made self-priming by setting it in a dry, water-tight vault below the low level of sewage flow. Where possible it is desirable not to set the pump submerged as it will receive better care when easily accessible.
The suction pipe should be free from vertical bends where air might collect and should be straight for at least 18 to 24 inches from the pump casing. An elbow on the suction pipe, attached directly to the casing of the pump gives a lower efficiency than a suction pipe with a short straight run. Centrifugal pumps will operate with as high a suction lift as reciprocating pumps, but at the start they must be primed and some provision must be made for priming them. The suction pipe should be equipped with foot valves to hold the priming, or some method may be provided for exhausting the air from the suction pipe. The foot valves should be so installed as to form no appreciable obstruction to the flow of water. They should have an area of opening at least 50 per cent greater than the cross-section of the suction pipe. A strainer on the suction pipe is undesirable as it becomes clogged and is usually in an inaccessible position for cleaning. A screen should be placed at the entrance to the suction well to prevent the entrance of objects that are likely to clog the pump. A gate-valve and a check-valve should be provided on the discharge pipe, the former to assist in controlling the rate of discharge and the latter to prevent back flow into the pump when it is not operating.
Centrifugal pumps are well adapted to service in either large or small units. An installation in a manhole at Park Point, Duluth, is shown in Fig. 61. This station is controlled by an automatic electric device which is operated by a float in the suction pit. Such automatic control is an added advantage of the use of electrically driven centrifugal pumps. The Calumet Pumping Station in Chicago, shown in Fig. 49, has a capacity of approximately 1,000 cubic feet per second. The simplicity of the layout of this station is shown in Fig. 62.
=80. Steam Pumps and Pumping Engines.=—The direct-acting steam pump, one type of which is shown in Fig. 63, is adapted to pumping sewage the character of which will not corrode or clog the valves. In this form of pump it is necessary to utilize the steam at full pressure throughout the entire length of the stroke, which results in high steam consumption. A flywheel permits the use of steam expansively during a part of the stroke, thus increasing the economy of operation. Other devices used for the same purpose are known as compensators. They are not in general use.
Steam engines are classified in many different ways, for example; according to the type of valve gear, as, plain slide valve, Corliss, Lentz, etc.; or according to the number of steam expansions, as, simple, compound, triple-expansion, etc.; or according to the efficiency of the machine as low duty or high duty; or as
STEAM END
2 Steam cylinder and housing combined.
8 Steam piston head.
9 Steam piston follower.
10 Steam piston inside ring.
11 Steam piston outside ring (2).
12 Steam cylinder head.
14 Steam chest.
16 Steam chest cover.
17 Steam slide valve.
18 Steam valve rod.
20 Steam valve rod, pin and nut.
22 Steam valve rod, collar and set screw.
23 Steam valve rod, stuffing box.
24 Steam valve rod, stuffing box, nut and gland.
38 Piston rod.
47 Piston rod stuffing box.
48 Piston rod, stuffing box, nut and gland.
49 Valve gear stand.
51 Long valve crank and shaft.
52 Short valve crank and shaft.
PUMP END
115 Pump body.
127 Brass liner.
129 Water piston head.
130 Water piston follower.
137 Cylinder head.
139 Valve plate.
140 Cap.
152 Suction flange.
161 Discharge flange.
162 Valve seat, suction or discharge.
163 Valve, suction or discharge.
164 Suction valve spring.
167 Discharge valve spring.
168 Valve plate, suction or discharge.
169 Valve stem, suction or discharge.
STEAM END
55 Crank pin.
56 Valve rod link.
61 Long rocker arm.
62 Short rocker arm.
63 Rocker arm wiper.
69 Cross head.
condensing or non-condensing, etc. Throttling engines or automatic engines refer to the method of control of the steam by the governor. In throttling engines the governor controls the amount of opening of the throttle valve, in automatic engines the governor controls the position of the cut-off.
The simple slide valve, low-duty, non-condensing, throttling engine, is the lowest in first cost and the most expensive in the consumption of fuel. The triple-expansion Corliss, or the non-releasing Corliss, high-duty pumping engine is the most expensive in first cost but consumes less steam for the power delivered than any other form of reciprocating engine. For pumps of very small capacity the cost of fuel is not so important an item as the first cost of the machine. For this reason and because of the lower cost of attendance low-duty pumps are more frequently found in small pumping stations.
TABLE 27
WATER RATES OF PRIME MOVERS AT FULL AND PART LOADS
───────────────────────────────┬──────┬─────────────────────────┬────── Type of Engine │ │ │Boiler │Power,│ │Press. │ K.W. │ Per Cent of Full Load │ Lbs. ───────────────────────────────┼──────┼────┬────┬────┬─────┬────┼────── │ │ 25 │ 50 │ 75 │ 100 │125 │ ───────────────────────────────┼──────┼────┼────┼────┼─────┼────┼────── Single cylinder, high speed, │ │ │ │ │ │ │100 to non-condensing │ 25│ 33│ 27│26.3│ 27.0│27.5│ 150 │ 250│ 42│37.5│ 35│ 34.0│34.0│ │ │ │ │ │ │ │ Automatic, flat four valve, │ │ │ │ │ │ │100 to high speed │ 150│ │ 32│ 30│ 26.5│29.0│ 125 │ 250│ │ 33│ 31│ 28│30.0│ │ │ │ │ │ │ │ Tandem compound condensing, │ │ │ │ │ │ │100 to high speed │ 125│ │ 23│ 19│ 17│ 18│ 150 │ │ │ 25│ 20│ 19.5│ 21│ │ │ │ │ │ │ │ Cross compound, condensing, │ │ │ │ │ │ │ 125 high speed │ │ 30│ 26│ 24│ 23│23.5│ │ │ │ │ │ │ │ Cross compound, non-condensing,│ │ │ │ │ │ │ 125 high speed │ │ 39│ 31│ 27│ 26│27.5│ │ │ │ │ │ │ │ Single cylinder Corliss, │ │ │ │ │ │ │ 100 condensing │ 120│23.7│20.4│ 19│ 18.5│19.0│ │ 500│26.3│22.8│21.3│ 20.8│21.3│ 125 │ │ │ │ │ │ │ Compound Corliss, condensing │ │16.5│ 14│12.5│ 12.1│12.5│ 100 │ │22.2│ 19│17.0│ 16.5│17.0│ 150 │ │ │ │ │ │ │ Single cylinder, rotary four │ │ │ │ │ │ │ 100 valve, non-condensing │ 75│26.2│22.3│21.3│ 21.6│22.8│ │ 400│35.0│27.2│26.4│ 26.0│26.8│ 180 │ │ │ │ │ │ │ Rotary four valve, tandem │ │ │ │ │ │ │ 100 compound non-condensing │ 125│32.0│22.0│ 20│18.25│18.5│ │ 600│40.0│28.3│23.2│ 22.5│22.7│ 150 │ │ │ │ │ │ │ Cross compound, non-condensing │ │ │ │ │ │ │ 100 rotary four valve │ 125│ 25│ 21│19.1│ 18.5│19.0│ │ 600│39.4│ 28│22.3│ 20.6│20.7│ 150 │ │ │ │ │ │ │ Single cylinder, poppett valve,│ │ │ │ │ │ │ 100 non-condensing │ 120│22.7│20.5│19.7│ 19.1│20.1│ │ 600│28.5│26.0│25.0│ 24.3│25.5│ 150 │ │ │ │ │ │ │ Single cylinder, poppett valve,│ │ │ │ │ │ │ 100 condensing │ 120│18.5│16.7│16.1│ 15.6│16.4│ │ 600│24.6│22.3│21.4│ 20.8│21.9│ 150 │ │ │ │ │ │ │ Compound condensing, poppett │ │ │ │ │ │ │ 100 valve │ 200│14.2│13.0│12.5│ 12.2│12.9│ │ 1200│18.4│16.9│16.3│ 15.9│16.8│ 150 │ │ │ │ │ │ │ Uniflow │ 125│14.6│13.7│13.4│ 13.4│13.3│ 150 │ 600│15.0│14.3│13.7│ 13.5│14.0│ │ │ │ │ │ │ │ Steam turbines, condensing, │ │ │ │ │ │ │ 125 Allis-Chalmers │ 300│ │ 24│ 17│ 160│16.5│ │ 2000│ │31.9│26.3│ 23.8│23.0│ 175 │ │ │ │ │ │ │ Steam turbines, condensing, │ │ │ │ │ │ │ 125 Westinghouse │ 300│ │13.7│12.8│ 12.2│12.6│ │ 2000│ │18.2│16.9│ 16.2│16.8│ 175 │ │ │ │ │ │ │ Steam turbines, high pressure, │ │ │ │ │ │ │ non-con., 12″ to 36″ wheel, │4 to 8│ │ │ │ │ │ 1000 to 3600 R.P.M. │stages│ │ │ │ 28 5│ │ │ │ │ │ │116.5│ │ │ │ │ │ │ │ │ Ditto. Condensing, 26–inch │ │ │ │ │ 17 3│ │ │ │ │ │ │112.0│ │ │ │ │ │ │ │ │ ───────────────────────────────┴──────┴────┴────┴────┴─────┴────┴──────
The steam consumption per indicated horse-power, better known as the water rate of the engine, for various types of engines at full and at part load is shown in Fig. 64. The steam consumption of other types at full load is shown in Table 27. The indicated horse-power (I.H.P.) of a steam engine is the product of the mean effective pressure (M.E.P.), the area of the steam pistons, the length of the stroke, and the number of strokes per unit of time. A common form of this expression is,
I.H.P = _PLAN_⁄33,000,
in which _P_ = the M.E.P. in pounds per square inch;
_L_ = the length of the stroke in inches;
_A_ = the sum of the areas of the pistons in square inches;
_N_ = the number of revolutions per minute.
The I.H.P. multiplied by the mechanical efficiency of the machine will give the brake or water horse-power, that is, the horse-power delivered by the machine. The product of the M.E.P., the sum of the areas of the steam pistons and the mechanical efficiency of the machine, should equal the product of the total head of water pumped against expressed in pounds per square inch and the sum of the areas of the water pistons or plungers. The M.E.P. is determined from indicator cards taken from the steam cylinders during operation. These cards show the steam pressure on the head and crank ends of each cylinder at all points during the stroke.
=81. Steam Turbines.=—Among the advantages in the use of steam turbines as compared with reciprocating steam engines for driving centrifugal pumps are their simplicity of operation, the small floor space needed, their freedom from vibration requiring a relatively light foundation, and their ability to operate successfully and economically either condensing or non-condensing under varying steam pressure. They can be operated with steam at atmospheric or low pressure, thus taking the exhaust from other engines. The greatest economy of operation for the turbine alone will be obtained by operating with high pressure, superheated steam and with a vacuum of 28 inches. In large units the economy of operation of steam turbines is equal to that of the best type of reciprocating engines. In order to develop the highest economy turbines are operated at speeds from about 3,600 to 10,000 r.p.m. or greater, the smaller turbines operating at the higher speeds. As these speeds are usually too great for the operation of centrifugal pumps for lifting sewage, reduction gears must be introduced between the turbine and the pump. Although the best form of spiral-cut reduction gears may obtain efficiencies of 95 to 98 per cent, or even higher, their use, particularly in small units, is an undesirable feature of the steam turbine for driving pumps.
The steam consumption of DeLaval turbines of different powers, and the steam consumption of a 450 horse-power DeLaval turbine at different loads are shown in Fig. 64. Some steam consumptions of other turbines are recorded in Table 27. It is to be noted that the steam consumption of the 450 horse-power turbine at part loads is not markedly greater than that at full loads. This is an advantage of steam turbines as compared with reciprocating engines. The steam consumption of any turbine is dependent on the conditions of operation and is lower the higher the vacuum into which the exhaust takes place.
There are two types of turbines in general use, the single stage or impulse machines, and the compound or reaction type. The DeLaval is a well-known make of the single stage or impulse type. The principle of its operation is indicated in Fig. 65, which is the trade mark of the DeLaval Steam Turbine Co. The energy of the steam is transmitted to the wheel due to the high velocity of the steam impinging against the vanes. In the compound or reaction type of machine the steam expands from one stage to the next imparting its energy to the wheel by virtue of its expansion in the passages of the turbine. For this reason the single-stage or impulse type is operated at higher speeds than the compound or reaction machines.
=82. Steam Boilers.=—Among the important points to be considered in the selection of a steam boiler for a sewage pumping station are: the necessary power; the quality of the feed water; the available floor space; the steam pressure to be carried; and the quality and character of the fuel. Tubular boilers of the type shown in Fig. 66, are lower in first cost than other types of boilers. They are not ordinarily built in units larger than 250 to 300 horse-power and where more power is desired a number of units must be used. They are objectionable because of the relatively large floor space required, and because of their relatively poor economy of operation. The efficiencies of water-tube boilers of different types are given in Table 28. Large power units of the water-tube type, as shown in Fig. 67, although more expensive in first cost, require less floor space. Almost any desired steam pressure can be obtained from either type but water-tube boilers are more commonly used for high pressures. The grate or stoker can be arranged to burn almost any kind of fuel under either water-tube or fire-tube boilers. The use of poor quality of water in water-tube boilers is undesirable as the tubes are more likely to become clogged than the larger passages of the fire-tube boilers. If necessary, a feed-water purification plant should be installed, as it is usually cheaper to take the impurities out of the water than to take the scale out of the boiler.
Not less than two boiler units should be used in any power station, regardless of the demands for power, and if the feed water is bad, three or even four units should be provided, as two units may be down at any time. An appreciable factor of safety is provided by the ability of a boiler to be operated at 30 to 50 per cent overload, if sufficient draft is available, but with resulting reduction in the economy of operation. The number of units provided should be such that the maximum load on the pumping station can be carried with at least one in every 6 units or less, out of service for repairs or other cause.
TABLE 28
EFFICIENCIES OF STEAM BOILERS
From Marks’ Mechanical Engineer’s Handbook ────────┬───────────┬──────────┬──────┬────────┬──────┬──────┬────────── Type │Horse-power│ Furnace │ │ │ │Evap. │ │ │ │ │ │ │ from │ │ │ │ │ │ │and at│ │ │ │ │ │B.T.U.│ 212° │ Combined │ │ │ Sq. │Per Cent│ per │ per │Efficiency │ │ │ Ft. │of Rated│ Lb. │ Lb. │of Boiler │ │ │Grate │Capacity│ Dry │ Dry │ and │ │ │ Area │D’v’l’d │ Coal │ Coal │ Furnace ────────┼───────────┼──────────┼──────┼────────┼──────┼──────┼────────── Babcock │ 300│Hand-fired│ │ │ │ │ & │ │ │ │ │ │ │ Wilcox│ │ │ 84│ 118.7│11,912│ 8.81│ 71.8 Babcock │ 640│Hand-fired│ │ │ │ │ & │ │ │ │ │ │ │ Wilcox│ │ │ 118│ 121.5│14,602│ 10.83│ 72.0 Stirling│ 1128│B. & W. │ │ │ │ │ │ │ chain │ │ │ │ │ │ │ grate │ 187│ 198.3│12,130│ 9.51│ 76.1 Rust │ 335│Hand-fired│ 68│ 210.5│13,202│ 9.42│ 68.9 Heine │ 400│Green │ │ │ │ │ │ │ chain │ │ │ │ │ │ │ grate │ 83.5│ 123.8│11,608│ 8.79│ 73.5 Maximum efficiency recorded │ │ │ │ │ 83 ───────────────────────────────┴──────┴────────┴──────┴──────┴──────────
The steam delivered by a boiler is the basis of the measurement of its capacity or power. A boiler horse-power is the delivery of 33,320 B.T.U. per hour. It is approximately equal to the raising of 30 pounds of water per hour from a temperature of 100° Fahrenheit, to steam at a pressure of 70 pounds per square inch, or to 34 pounds of water per hour changed to steam from and at 212° Fahrenheit, at atmospheric pressure. The horse-power of a boiler is sometimes approximated by the area of its grate or heating surface. Such a method of measuring has a low degree of accuracy on account of the variations in the quality of the fuel, and the rate of combustion. For example, the rate of combustion under a locomotive boiler is high and there is less than ⅒th of a square foot of grate area and about 4.5 square feet of heating surface per boiler horse-power. The Scotch Marine type of boiler used on steam ships, has slightly more grate area and slightly less heating surface than the locomotive type of boiler, because the rate of combustion is lower. Stationary water-tube boilers may have 2 to 3 times as much grate area and heating surface per horse-power as is found in locomotive boilers. If a poor type of fuel is to be used the area of the grate should be increased about inversely as the heat content of the fuel. The approximate heat content of various types of fuels is shown in Table 29.
TABLE 29
APPROXIMATE HEAT VALUE OF FUELS
─────────────────────────────────────┬────────────────┬──────────────── Fuel │ │Pounds of Water │ │Evaporated from │ │ and at 212° F. │ │ All heat │B.T.U. per Pound│ utilized ─────────────────────────────────────┼────────────────┼──────────────── Anthracite │ 13,500│ 14.0 Semi-bituminous, Pennsylvania │ 15,000│ 15.5 Semi-bituminous, best, West Virginia │ 15,000│ 15.8 Bituminous, best, Pennsylvania │ 14,450│ 15.0 Bituminous, poor, Illinois │ 10,500│ 10.9 Lignite, best, Utah │ 11,000│ 11.4 Lignite, poor, Oregon │ 8,500│ 8.8 Wood, best oak │ 9,300│ 9.6 Wood, poor ash │ 8,500│ 8.8 ─────────────────────────────────────┴────────────────┴────────────────
=83. Air Ejectors.=—The Ansonia compressed-air sewage ejector is shown in Fig. 68. In its operation, sewage enters the reservoir through the inlet pipe at the right, the air displaced being expelled slowly through the air valve marked B. The rising sewage lifts the float which actuates the balanced piston valve in the pipe above the reservoir when the reservoir fills. The lifting of the valve admits compressed air to the reservoir. The air pressure closes valve A and the inlet valve at the right, and ejects the sewage through the discharge pipe at the left. As the float drops with the descending sewage it shuts off the air supply and opens the air exhaust through the small pipe at the top center. Sewage is prevented from flowing back into the reservoir by the check valve in the discharge pipe. Other ejectors operating on a similar principle are the Ellis, the Pacific, the Priestmann and the Shone.
=84. Electric Motors.=—The most common form of alternating current electric motor used for driving sewage pumps where continuous operation and steady loads are met is the squirrel-cage polyphase induction motor. These motors operate at a nearly constant speed which should be selected to develop the maximum efficiency of the pump and motor set. While Fig. 59 shows the best efficiency under varying heads to be obtained with variable speed, the advantages of cost, attention, and availability make the use of a constant speed motor common.[47] This type of motor is undesirable where stopping and starting are frequent because it has a relatively small starting torque and it requires a large starting current. Such motors can be constructed in small sizes for high starting torques by increasing the resistance of the rotor, but at the expense of the efficiency of operation.
Alternating current motors are more generally used than direct-current motors because of the greater economy of transmission of alternating current, but where direct current is available constant speed shunt wound motors should be adopted.
In the selection of a motor to drive a centrifugal pump it is important that the motor have not only the requisite power, but that its speed will develop the maximum efficiency from the pump and motor combined. If the pump and motor operate on the same shaft the speed of the two machines must be the same. If the two are belt connected, the size of the pulleys may be selected so as to give the required speed. If the motor is to be connected to a power pump an adequate automatic pressure relief valve should be provided on the discharge pipe from the pump, to prevent the overloading of the motor or bursting of the pump in case of a sudden stoppage in the pipe. The motor must be selected to suit the conditions of voltage, cycle, and phase on the line. Transformers are available to step the voltage up or down to practically any value. Rotary converters are used to change direct to alternating current or vice versa.
=85. Internal Combustion Engines.=—Internal combustion engines are used for driving pumps. Units are available in size from fractions of 1 horse-power to 2,000 horse-power or more, although the use of the larger sizes is exceptional. These engines are not commonly used for sewage pumping but when used they are ordinarily belt connected to a centrifugal pump, or to an electric generator which in turn drives electric motors which operate centrifugal pumps. This type of engine is more commonly adapted to small loads, although not entirely confined to this field, as they serve admirably as emergency units to supplement an electrically equipped pumping station. The fuel efficiency of internal combustion engines is higher than for steam engines as is indicated in Table 30, but the fuel is more expensive.
The four-cycle gas engine shown in Fig. 69 is the type most commonly used. Its horse-power is the product of: the mean effective pressure, the length of the stroke, the area of the piston, and the number of explosions per second divided by 550. The M.E.P. is dependent on the character of the fuel used and the compression of the gas before ignition. Producer gas will furnish mean effective pressures between 60 and 70 pounds per square inch, natural gas and gasoline, 85 to 90 pounds per square inch, and alcohol from 95 to 110 pounds per square inch.
TABLE 30
COMPARATIVE FUEL COSTS FOR PRIME MOVERS
───────────────────────────────────────┬───────────────┬─────────────── Type of Engine │ Quantity of │Cost of Fuel in │ Fuel per H.P. │ Cents per │ Hour │ Horse-power │ │ Hour ───────────────────────────────────────┼───────────────┼─────────────── Reciprocating steam engines, simple, │ 21 to 8 lb. │ 4.2 to 1.6 non-condensing, 25 to 200 H.P. │ coal │ Triple condensing, 2000 to 10,000 │2.3 to 1.9 lb. │ 0.46 to 0.37 H.P. │ coal │ ───────────────────────────────────────┼───────────────┼─────────────── Steam turbines, high pressure, │ │ non-condensing, │ │ 200 to 500 K.W. │6.5 to 4.2 lb. │ 1.3 to 0.86 │ coal │ 500 to 3000 K.W. │2.6 to 1.9 lb. │ 0.52 to 0.37 │ coal │ Condensing 5000 to 20,000 K.W. │1.8 to 1.43 lb.│ 0.36 to 0.28 │ coal │ ───────────────────────────────────────┼───────────────┼─────────────── Gas engines │ │ Natural gas, 50 to 200 H.P. │ 19 to 11 cu. │ │ ft. │ Producer gas, 50 to 200 H.P. │ 2 to 1.5 cu. │ │ ft. │ Illuminating gas, 10 to 75 H.P. │ 26 to 19 cu. │ 2.1 to 1.5 │ ft. │ Gasoline, 10 to 75 H.P. │ 1.5 to 0.8 │ 5.6 to 3.0 │ pints │ ───────────────────────────────────────┼───────────────┼─────────────── Oil engines, 100 to 500 H.P. │1.1 to 0.75 lb.│ │ oil │ ───────────────────────────────────────┴───────────────┴─────────────── NOTE.—Coal assumed at $4.00 per ton, illuminating gas at 80 cents per thousand cubic feet, and gasoline at 30 cents per gallon.
The Diesel Engine is the most efficient of internal combustion engines. The original aim of the inventor, Dr. Rudolph Diesel, was to avoid the explosive effect of the ordinary internal combustion engine by injecting a fuel into air so highly compressed that its heat would ignite the fuel, causing slow combustion of the fuel thus utilizing its energy to a greater extent. The fuel and air were to be so proportioned as to require no cooling. Although the ideal condition has not been attained, the heat efficiency of Diesel engines is high. They will consume from 0.3 to 0.5 of a pound of oil (containing 18,000 B.T.U. per pound) per brake horse-power hour, giving an effective heat efficiency of 25 to 30 per cent. Although not now in extensive use in the United States it is probable that this engine will be more generally adopted for conditions suitable for internal combustion engines.
=86. Selection of Pumping Machinery.=—Centrifugal pumps are particularly adapted to the lifting of sewage because of their large passages, and their lack of valves. The low lifts, nearly constant head, and the possibility of equalizing the load by means of reservoirs are particularly suited to efficient operation of centrifugal pumps. They require less floor space than reciprocating pumps of the same capacity, and because of their freedom from vibration they do not demand so heavy a foundation. The discharge from the pump is continuous thus relieving the piping from vibration. In case of emergency the discharge valve can be shut off without shutting down the pump, an important point in “fool proof” operation.
Volute pumps are better adapted to pumping sewage as their passages are more free and they are better suited to the low lifts met. Gritty and solid matter will cause wear on the diffusion vanes of turbine pumps in spite of the most careful design. Although turbine pumps can possibly be built with higher efficiency than volute pumps, their efficiency at part load falls rapidly and the fluctuations of sewage flow are sufficient to affect the economy of operation. Turbine pumps are more expensive and heavier than volute pumps on account of the increased size necessitated by the diffusion vanes.
Multi-stage pumps are used for high lifts and are seldom if ever required in sewage pumping. As ordinarily manufactured, each stage is good for an additional 40 to 100 pounds pressure, but wide variations in the limiting pressures between stages are to be found.
Reciprocating plunger pumps are sometimes used for sewage pumping where the character of the sewage is such that the valves will not be clogged nor parts of the pump corroded. These pumps are seldom used in small installations or for low lifts. They are not adapted to automatic or long distance control as are electrically driven centrifugal pumps. The use of reciprocating pumps for sewage pumping is practically restricted to very large pumping stations with capacities in the neighborhood of 50,000,000 gallons per day or more. Steam-driven pumps are the most common of the reciprocating type, but power pumps are sometimes used in special cases for small installations and may be driven by either a steam or gas engine or an electric motor.
Compressed air ejectors, as described in Art. 83 are used for lifting sewage and other drainage from the basement of buildings below the sewer level.
Centrifugal pumps electrically driven are, as a rule, the most satisfactory for sewage pumping. Electric drive lends itself to control by automatic devices, which are particularly convenient in small pumping stations. The control can be arranged so that the pump is operated only at full load and high efficiency, and when not operating no power is being consumed, as is not the case with a steam pump where steam pressure must be maintained at all times. The electric driven pump is thrown into operation by a float controlled switch which is closed when the reservoir fills, and opens when the pump has emptied the reservoir. The choice between steam and electric power for large pumping stations is a matter of relative reliability and economy.
The selection of the proper type of pump, whether reciprocating or otherwise, requires some experience in the consideration of the factors involved. Fig. 70 is of some assistance. In discussing this figure, Chester states:
“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.
=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│ │
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──────────────────────────────────┬─────────────── 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│ │
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──────────────────────────────────┬─────────────── 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│ │
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──────────────────────────────────┬─────────────── 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│ │
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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.