Chapter 6
Saturation Pressure & Vapor Quality
Liquid-vapor phase change (evaporation and condensation) are extremely important to many, many industries. Processes such as distillation and separation in petroleum refineries, electrical power generation in steam power plants, and refrigeration cycles all depend upon control of evaporation and condensation.6.1 Background
Evaporation (and boiling) is the process in which liquid becomes vapor and in doing so absorbs a measure of thermal energy known as latent heat. As an example, to maintain a constant temper-ature the human body requires cooling to offset the thermal energy released during the metabolic process. Perspiration, consisting primarily of salt water, evaporates thereby cooling the surface of the skin. The process of evaporation occurs at a constant temperature. The cooling effect arises from the loss of thermal energy; that is, the transfer of latent heat. The temperature at which evap-oration and condensation occurs is known as the saturation temperature. The corresponding pressure is known as the saturation pressure. The temperature at which evaporation or boiling occurs varies with pressure. It is a common observation that water boils at a temperature less than
100○C at a high altitude, such as encountered on mountains, because the atmospheric pressure is
less at these elevations.
t e m p e r a t u r e pr es su re s o l i d l i q u i d v a p o r t r i p l e p o i n t c r i t i c a l p o i n t
Figure 6.1. General pressure-temperature relationship.
Figure 6.1 illustrates the relationship between pressure and temperature for the solid, liquid, and vapor phases of a substance. The triple point is the temperature and pressure at which all three phases can coexist. The line separating the solid-liquid regions represents a set of temperatures
and pressures at which the solid and liquid phases (ice and water) may coexist. Similarly, the line separating the liquid-vapor regions represents a set of temperatures and pressures at which the liquid and vapor phases (water and steam) may coexist. The critical point is the pressure-temperature state beyond which there is no distinction between liquid and vapor phases.
6.1.1 Quality of Vapor
The thermodynamic state of a single phase fluid (gas or liquid) can be determined if two properties are known. So, if the pressure and temperature are measured and the system is in thermal equilib-rium, then all of the other properties at this state can be determined. If two phases are present
(va-por and liquid), then three thermodynamic states must be known. For
l i q u i d
l i q u i d
v a p o r
v a p o r
v a p o r
x
1x
2> x
1x
3= 1
T
s a tT
s a tT
s a texample, consider a liquid is in equilibrium with its vapor in a closed system at some tempera-ture and pressure as illustrated. Since the two phases coexist in equilibrium, the temperature is
the saturation temperature, Tsat.
The exact same saturation tem-perature and pressure can be ob-tained with less liquid in the sys-tem. In fact, the exact same temperature and pressure can be obtained without any liquid in the system. Just knowing the temperature and pressure is insufficient to determine the system’s state because the mass, density, and specific volume are not a unique to this temperature and pressure. Any three properties may be used in specifying the thermodynamic state of a two-phase mixture. One property typically used, in addition to temperature and pressure, is quality. Quality, x, is
the ratio of vapor mass, mg, to mixture mass, mg+ mf:1
x= mg
mg+ mf
(6.1)
Therefore, x1 < x2 < x3 = 1. The quality of saturated liquid is 0 an the quality of saturated
vapor is 1. The thermodynamic properties of the mixture which are dependent upon mass can be expressed using quality. The specific volume (volume per mass) of the systems in the illustration is
v= (1 − x)vf+ xvg. Other properties dependent upon mass such as internal energy, enthalpy, and
entropy can be determined in a similar manner.
6.1.2 Pressure, Temperature and Density of a Saturated Mixture
Three properties are required to specify the thermodynamic state of a two-phase mixture. Of the numerous fluid properties, there are three which are relatively easy to determine; pressure, temperature, and density. The specific volume, v, is an intensive property which is the inverse of
density, v= 1/ρ.
Figure 6.2 illustrates the relationship between pressure, temperature and specific volume for a liquid-vapor system. The diagram is of pressure versus specific volume (P -v diagram) and lines of constant temperature (isotherms) are shown. The saturated state, that is the state at which vapor and liquid coexist, is defined by the saturation curve. The region to the right of the saturation curve is superheated vapor and the region to the left of the saturation curve is subcooled liquid. In
1
By convention, a subscript f is used to denote the liquid phase and a subscript g to denote the vapor phase.
6.1. BACKGROUND 39
pr
es
su
re
c r i t i c a lp o i n ts p e c i f i c v o l u m e
v
1 fv
1 gT
1 s u b c o o l e d l i q u i d r e g i o n s u p e r h e a t e d v a p o r r e g i o n s a t u r a t i o n c u r v eT
2 c o e x i s t a n c e r e g i o n ( v a p o r d o m e ) i s o t h e r mP
1Figure 6.2. Pressure vs Specific Volume (P-v) diagram for a fluid illustrating the relationship between the saturation curve, isotherms (T2> T1), and regions of subcooled liquid and superheated vapor.
order to condense superheated vapor at a constant pressure, the temperature must be reduced until the vapor reaches the saturation curve. Similarly, evaporation of a subcooled liquid at a constant pressure requires increasing the liquid temperature until the saturation curve is reached.
At a saturation temperature of T1 and saturation pressure of P1, the liquid specific volume is
v1f and the vapor specific volume is v1g. The specific volume of the mixture is a ratio of the liquid
and vapor specific volumes based on the mass ratio of liquid and vapor as defined by the quality.
v1= (1 − x)v1f + xv1g
Note, however, that there is no saturated fluid, vapor or liquid, which has a specific volume between
these two values. All of the liquid is at v1f and all of the vapor is at v1g. When a portion of the
liquid evaporates, the specific volume immediately jumps to v1g. There is no stable thermodynamic
state under the saturation curve. The saturation curve delineates the stable liquid thermodynamics states from the stable thermodynamic states of the vapor.
6.1.3 Thermodynamic Property Data
The relationship between saturation pressure, saturation temperature and other thermodynamic properties such as specific volume, internal energy, enthalpy, specific heats, and entropy for water and common refrigerants can be found in most standard thermodynamic textbooks [1, 10]. More extensive property data bases for a wide variety of fluids is available in software programs [9] and online data bases such as that provided by the National Institute of Standards and Technology (NIST). The saturation tables generally list temperature, pressure, and then saturated liquid and
vapor values for specific volume (vf, vg), internal energy (uf, ug), enthalpy (hf, hg), and entropy
(sf, sg). The specific volume, internal energy, enthalpy and entropy of the liquid-vapor mixture
can only be determined once the quality is known.
If the calculated quality is greater than 1, then the fluid is not in a saturated state. There is no liquid present and the thermodynamic state is that of superheated vapor. A separate sett of property tables and data bases are required to determine the properties of superheated vapor. Likewise, if the quality is calculated to be less than 0, then there is no vapor present and the system
is a subcooled liquid. Still another property table or data base is required for subcooled liquid. Quality is only a property of saturated liquid-vapor and must have a value between zero and one
(0≤ x ≤ 1).
6.1.4 Measuring Quality
Measuring quality directly is extremely difficult, especially in an open system where fluid is flowing in and out of a process. To measure quality, a two-phase mixture with two known properties such as pressure and temperature is passed through a constant temperature process where all of the liquid evaporates so that only vapor exists. This is known as throttling a mixture.
Figure 6.3 illustrates the process. Saturated liquid and vapor at high pressure (Psat) is allowed
to expand through a flow restriction resulting in a sharp decrease in pressure. If the temperature can be held constant and the pressure is decreasing, then the vapor moves from a saturated state
to a superheated state. This process can be seen in Fig. 6.2. Starting with saturated vapor at T1,
P1, and v1g, if the pressure drops but the temperature remains constant then the vapor will travel
downward on the isotherm T1 into the superheated region. As this occurs, any liquid present will
“flash” to vapor in order to follow the drop in pressure. If the process illustrated in Fig. 6.3 can be thoroughly described, then there should be sufficient information to determine the quality of the liquid-vapor mixture prior to throttling.
l i q u i d - v a p o r m i x t u r e , x = ?
P s a t P t h r o t t l e < P s a t
v a p o r , x = 1 T s a t
T s a t
Figure 6.3. Throttling process for a liquid-vapor mixture.
The throttling process can be analyzed by applying Conservation of Energy (the First Law of Thermodynamics) to a Control Volume surrounding the throttle in Fig. 6.3. There will be flow across the control surface – into the left side and out of the right side – so this is considered an open system. A number of simplifying assumptions are appropriate for this control volume:
steady flowÔ⇒ there is no accumulation of energy or mass within the
control volume
uniform flowÔ⇒ there is no variation in properties over the flow areas;
there is no velocity profile to the inlet or outlet flow so it is not necessary to integrate the property variation over the flow area.
With these assumptions the Conservation of Energy for the control volume is reduced to: ∑ ˙Q − ∑ ˙W = ∑ exits ˙ me(he+ Ve2 2 + gze) − ∑inlets ˙ mi(hi+ Vi2 2 + gzi) (6.2)
where ˙Q is the transfer of heat across a control surface, ˙W is the transfer of work across a control
surface, ˙m is the mass flow rate across a control surface and(hi+V2/2+gz) is the energy associated
with the mass flow with the terms representing enthalpy, kinetic energy and potential energy, respectively. If the throttle is well insulated, then there will be no heat transfer (adiabatic) and there is no work which crosses the control surface. The change in kinetic energy and potential
6.1. BACKGROUND 41 energy across the throttle is nearly always negligible. Finally, since there is no accumulation of
mass (steady flow), ˙me= ˙mi. Thus, equation (6.2) for the throttling process reduces to
hi= he (6.3)
The enthalpy at the exit, he, can be determined if the pressure and temperature are known because
the exit condition is superheated vapor. This is a single phase so only two properties need to be
measured to define the thermodynamic state. The value of the enthalpy at the inlet, hi, is defined
by the amount of fluid in the liquid state and vapor state.
hi= (1 − x)hf + xhg (6.4)
The saturation enthalpies, hf and hg, can also be determined if the pressure and temperature are
known. Thus, by combining equations (6.3) and (6.4), the quality can be found:
x= he− hf
hg− hf
(6.5)
6.1.5 Empirical Correlation for Saturation Pressure and Temperature
There are times when tables of numbers for saturation properties are not convenient to use; such as with spreadsheet programs like Excel, Lotus123, and Quattro. An empirical correlation be-tween saturation pressure and temperature could be useful. When plotted on a graph of absolute
temperature, Tabs, against absolute pressure, Pabs, the result is a smooth curve (Fig. 6.4). The
saturation curve is not described completely by any single, simple equation, but over a limited range of pressure it is possible to obtain a good fit using:
Pabs= b e
a/Tabs (6.6)
where a and b are empirically determined coefficients. This equation is not derived from any theory or underlying physical laws. It only approximately describes the relationship between saturation temperature and pressure. For any particular range of pressures, there will be specific values of the coefficients a and b which minimize the differences between the measured values and the curve described by equation (6.6). These differences arise both through experimental errors (random, scale and zero errors) and because the real behavior does not perfectly match the equation.
Attempting to fit experimental data to equation (6.6) is extremely difficult and likely to result in very large discrepancies in the calculated coefficients. A more accurate approach would be to linearize equation (6.6) using logarithms.
ln Pabs= ln b + a (
1
Tabs
) (6.7)
Thus, plotting ln P vs T (semilog plot) results in a straight line and standard least squares methods may be used to determine accurate values for the coefficients a and b which are the slope and the
intercept, respectively, of the plot of ln Pabs vs 1/Tabs. Rearranging equation (6.7) reveals that b is
a reference pressure and a is a reference temperature.
ln(Pabs
b ) =
a
Tabs
(6.8)
Figure 6.4. Saturation Temperature Plot for Water
6.1.6 Atmospheric Pressure
The pressure gauge you will be using in the saturation pressure and throttling experiments reads a gauge pressure; that is, a differential pressure relative to the local atmospheric pressure measure-ment. As such, you must add atmospheric pressure to the pressure reading in order to develop an accurate correlation between saturation temperature and pressure. It is not sufficient to add a standard sea-level value of atmospheric pressure. You must measure the local atmospheric pressure. Mercury Barometer
A barometer is a well-type manometer used to measure atmospheric pressure. The measurement tube is sealed so that the pressure at the top of the liquid column is the vapor pressure. The height of the liquid column is balanced by the difference between the vapor pressure in the measurement tube and atmospheric pressure at the well. Mercury is used in barometers because of its high density (SG = 13.58) and because its vapor pressure is extremely low.
6.2. OBJECTIVES 43 at 0○C (32○F) P v= 0.0247 Pa (3.58 × 10−6 psia) at 20 ○C (68○F) Pv= 0.16 Pa (2.32 × 10−5 psia) h P a t m m e r c u r y v a p o r p r e s s u r e , P v ~ 0 sc ale
The vapor pressure of mercury is so low that it can be neglected in the calculation of atmospheric pressure.
Patm= (ρHg,liq−
0
ρHg,vap)gh (6.9)
An accurate measure of atmospheric pressure requires use of the local value of the gravitational acceleration and the mercury density at the current temperature. If the local gravitational acceleration and/or the density of mercury are not known, then standard values for both may be used with correction factors added to the height:
Patm= (ρHg at 0○C)(gstd) (h + ∆hg+ ∆hT) (6.10)
where ∆hg is the correction to the gravitational
accelera-tion based on latitude. The standard gravitaaccelera-tional acceleraaccelera-tion is gstd= 9.80664 m/s2 (32.124 ft/s2)
at 45.5○ latitude. Houghton is at a latitude of 47○ 7.5’. The temperature correction, ∆hT, corrects
the observed height, h, to both the standard temperature of the measurement scale of 16.7 ○C
(62○F) and the standard density of mercury at 0○C (32○F) which is ρHg= 13595.5 kg/m3 = 26.35
slug/ft3. Correction tables for ∆hg and ∆hT are available in the laboratory.
6.2 Objectives
The objectives of this laboratory exercise are to:
• study the relationship between saturation pressure and temperature of a water-steam mixture, • use property tables (steam tables) to determine the thermodynamic state of a liquid-vapor
mixture,
• use linearization methods to obtain best fit correlations to non-linear data, • measure the quality of a liquid-vapor mixture via throttling, and
6.3 Experiment
The saturation and throttling experiments will be conducted on the Armfield TH3 Saturation Pressure Units. Figure 6.5 is a schematic of the basic system. Refer to the Fig. 6.6, 6.7, and 6.8 and Table 6.1 for location and description of the part numbers.
Figure 6.5. Schematic of Saturation Pressure Rig.
The saturation pressure apparatus consists of a fluid loop with an insulated cylindrical boiler (2) in one of the vertical lines. Distilled water in the boiler is heated to the boiling point using a pair of cartridge heaters (11) that are located near the bottom of the boiler. A sight glass (10) on the front of the boiler allows the internal processes to be observed, namely boiling patterns at the surface of the water while heating or reducing the system pressure and cessation of boiling/condensation during cooling. The sight glass also allows the water level in the boiler to be monitored. Saturated steam leaving the top of the boiler passes around the loop before condensing and returning to the base of the boiler for reheating. The operating range of the boiler and loop is 0 to 8 bar gauge. A pressure relief valve (5) is set to open at 8 bar. NEVER lean over or place your hand above the pressure relief valve! The top line of the loop incorporates an platinum RTD (3) and a pressure transducer (9) to measure the properties of the saturated steam. A Bourdon tube pressure gauge allows for monitoring of the boiler pressure even when there is no power to the unit. A fill/vent tube (38) connected to the fill/vent valve (4) on the line allows the loop to be filled with distilled water and allows all air to be vented safely before sealing the loop for pressurized measurements. The bottom of the fluid loop has a drain valve (39).
A throttling valve (6) and a throttling calorimeter (7) are attached to the vapor line, the purpose of which is to demonstrate the measurement of steam quality, x. The steam expands to atmospheric pressure as it passes through the throttling calorimeter. A platinum RTD (14) measures the temperature of the superheated vapor. A container (15) below the calorimeter collects condensing vapor and allows it to be drained safely from the apparatus.
6.3.1 Procedures
Review all of the experiment procedures prior to starting this experiment. Refer to the Fig. 6.6, 6.7, and 6.8 and Table 6.1 for location and description of the part numbers.
6.3. EXPERIMENT 45
Startup
1. Verify proper water level in the sight glass (10) of the boiler (2).
2. Verify that the fill/vent valve (4), the throttling valve (6), and the drain valve (39) are closed. The throttling valve is closed when the valve handle is perpendicular to the tube; for this apparatus, the valve is closed when the handle is vertical.
Saturation Pressure Experiment
3. Switch the heaters (36) ON and turn the heater power control (37) to MAXIMUM. Verify that the throttling valve closed (6).
4. Observe the appearance of the fluid in the boiler (2) through the sight glass (10) as the temperature increases.
5. Record in the saturation curve data table the pressure and temperature at approximately every 1 bar (100 kPa) increment until the boiler reaches the maximum working pressure of 7 bars gauge. The pressure can be read from the sensor readout display (26) on the console (20). The sensor selector switch (27) on the console may be used to toggle the readout between the platinum RTD sensor, PT100(1), and the pressure transducer. The pressure reading is gauge pressure so the atmospheric pressure will have to be measured in order to convert the transducer reading to absolute pressure. The temperature reading is the resistance of the RTD. The resistance can be converted to temperature using Table 6.2.
Throttling Experiment
6. When a pressure of 7 bar gauge has been reached, turn off the heaters (36) and reset the heater power control (37) to zero.
7. OPEN the throttling valve (6).
8. As the pressure decreases, record in the throttling process data table the pressure and both RTD readouts at every 100 kPa decrement until the boiler reaches zero pressure. The pressure decreases rapidly so plan in advance who will be switching the display and who will be recording each of the sensor readouts. Note that since the throttling calorimeter insulation has been removed, the first few seconds of throttling is not adiabatic. Heat is being transferred from the fluid to the throttling calorimeter (7). Therefore, the assumption that the process is adiabatic is incorrect and equation (6.3) is invalid. The temperature of the throttling calorimeter will increase quickly and after a few seconds the process becomes adiabatic and equation (6.3) will be valid.
Shutdown
9. After the last set of readings SWITCH OFF the unit. LEAVE THE THROTTLING VALVE OPEN to bleed some steam. Leaving the valve closed when the system is at high temperature may produce a partial vacuum upon cooling which could damage the apparatus.
Figure 6.6. Top view of Armfield TH3 Saturation Pressure Rig.
6.3. EXPERIMENT 47
Figure 6.8. Front and back panels of experiment control console.
Table 6.1. Component Description for the Armfield TH3 Saturation Pressure Apparatus 1 frame
2 boiler
3 temperature probe, PT100 (1) 4 fill/vent valve
5 pressure relief valve 6 throttling valve 7 throttling calorimeter 8 Bourdon tube pressure gauge 9 pressure transducer 10 sight glass 11 cartridge heaters 12 shield 13 14 temperature probe, PT100 (2) 15 condenser cup 16 RTD connector, PT100 (1) 17 RTD connector, PT100 (2) 18 pressure transducer connector 19 cartridge heater connector 20 TH3 control console
21
22 console power breaker, CONT 23 cartridge heater breaker, HEAT 24 auxiliary power breaker, O/P 25 power input
26 sensor readout 27 sensor selector switch
28 input/output data port, IFD3 29 power cable
30 power switch 31 heater connector
32 pressure transducer connector 33 PT100 (2) RTD connector 34 PT100 (1) RTD connector 35 auxiliary 120 A/C power 36 heater switch
37 heater power control 38 fill/vent tube 39 drain valve 40
Name: Date: Data Sheet for Saturation Curve
Patm: mm Hg
kN/m2
R1 T1 Tabs P1,gauge Pabs
Ω ○C K 1/Tabs kN/m2 kN/m2 ln(Pabs)
Data Sheet for Throttling Process
Patm: mm Hg
kN/m2
R1 T1 T1 R2 T2 T2 P1,gauge hf hg h2 quality
Ω ○C K Ω ○C K kPa KJ/kg KJ/kg KJ/kg x
6.3. EXPERIMENT 49 T able 6. 2. R TD Resistance – T emp erature Con v ersion T able
6.4 Measuring Atmospheric Pressure
During this experiment you will determine the local value of the barometric pressure using a Fortin
barometer. Record all data in the table provided in§6.4.1. The basic procedures are as follows:
V
S
F
P
A
1. Set the fiducial point: The lower mercury surface in a Fortin barometer has to be set to a datum level before adjusting its vernier and the accuracy of pres-sure meapres-surement depends crucially upon proper setting. The mercury surface should first be lowered until it is clearly below the fiducial point (F). Tap the barometer lightly to stabilize the meniscus. Then very slowly turn adjusting knob (A) until the gap between fiducial point and the reservoir mercury surface just disappears when viewed horizontally. The point should make no more than the slightest dimple in the mercury surface. If the mercury surface is bright and the level correct, the tip of the fiducial point will coincide with the reflected image on the mercury surface. The setting will only be correct if the mercury surface is raised to the fiducial point, not lowered. If while raising the surface the fiducial point penetrates the surface, the mercury level should be lowered and the procedure restarted. A dirty mercury surface, poorly shaped fiducial point or a partially clogged porous plug (P) can make proper and repeatable setting very difficult.
2. Setting the Vernier: The vernier (V) should be lowered until both the front
and back edges of the vernier coincide with the apex of the mercury meniscus when viewing exactly horizontal.
3. Reading the Vernier: There are two measurement scales (S); an English unit scale (inches) and a SI unit scale (mm). The vernier has two gradations corresponding to each scale. After setting the vernier, read both scales simul-taneously.
4. Measure the Barometer’s Temperature: A thermometer is attached to the barometer for measuring the temperature.
5. Apply the Gravitational and Temperature Corrections to the Ob-served Height: The barometer manual contains both English and SI correc-tion factors for latitude and temperature.
6.4. MEASURING ATMOSPHERIC PRESSURE 51
6.4.1 Data Log for Atmospheric Pressure Measurement
Name: Date: Lab Partners:
Complete the table for both sets of units.
SI Units English Units
Room Temperature ○C ○F
Mercury Density (std) kg/m3 slug/ft3
Mercury Height (observed) mm in
temperature correction mm in
latitude correction mm in
atmospheric pressure mm Hg in Hg
kPa psia
National Weather Service mm Hg in Hg
kPa psia
Bibliography
[1] Yunus A. C¸ engel and Michael A. Boles. Thermodynamics: An Engineering Approach.
McGraw-Hill, 5th edition, 2006. ISBN 0-07-288495-9.
[2] Michael J. Moran, Howard N. Shapiro, Bruce R. Munson, and David P. DeWitt. Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer. John Wiley & Sons, Inc., 2003. ISBN 0-471-20490-0.
[3] Agilent Technologies. Agilent 54621A/22A/24A/41A/42A User’s Guide. Publication Number 54622-97036, September 2002.
[4] L. Solnik manag. ed. M. Kromida D. Irizarry L. C. Forier, ed. and assoc. ed. W. Schildknecht, editors. MOTOR Auto Engines and Electrical Systems. Motor, New York, NY, 1977. ISBN 0-910992-73-8.
[5] Edward F. Obert. Internal Combustion Engines and Air Pollution. Harper & Row, Publishers, Inc., New York, NY, 1973.
[6] Bruce R. Munson, Donald F. Young, and Theodore H. Okiishi. Fundamentals of Fluid Me-chanics. John Wiley & Sons, Inc., 5th edition, 2006. ISBN 0-471-67582-2.
[7] Frank M. White. Viscous Fluid Flow. McGraw-Hill Co., 1974. ISBN 0-07-069710-8. [8] Frank M. White. Fluid Mechanics. McGraw-Hill, 2003. ISBN 0-07-283180-4. [9] F-Chart Software. EES Manual. www.fchart.com, v7.663 edition, 2006.
[10] Stephen R. Turns. Thermodynamics: Concepts and Applications. Cambridge University Press, 40 West 20th Street, New York, NY 10011-4211, USA, 2006. ISBN 0-521-85042-8.
[11] J.P. Holman. Experimental Methods for Engineers. McGraw-Hill, 7th edition, 2001. ISBN 0-07-366055-9.
[12] Duane Abata. ME223 Thermodynamics Laboratory Manual. Mechanical Engineering - En-gineering Mechanics Department, Michigan Technological University, Houghton, Michigan 49931, 2nd edition, 1983.
[13] N.V. Suryanarayana and ¨Oner Arici. Design and Simulation of Thermal Systems.
McGraw-Hill, Inc., 2003. ISBN 0-07-249798-X.
[14] Faye C. McQuiston and Jerald D. Parker. Heating, Ventilating, and Air Conditioning. John Wiley & Sons, Inc., 2nd edition, 1982. ISBN 0-471-08259-7.
158 BIBLIOGRAPHY [15] Michael J. Moran and Howard N. Shapiro. Fundamentals of Engineering Thermodynamics.
John Wiley & Sons, Inc., 5th edition, 2004. ISBN 0-471-27471-2.
[16] J.A. Goff. Standardization of thermodynamic properties of moist air. Transactions ASHVE, 55, 1949.
[17] Richard E. Sonntag, Claus Borgnakke, and Gordon J. Van Wylen. Fundamentals of Thermo-dynamics. John Wiley & Sons, Inc., 5th edition, 1998. ISBN 0-471-18361-X.
[18] Jim Lally and Dan Cummiskey. Dynamic Pressure Calibration. TN-15-0205, PCB Piezotronics, Inc., Depew, NY 14043 USA, 2005.
[19] Robert Fox and Alan McDonald. Introduction to Fluid Mechanics. John Wiley & Sons, Inc., 1985. ISBN 0-471-88598-3.
[20] C.C. Heald, editor. Cameron Hydraulic Data. FlowServe Corporation, Canada, 19th edition, 2002.
[21] T. Baumeister, E. A. Avallone, and T. Baumeister III, editors. Marks’ Standard Handbook for Mechanical Engineers. McGraw-Hill Book Company, 8th edition, 1978. ISBN 0-07-04123-7.