5. Compressed-Air Systems Piping
Compressed air is clean and easily available. As an energy source it can beput to use in many dierent forms. However, the cost of producingcompressed air must be compared against that of other forms of energy suchas electricity. For several decades, despite the advent of new energyservices, compressed airdriven equipment and tools have continued to beused in many industrial applications. In addition, the eciency of thesesystems has increased in recent years.
Compressed air is used in food processing, material handling, and theoperation of machines and tools. In plants that use compressed air thepressures range from 60 to 150 pounds per square inch (lb/in or psi). Low-pressure compressed air, in the range of 10 to 25 psi, is used for the controlof instruments. Low-pressure air is also used in heating, ventilating, and air-conditioning (HVAC) systems. Portable air compressors are used inconstruction, road building, painting, etc. The ow rates used in theseapplications range from 20 to 1500 cubic feet per minute (ft /min or CFM)with power ranging from 2 to 400 horsepower (HP).
5.1. Properties of Air
Air consists of approximately 78 percent nitrogen and 21 percent oxygen andsmall amounts of other gases such as argon, CO , and helium. Generally, formost calculations the composition of air is assumed to be 79 percent nitrogenand 21 percent oxygen on a volumetric basis. The corresponding values on aweight basis are 76.8 percent nitrogen and 23.2 percent oxygen. Air has a
Compressed-Air Systems Piping
molecular weight of 28.97. The gas constant R for air is 53.33 (ft lb)/(lb R)[29.2 (N m)/(N K) in SI units].
In most instances, example problems are discussed in English units, alsocalled U.S. Customary (USCS) units. However, Systme International (SI) unitsare also illustrated in some examples.
The pressure of air in a vessel or pipe may be expressed as gauge pressureor absolute pressure. The gauge pressure, denoted by psig, is that which ismeasured by a pressure gauge or instrument that records the magnitude ofpressure above the atmospheric pressure at a particular location. Theabsolute pressure, denoted by psia, includes the local atmospheric pressure.This is illustrated in Fig. 5.1. Mathematically, the gauge pressure andabsolute pressure are related by the following equation:
All calculations involving air such as the perfect gas laws require knowledgeof the local atmospheric pressure. The pressure drop due to friction, whichrepresents the dierence between the absolute pressure at two points alonga compressed air pipeline, is expressed in psig. This is because the commonpressure representing the atmospheric pressure cancels out when thedownstream pressure is subtracted from the upstream pressure. Thus, if wedenote the upstream pressure as P in psia and the downstream pressure asP in psia, the pressure loss is simply P -P , measured in psig. Althoughsometimes pressure dierences are indicated in absolute terms, gaugepressures are more appropriate.
In SI units, the pressures are measured in kilopascals (kPa) or megapascals
Figure 5.1. Absolute pressure and gauge pressure.
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(MPa), and we must clearly state whether the pressure is in absolute orgauge values. In USCS units, the psig and psia designations are self-explanatory. Other SI units for pressure are bar and kg/cm .
For many calculations air may be considered a perfect gas and, therefore,said to obey Boyle's law, Charles's law, and the ideal gas equation. However,at high pressures the behavior of compressed air deviates from that of idealgas, and hence compressibility eects must be considered.
Considering the perfect gas equation of state, we can calculate the density ofair at the standard conditions of 14.7 psia and 60F as follows:
where P = pressure, lb/ft
= air density, lb/ft
R = gas constant for air
T = air temperature, R (F + 460)
Mw = molecular weight of air, equal to 28.97
1545 = universal gas constant
In some books you will see the specic weight of air used instead of thedensity . We will use the mass density in this chapter. Care must be takento use proper conversion factors to ensure that correct units are maintained.
Sometimes mass is expressed in slugs in USCS units. The unit of pound (lb) isreserved for force, including weight. Since it is more common to talk aboutmass ow rate (or weight ow rate) of air in lb/s or lb/min, we will use lb formass throughout this chapter when using USCS units. In this regard, themass ow and weight ow rates are interchangeable. Strictly speaking, massis a scalar quantity while weight is a vector quantity, like force. Numerically 1lb mass and 1 lb weight will be considered equal.
The mass ow rate of air in SI units may be expressed in kg/s, kg/min,kilonewtons/s (kN/s), or kN/min, even though the newton is actually dened
as the force that is necessary to accelerate a mass of 1 kg at the rate of 1m/s .
Standard conditions are an atmospheric pressure of 14.7 psia and atemperature of 60F. Substituting these temperature and pressure valuesand the molecular weight of air into Eq. (5.1), we calculate the density of airat standard conditions (also referred to as base conditions) as
Thus, dry air has a density of 0.07633 lb/ft at standard conditions (14.7 psiaand 60F). In SI units the base temperature and pressure used are 0C and760 mm pressure (1.033 kg/cm ). Sometimes 15C and 101 kPa are also used.
Even though temperatures are normally reported in F or C, calculationsrequire that these temperatures be converted to absolute scale. In USCSunits we use the absolute temperature scale of Rankine. In SI units theabsolute temperature is denoted by the kelvin scale. The conversion from theordinary temperatures of F and C to absolute scales are as follows:
The temperature in kelvin is usually given without the degree symbol. Thus60F is 520R and 20C is 293 K.
The pressure of air may be expressed in psi in USCS units. To ensure properunits, the pressure in psi is multiplied by 144 to result in lb/ft pressure ascan be seen in the earlier calculation of the density of air using Eq. (5.1). InSI units, pressure may be expressed in kilopascals, megapascals, or bars.
The critical temperature is dened as the temperature above which,regardless of the pressure, a gas cannot be compressed into the liquid state.The critical pressure is dened as the least pressure at the criticaltemperature necessary to liquefy a gas. The critical temperature and criticalpressure of air are -221 F and 546 psia, respectively. In comparison with acritical pressure and temperature, atmospheric air may be assumed to obeythe perfect gas law fairly accurately.
The specic heat of air at constant pressure C is approximately 0.239Btu/(lb R) at temperatures up to 400R. The ratio of specic heat for airC /C is approximately 1.4. It is found that as temperature increases, Cincreases and the specic heat ratio denoted by k decreases. At 60F, C =0.24 and k = 1.4. Air tables (Tables 5.1 to 5.4) are used in calculationsinvolving expansion and compression of air.
Table 5.1. Properties of Air for Temperatures in F
Table 5.2. Properties of Air for Temperatures in C
p v pp
0.0 0.00268 0.0862 12.6 10 3.28 10
20.0 0.00257 0.0827 13.6 10 3.50 10
40.0 0.00247 0.0794 14.6 10 3.62 10
60.0 0.00237 0.0764 15.8 10 3.74 10
68.0 0.00233 0.0752 16.0 10 3.75 10
80.0 0.00228 0.0736 16.9 10 3.85 10
100.0 0.00220 0.0709 18.0 10 3.96 10
120.0 0.00215 0.0684 18.9 10 4.07 10
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s/m0.0 1.29 12.7 13.3 10 1.72 10
10.0 1.25 12.2 14.2 10 1.77 10
20.0 1.20 11.8 15.1 10 1.81 10
30.0 1.16 11.4 16.0 10 1.86 10
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Table 5.3. Correction Factor for Altitude
Table 5.4. Correction Factor for Temperature
40.0 1.13 11.0 16.9 10 1.91 10
50.0 1.09 10.7 17.9 10 1.95 10
60.0 1.06 10.4 18.9 10 1.99 10
70.0 1.03 10.1 19.9 10 2.04 10
80.0 1.00 9.8 20.9 10 2.09 10
90.0 0.972 9.53 21.9 10 2.19 10
100.0 0.946 9.28 23.0 10 2.30 10
(Altitude) ft (Altitude) m Correction factor0 0 1.00
1600 480 1.05
3300 990 1.11
5000 1500 1.17
6600 1980 1.24
8200 2460 1.31
9900 2970 1.39
(Temperature ofintake) F
(Temperature ofintake) C Correction factor
-50 -46 0.773
-40 -40 0.792
-30 -34 0.811
The viscosity of air, like that of other gases, increases with a rise intemperature. At 40F the viscosity of air is approximately 3.62 10 (lb s)ft ; at 240F the viscosity increases to 4.68 10 (lb s)/ft . The variation ofviscosity of dry low-pressure air with temperature is listed in Tables 5.1 and5.2. Although the viscosity variation is nonlinear for most calculations, wecould use an average viscosity based on interpolation of values from thetables.
In many industrial processes we encounter air mixed with vapor. In the eldof air-conditioning, air is mixed with water vapor. If we assume that eachconstituent obeys the perfect gas law, we can use Da