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.

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.

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.

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.

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

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

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

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

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

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.

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.