9.1
SECTION 9
AIR AND GAS COMPRESSORS
AND VACUUM SYSTEMS
Estimating the Cost of Air Leaks in
Compressed-Air Systems
9.1
Selecting an Air Motor for a Known
Application
9.4
Air-Compressor Cooling-System Choice
for Maximum Coolant Economy
9.10
Economics of Air-Compressor Inlet
Location
9.14
Power Input Required by Centrifugal
Compressor
9.16
Compressor Selection for Compressed-
Air Systems
9.18
Sizing Compressed-Air System
Components
9.24
Compressed-Air Receiver Size and
Pump-Up Time
9.26
Vacuum-System Pump-Down Time
9.27
Vacuum-Pump Selection for High-

of compressed air is $1.25 per 1000 ft
3
(28.3 m
3
). What is the cost of the leaking
air when the pipe pressure is 50 lb/in
2
(gage) (344.5 kPa) and the other variables
are the same as given above?
Calculation Procedure:
1. Find the volume of air discharged to the atmosphere
Air flowing through an orifice or nozzle attains a critical pressure of 0.53 times the
inlet or initial pressure. This reduced pressure occurs at the throat or vena contracta,
which is the point of minimum stream diameter on the outlet side of the air flow.
If the outlet or back pressure exceeds the critical pressure then the vena contracta
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
9.2
PLANT AND FACILITIES ENGINEERING
FIGURE 1 Typical compressed-air system main and branch pipes (Factory Manage-
ment and Maintenance).
or throat pressure rises to equal the backpressure. Air flow through a hole in a pipe
or tank replicates the flow through an orifice or nozzle.
When an inlet air pressure of 10 lb/ in
2
(gage)
ϩ
14.7

, where W
ϭ
leakage rate, lb /s (kg /s); A
ϭ
area of leakage
hole, in
2
(cm
2
); P
ϭ
pipeline or initial air pressure, lb/ in
2
(abs) (kPa); P
1
ϭ
outlet
or backpressure, lb/ in
2
(abs); T
ϭ
absolute temperature of the air before leakage
ϭ Њ
F
ϩ
460.
Substituting, using the values given above, W
ϭ
1.06
ϫ

This compressed-air plant operates 7500 h/ yr. Since the leakage rate is 328.8
ft
3
/h, the annual leakage through this opening is 7500
ϫ
328.8
ϭ
2,466,000 ft
3
(58,691 m
3
). At a cost of $1.25 per 1000 ft
3
, the annual total cost of this leak is
$1.25
ϫ
2,466,000/ 1000
ϭ
$3,082.50. This is a sizeable charge, especially if there
are several leaks of this size, or larger, in the system.
3. Find the rate of leakage at the higher line pressure
When the backpressure is less than the critical pressure, a different flow equation
must be used. In the second instance, the critical pressure is 0.53 (50 lb/in
2
(gage)
ϩ
14.7)
ϭ
34.29 lb /in
2

ϭ
0.5303(0.012272)(1.0)(64.7)/ (530)
0.5
ϭ
0.01829 lb /s (0.0083
kg/ s). Converting to an hourly flow rate as earlier, 3600
ϫ
0.01828
ϭ
65.84 lb/ h
(29.89 kg/ h).
4. Compute the annual cost of air leakage at the higher pressure
Following the same steps as earlier, annual leakage cost
ϭ
65.84 lb /h (7500
h/ yr)(1.25/ 1000 ft
3
)/ 0.075 lb /ft
3
ϭ
$8,230.00 per year. Again, this is a significant
loss of revenue. Further, the loss at the higher pressure is $8230 /3082.50
ϭ
2.67
times as great. This points out the fact that higher pressures in a compressed-air
system can cause more expensive leaks.
Related Calculations. Compressing air requires a power input to raise the air
pressure from atmospheric to the level desired for the end use of the air. When
compressed air leaks from a pipe or storage tank, the power expended in compres-
sion is wasted because the air does no useful work when it leaks into the atmo-

arrangement supplies high horsepower per unit weight. Axial-piston motors are
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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
9.5
FIGURE 3 (a) Five-cylinder piston-type radial air motor used in sizes from about 2 hp (1.5
kW) to 22 hp (16.4 kW) and at speeds from 85 to 1500 rpm. (b) How five-cylinder air motor
distributes power. Two cylinders are always on power stroke at any instant (Gardner-Denver
Company).
available in sizes from 0.5 to 2.75 hp (0.37 to 2.1 kW). They run equally well in
either direction. To make the motor reversible, a four-way air valve is inserted in
the line.
(3) Multi-vaned motors, Fig. 5, are suitable for loads from fractional hp (kW)
to 10 hp (7.5 kW). They are relatively high-speed units which must be geared down
for usable speeds. The major advantages of multi-vaned motors is light weight and
small size. However, if used at slow speed, the gearing may add significantly to
the weight of the motor.
(4) Air-turbine motors deliver fractional horsepowers at exceptionally high
speeds, from 10,000 to 150,000 rpm, and are an economical source of power. They
are tiny impulse-reaction turbines in which air at 100 psi (689 kPa) impinges on
buckets for the driving force. Force-feed automatic lubrication sprays a fine film of
oil on to bearings continuously, minimizing maintenance.
Based on the load requirements, 2 hp (1.5 kW) at 1000 rpm, a reversible radial-
piston air motor, Table 1, would be a suitable choice because it delivers up to 2.8
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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS

ft—lbs
Air consumption
at rated hp ft
3
free air/min
Radial piston motors (non-reversible)*
2.9 (2.2) 1,500 3,200 130 (59) .......... ..............
3.3 (2.5) 1,300 3.000 130 (59) .......... ..............
3.8 (2.8) 1,200 2,700 130 (59) .......... ..............
Radial piston motors (reversible)*
2.5 (1.7) 1,200 2,200 135 (61.3) .......... ..............
2.8 (2.1) 1,000 1,950 135 (61.3) .......... ..............
3.2 (2.4) 900 1,600 135 (61.3) .......... ..............
5.2 (3.9) 750 1,600 200 (90.8) .......... ..............
*at 90 lb / in
2
(620 kPa).
Ingersoll-Rand.
hp (2.1 kW) at 1000 rpm with air delivered to the motor at 90 lb/ in
2
(620 kPa).
The weight of this motor, Table 1, is 135 lb (61.3 kg).
2. Compare the advantages of air motors to other types of motive power
Air motors have a number of advantages over their usual competitors—electric
motors. These advantages are: (1) In explosive or gaseous environments, air motors
are lower in cost than larger, heavier, explosion-proof electric motors. Air motors
operate relatively trouble-free in moist, humid environments where the electric mo-
tor may suffer from a buildup of fungus and corrosion. And since the air motor
requires little maintenance, it can be mounted in inaccessible locations. (2) With
an air motor, the output speed can be varied from zero to free-speed no-load rotation

Governor
controlled
curves
Rated performance
Horsepower
Torque
Speed RPM
1
Free speed
0
Stall speed
FIGURE 6 Performance curve of a typical air motor. Note how a built-in governor can change
the shape of the curve by limiting the maximum speed of the air motor (Product Engineering).
The duty cycle will usually determine the type of motor and the size of compressor
that must be used.
4. Check the horsepower and speed required
Performance curves, Fig. 6, show an air motor’s torque and horsepower (kW) output
at various rpm. Such curves can be varied somewhat by using governors or by
modifying the air intake or exhaust ports. However, the basic shape of the perform-
ance curve depends on the fundamental design of the air motor. It is common
practice to rate an air motor at its maximum output, i.e., at the top of the dome-
shaped performance curve. The reversible radial-piston motor chosen here has ad-
equate horsepower and speed for the anticipated load.
5. Determine the effect of air pressure and quantity on the air motor output
Table 2 shows how the air pressure available at the motor inlet affects both the
power output and rpm of typical air motors. For the motor being considered here,
the output would be sufficient at the lowest air pressure listed. Thus, the motor
choice is acceptable.
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motor choice is made.
As a general rule of thumb, stall torque ranges between 2 and 2.5 times the
torque developed when operating at maximum horsepower output.
In small motors, up to 2.5 hp (1.9 kW), air consumption varies from 35 to 40
ft
3
/min (0.99 to 1.1 m
3
/min) of free air per hp (0.746 kW). Larger air motors
consume 20 to 25 ft
3
/min (0.57 to 0.70 m
3
/min) of free air per hp. These con-
sumption rates apply to non-reversible motors. Reversible air motors consume 30
to 35 percent more air.
The data, tables and illustration in this procedure are from Product Engineering
magazine.
AIR-COMPRESSOR COOLING-SYSTEM CHOICE
FOR MAXIMUM COOLANT ECONOMY
Select a suitable cooling system for a two-stage 5000-hp (3730-kW) engine-driven
air compressor, Fig. 7, installed in a known arid hard-water area when the rated
output of the compressor is 25,000 ft
3
/min (708 m
3
/min) at 100 lb/ in
2
(abs) (689
kPa). Water conservation is an important requirement for this compressor because

Bessemer Corp.).
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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
9.12
PLANT AND FACILITIES ENGINEERING
FIGURE 8 Heat exchanger, center, for power-cylinder cooling and raw-water cooling
for the compressor (Ingersoll-Rand Co.).
FIGURE 9 Closed cooling system for power and air cylinders utilizing pipe coil in
the cooling tower (Ingersoll-Rand Co.).
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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
9.13
FIGURE 10 Raw water cools the air cylinders; power cylinders use
closed system protected by thermostatic valve (Ingersoll-Rand Co.).
110°F (43.3°C) 130°F (54.4°C)
FIGURE 11 Cooling-tower recirculating system is not recommended because of the
possibility of scale and impurities buildup (Ingersoll-Rand Co.).
at a higher temperature, are cooled by a closed system protected by a thermostatic
valve.
An open cooling-tower system, Fig. 11, is not recommended for installations
such as this because of the possible heavy scale buildup. However, such an open
cooling system might be used where the economics of the installation permit it and
scale buildup is unlikely to occur.
2. Determine the air-compressor cooling load
Use flow rates given in Table 6, page 9.24 to estimate the cooling water flow rate

ϭ
3000 gal/ min (189.3 L /s).
Additional cooling water may be used for the turbocharger, if fitted, and for
aftercooling. Steps for calculating these cooling-water flows are given in the section
cited above. Such cooling-water flows are usually additive to the jacket-water flow,
depending on the cooling arrangement used.
Related Calculations. Cooling systems for air and gas compressors are im-
portant for reliable and safe operation of these units. Hence, great care must be
exercised in choosing the most reliable and economic cooling system.
Today, both mechanical-draft and natural-draft cooling towers are popular
choices. An economic study is needed to determine the best choice when the cool-
ing effectiveness of both types of towers are about equal. Data given on cooling
towers elsewhere in this handbook can be helpful to the designer in choosing the
best type of tower to use for a given installation of air or gas compressors.
Straight flow-through cooling of small compressors and their drive engines is
often used where adequate water supplies are available. Thus, in large cities the
cooling water may be taken from the water main and discharged to the sewer after
passage through the compressor and engine. Cost of the water may be small com-
pared to the investment in a cooling tower. But with increased environmental con-
cerns, this scheme of cooling may soon be extinct.
ECONOMICS OF AIR-COMPRESSOR INLET
LOCATION
A plant designer has the option of locating an air-compressor inlet pipe either inside
the compressor building or outside the structure. The prevailing average indoor
temperature is 90
Њ
F (32.2
Њ
C) while the average outdoor temperature is 50
Њ

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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
9.15
density of air at inlet temperature, lb/ft
3
), where I
ϭ
intake volume, ft
3
(m
3
), re-
quired at the air inlet temperature.
For inlet air at 50
Њ
F (21.1
Њ
C), the outside intake air temperature, using a table
of air properties, I
ϭ
1000(0.07493/ 0.7785)
ϭ
962.49 ft
3
(27.2 m
3
). With an inlet

ϭ
(hp saving/100)(motor
hp)(0.746 kW /hp)(annual operating hours). Since the compressor operates at full
load 7500 h/ yr using 200 hp, the annual power saving is P
ϭ
(7.32/ 100)(200
hp)(0.746)(7500)
ϭ
81,910.8 kWh.
The annual cost saving, A
ϭ
(kWh/ h per yr saved)(power cost, $/ kWh). With
a power cost of $0.04 /kWh, the annual cost saving, A
ϭ
(81,910.8)(0.04)
ϭ
$3276.43. If an outside inlet were more expensive than an indoor inlet, this saving
could be used to offset the increased cost.
Related Calculations. As a general rule, an outside air intake, Fig. 12, is more
economical than an inside air intake when the air in the building is at a higher
temperature than the outside air. The only time an outside air intake might be less
desirable than an indoor air intake is when the outside air is polluted with corrosive
vapors, excessive dust, abrasive sand, etc., which would be injurious to people or
machines. Under these circumstances the designer might elect an indoor air intake.
However, before choosing an indoor intake, review the efficacy of outdoor air filters
of various types, Fig. 13.
Air in industrial districts may contain from 1 to 4 grains of dirt per 1000 ft
3
(28.3 m
3

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AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS
9.16
PLANT AND FACILITIES ENGINEERING
(a)
(b)
10-ft (3-m)
FIGURE 12 (a) Outside intake-air filter for air compressor should have intake pipe as
short as possible and be fitted with long-radius elbows (Ingersoll-Rand Co.). (b) Glazed-
tile tunnel for outdoor-air intake.
Compressed-Air and -Gas System
Components and Layouts
POWER INPUT REQUIRED BY CENTRIFUGAL
COMPRESSOR
A centrifugal compressor handling air draws in 12,000 ft
3
/min (339.6 m
3
/min) of
air at a pressure of 14 lb/in
2
(abs) (96.46 kPa) and a temperature of 60
Њ
F (15.6
Њ
C).
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