Pump Characteristics Essay, Research Paper
Experiment # 1
Prelab Proposal
Wednesday, September 15
Cooling TOWER PERFORMANCE
Jonathan Mettes and Shalin Sanjanwala
Submitted to
Professor Muthanna Al-Dahhan
Teaching Assistant Novica Rados
Chemical Engineering Laboratory & # 8211 ; I
ChE 374
Fall 1999
Table OF CONTENTS
Page
Table of Contentss i
Notation two
List of Figures iii
Introduction 1
Aims 2
Experimental Set-Up 2
Experimental Procedure and Data Collection 3
Theory and Calculation Procedure 6
Mentions 15
Notation
Letter Symbols
a Contact country per tower volume, ft2/ft3
A Contact country, ft2
BDA Bone Dry Air
Cp Heat capacity, Btu/ ( lb? F )
E Voltage, Vs
G Air flow rate, lbdry air/ ( hr ft2 )
H Enthalpy, Btu/lb
hgt Height, foot
H Humidity, lbwater/lbBDA
I Current, amperes
K Mass Transfer Coefficient, lbwater/ ( hr ft2 )
L Liquid flow rate, lb/ ( hr ft2 )
thousand Mass flow rate, lb/hr
NTU Number of Transfer Unit of measurements
PF Power factor, %
T Temperature, ? F
V Velocity, ft/sec
V Active chilling volume, ft3/ft2 of apparent country
Vh Humid volume, ft3moist air/lbBDA
tungsten Width, foot
wt % Weight Percentage
Grecian Letterss
H Efficiency, %
cubic decimeter Latent heat of vaporisation, Btu/lb
List OF FIGURES
Page
Figure 1: Procedure Flow Diagram for Bryan Hall Cooling Tower 3
Figure 2: Counterflow Cooling Diagram for Bryan Hall Cooling Tower 6
Introduction
The intent of this experiment is to analyze the map and usage of chilling towers in industry, while by experimentation finding the public presentation of a peculiar chilling tower, located on the roof of Bryan Hall. The chilling tower in this instance is used in an air-conditioning system, whereby the heat rejected by the heat pump is transferred to a & # 8220 ; capacitor H2O & # 8221 ; circulation system, and is in bend rejected to the ambiance via the chilling tower.
The primary measured parametric quantities in this experiment are the temperature of the recess and mercantile establishment H2O watercourse, the temperature of the recess and mercantile establishment air watercourse, the air flow rate, and the liquid flow rate. From these values, other of import features of the chilling tower can be evaluated and studied, including: the chilling scope, which is the difference between Tw, recess and Tw, mercantile establishment ; the cooling-tower attack, calculated as the difference between the Tw, mercantile establishment and the recess air wet-bulb temperature ; the figure of transportation units ( NTU ) of the tower, stand foring the size of the equipment that allows the transportation to come to equilibrium ; the rate of H2O loss, which is the rate of the H2O that is lost by vaporization, blow down, etc. ; the rate of makeup, which is the rate of H2O added to the go arounding system to H2O loss ; and the heat burden of the tower, stand foring the heat that is lost to the ambiance.
Since a big figure of chemical industrial processes employ a heat transportation from a beginning watercourse to a heat watercourse, chilling towers are an of import constituent for the design and building of these procedures. It is necessary to be able to mensurate and analyse the public presentation of the chilling tower to guarantee it meets the demands of a peculiar procedure, and if it does non, to be able to rectify any jobs therein.
Aim
1. Develop a chilling diagram for the Bryan Hall chilling tower, and discourse its properties.
2. Estimate the Number of Transfer Units ( NTU ) of the chilling tower to measure its features.
3. Calculate the flow rate of H2O into the chilling tower by mensurating the horsepower input of the H2O pump ( via the electromotive force and current ) , so utilizing the public presentation graph of the pump that relates horsepower input to pumping rate.
4. Determine the rate of H2O lost to vaporization, blow down, impetus, etc. , every bit good as the rate of makeup.
5. Measure the heat lost to the ambiance from the hot H2O.
EXPERIMENTAL SET-UP
A procedure flow diagram of the chilling tower system is shown in Figure 1. The chief constituents are the chilling tower itself, the H2O pump, and the capacitor. The chilling tower in this apparatus is of the induced bill of exchange type. The fan that drives the air flow is located on top of the tower, and the ensuing suction pulls in the air through the two side panels, where it cools the H2O that is trickled down across it. Pump P-101 draws the cooled H2O from the underside of the chilling tower, and provenders it through valve V-102a ( or V-102b, depending on which capacitor is runing ) , where pump P-102a circulates it into capacitor # 1. After heat exchange takes topographic point, the warmed H2O is pumped back up through valve V-104a by pump P-103, and is trickled down the panels in the chilling tower, to be cooled by the atmospheric air blowing across it.
Figure 1: Procedure Flow Diagram for Bryan Hall Cooling Tower
Experimental PROCEDURE AND DATA COLLECTION
There are three locations from which informations need be collected during this experiment: the top of the chilling tower, the underside of the chilling tower, and the cellar of Bryan Hall. At the top of the tower, the recess H2O temperature is measured, every bit good as the humidness of the go outing air utilizing a sling psychrometer. At the underside of the tower, the mercantile establishment H2O temperature, the humidness of the recess air ( once more utilizing a sling psychrometer ) , the speed of the recess air ( utilizing an wind gauge ) , and the country of the recess air blowholes ( utilizing a measurement tape ) demand to be measured. In the cellar of Bryan Hall, a reading from the voltmeter and ammeter on the power line to the pump motor is measured.
Get downing at the chilling tower itself, load the equipment you will necessitate ( psychrometer, thermometer, books, manual, etc. ) into a pail. Using cautiousness, climb the perpendicular ladder to the top of the tower, and so draw up the pail with a rope. Open the metal screen of the H2O recess chamber to the right of the fan and take a temperature reading of the recess H2O ( Twater in1 ) , so do the same for the recess chamber to the left of the fan ( Twater in2 ) . To find the humidness of the air go outing the tower, whirl the sling psychrometer merely above the fan for about 15 seconds, doing certain that the reservoir contains distilled H2O, that the wick covers the moisture bulb, and there is no wet on the dry bulb, so rapidly look into the temperatures, reading the wet-bulb temperature ( Twet-bulb, air out ) foremost, so the dry-bulb ( Tdry-bulb, air out ) . Repeat this process until there is no alteration in the temperatures for three back-to-back measurings. Once the wet-bulb, dry-bulb, and inlet H2O temperatures have been measured and recorded, put the equipment back in the pail, lower it to the land, and fall the ladder.
Following, at the underside of the tower, step the temperature of the pool of H2O nearest to the ladder in order to acquire a value for the issue H2O watercourse temperature ( Twater out1 ) . Use the sling psychrometer to take the humidness measurings for the recess air watercourse ( Twet-bulb, air in1 and Tdry-bulb, air in1 ) by twirling it in forepart of the vent country, reiterating the procedure as was used for the mercantile establishment air watercourse. To mensurate the air speed ( vair1 ) , place an wind gauge in the recess air watercourse so the traveling air blows forthrightly into the entryway face. The speed should be measured at the centres of nine equal countries over the recess vent country. Using the measurement tape, find both the tallness and breadth of the vent country face, so that the country can be calculated. Repeat all these measurings for the other side of the chilling tower, as air current humidness, wind velocity, etc. may be different for both sides.
Once all the temperatures, the recess air speed, and the vent country have been measured and recorded, continue to the cellar in Bryan Hall to acquire readings for the pump motor. On the circuit box for the pump motor is an ammeter and a voltmeter. Read the values off of the metres and enter them in the information sheet. A sample information sheet is shown below:
Top: Twater in1 ( ? F ) ___________ Twater in2 ( ? F ) ___________
Twet-bulb, air out ( ? F ) ___________ ___________ ___________
___________ ___________ ___________
Tdry-bulb, air out ( ? F ) ___________ ___________ ___________
___________ ___________ ___________
Bottom: Twater out1 ( ? F ) ___________
Twet-bulb, air in1 ( ? F ) ___________ ___________ ___________
Tdry-bulb, air in1 ( ? F ) ___________ ___________ ___________
vair in1 ( ft/s ) ___________ ___________ ___________
___________ ___________ ___________
___________ ___________ ___________
hgtvent ( foot ) ___________ wvent ( foot ) ___________
Twater out2 ( ? F ) ___________
Twet-bulb, air in2 ( ? F ) ___________ ___________ ___________
Tdry-bulb, air in2 ( ? F ) ___________ ___________ ___________
vair in2 ( ft/s ) ___________ ___________ ___________
___________ ___________ ___________
___________ ___________ ___________
Basement: Epump ( Vs ) ___________
Ipump ( As ) ___________
Theory AND CALCULATION PROCEDURE
Development of Cooling Diagram
Figure 2 represents a counterflow chilling diagram for the chilling tower in Bryan Hall. This diagram provides relationships between air and H2O and shows the drive forces ( H & # 8217 ; & # 8211 ; H ) nowadays in the counterflow chilling tower. Lines Cadmium and AB represent the air and H2O operating lines, severally, each being bound by the recess and mercantile establishment H2O temperatures. The air runing line starts ( indicate C ) below point A and at a point matching to the heat content of the come ining wet-bulb temperature. The perpendicular line AC represents the driving force at the base of the chilling tower. The air runing line ( Cadmium ) increases with a incline bing L/G as the heat that is removed from the H2O is added to the air. The line ceases at the heat content matching to that of the wet-bulb temperature out.
Figure 2: Counterflow Cooling Diagram for Bryan Hall Cooling Tower
The temperature of the hot H2O come ining the top of the tower corresponds with point B in figure 1. At this point, a movie ( saturated with H2O vapour ) surrounds the H2O. As heat is being removed from the H2O, the movie heat content follows the H2O runing line to the temperature of the cold H2O out ( Perry et.al, 12-13 ) .
One point included in the counterflow chilling diagram is the wet-bulb temperature. It is the liquid temperature ( at steady province ) that the heat needed to vaporize the liquid and heat the vapour to gas temperature is equal to the reasonable heat fluxing from the gas to the liquid ( McCabe et. Al, 748 ) . The moisture bulb temperature, along with the dry bulb temperature, can be used to happen heat contents of both air in and air out from psychrometric charts.
For air-water mixtures the wet-bulb temperature resembles the adiabatic impregnation temperature, the temperature at which a gas comes into equilibrium with any unevaporated H2O. It can be shown that Twb = Tad.sat..
Eqn. 23.19 and 23.21
Eqn. 23.11
To build the chilling curve, the wet-bulb temperature in, cold H2O temperature out, wet-bulb temperature out, and hot H2O temperature in are measured. From these measurings, the corresponding heat contents can be found. Psychrometric charts are used to happen the heat contents for the recess and mercantile establishment moisture bulb temperatures, which aides in the building of the air runing line ( Cadmium ) . Point C is plotted at the temperature of the cold H2O out and the heat content of the air matching to that of the recess wet-bulb temperature. Point D is plotted at the temperature of the hot H2O in and the heat content matching to that of the mercantile establishment wet-bulb temperature. Connecting these two lines gives the air runing line, and the incline of the line is tantamount to the L/G ratio.
To build the H2O runing line ( AB ) , the heat contents of the cold H2O out and hot H2O in must be found. Indicate A is plotted at the temperature of the cold H2O out and its corresponding heat content. Point B is plotted at the temperature of the hot H2O in and its corresponding heat content. A nonlinear line that goes through the recess and outlet wet-bulb temperatures and their heat contents connects A and B.
From the chilling curve merely developed, the L/G ratio can be found. It is merely the incline of the air runing line.
The hair out and hair in are found on psychrometric charts utilizing the recess and outlet wet-bulb temperatures.
L/G soap occurs when the mercantile establishment wet-bulb temperature of air is equal to the recess H2O temperature. To cipher this, a line is drawn from C to B and the incline is calculated.
The heat content of the recess and mercantile establishment H2O watercourses can be found by mentioning to the moist air charts, such as those in Perry & # 8217 ; s Handbook. The heat content can be found by reading off the temperature of the watercourse from the column and obtaining the corresponding heat content for that temperature. After the heat contents of the recess and mercantile establishment H2O watercourses are found, driving forces can be calculated. The driving force is the difference between the H2O runing line and the air runing line at any point along the tower. Driving force computations are utilized in the computation of tower features ( NTU ) utilized in the computation of tower features ( NTU ) .
The chilling scope is the difference between recess hot H2O temperature and the mercantile establishment cold H2O temperature and the heat burden is fixed. The chilling tower attack is the difference between mercantile establishment cold H2O temperature and ent
ering air wet-bulb temperature. Size and efficiency of the tower hole attack. Large towers that have mean efficiency do non “approach” given wet-bulb temperatures any closer than smaller towers with better efficiency ( Hensley 22 ) .
Appraisal of NTU
The Number of Transfer Units ( NTU ) can be estimated in two different ways: numerical solution or adiabatic humidification premise. The numerical solution involves utilizing the chilling diagram and different methods of integrating to gauge NTU. The adiabatic humidification premise involves the usage of expressions based on either mass or heat transportation.
Estimating NTU numerically involves utilizing the chilling diagram since NTU is related to the country of ABCD. The values of the different drive forces ( H & # 8217 ; -h ) vs. T are taken from the chilling diagram within the ABCD country. The opposite of the driving force 1/ ( H & # 8217 ; -h ) is plotted versus temperature. The country under the curve of 1/ ( H & # 8217 ; -h ) vs. T is calculated utilizing Trapezoidal or Simpson & # 8217 ; s regulation utilizing the bounds Tcw, out and Thw, in. The consequence is equal to NTU.
NTU can be estimated two different ways when utilizing the adiabatic humidification premise. Based on mass transportation:
where H is humidness. The humidness can be read off the psychrometric charts utilizing the dry-bulb and wet-bulb temperatures. NTU can besides be calculated based on heat transportation:
The size of the equipment that allows a transportation to come to equilibrium is what NTU measures.
Appraisal of Water Circulating Flow Rate
Since there is no flowmeter on the circulated H2O line and hence no direct manner to mensurate the H2O go arounding flow rate, it is necessary to utilize the power input to the pump to indirectly cipher the flow rate of H2O in the system. Using the expression:
the power input to the pump can be calculated, where Imeasured is the mensural current and Emeasured is the mensural electromotive force from the circuit box of the pump in the cellar of Bryan. PF is the power factor and can be determined from Table 2 ( pg. 18, Lab Manual ) by the undermentioned equation:
where Erated = 230V. After ciphering Icorrect from this expression, PF ( % ) can be obtained and so plugged into equation 6 to cipher power input. The efficiency of the pump ( H ) can besides be obtained from Table 2, and the power end product of the pump can be calculated from:
Once power end product is calculated, the flow rate of the H2O in gallons per minute can be determined from Figure 4 ( pg. 22, Lab Manual ) and converted to lb/ ( hr ft2 ) utilizing the undermentioned equation:
Using the power end product to gauge the circulating flow rates from Figure 4 is more accurate than utilizing the power input, since the power end product is straight correlated to the flow rate, whereas some of the power input is lost to clash, heat, etc. A possible beginning of mistake in the appraisal of the H2O flow rate prevarications in Figure 4 ( end product vs. power input ) itself. This graph is simply an by experimentation determined correlativity and is non an exact relation, so some mistake is introduced into the experiment. A better manner would be to put in a flowmeter on the H2O line to straight mensurate the flow rate. There is merely one pump operating in Bryan Hall because one pump can supply the necessary H2O flow rate capacity of the chilling tower. The tower can merely manage a certain sum of H2O per unit clip, so if all three of the pumps in the cellar of Bryan Hall were in operation, it would merely overload the tower.
Determination of Water Loss or Make-up
The H2O loss of the tower is the rate of the H2O that is lost by vaporization, blow down, etc. , and is measured in lb/hr. It can be calculated by taking the difference in the recess and mercantile establishment humidness of the atmospheric air used in the tower multiplied by the mass flow rate of the air:
Where Hair out, degree Celsius is the humidness of the mercantile establishment air watercourse, after rectification to the operating force per unit area, and Hair in, c is the humidness of the recess air watercourse after force per unit area rectification. The rate of H2O makeup is equal to the rate of H2O loss. To cipher the make-up per centum of the circulating H2O flow rate:
It is better for the rate of H2O loss to be little so that you do non hold to refill the go arounding capacitor H2O as frequently. If the rate of H2O loss is excessively big, the tower should be checked to do certain that there are no terrible leaks in the piping system, that the drip home bases are non damaged, etc.
Evaluation of Heat Load
The heat burden of the chilling tower is the entire heat to be removed from the go arounding H2O by the chilling tower per unit clip, and can be calculated two ways, both of which are in units of BTU/hr. The first manner is based on the sum of heat that is released from the H2O, and is calculated by finding the heat ( in BTU ) available in the recess H2O versus the heat ( in BTU ) available in the mercantile establishment H2O:
The 2nd manner is based on the sum of heat that is absorbed by the ambient air fed through the chilling tower, which is calculated by the difference in heat in the mercantile establishment air and the recess air:
where DT1 = Tair out & # 8211 ; Treference, and DT2 = Tair in & # 8211 ; Treference. lavg is the mean latent heat, calculated from the latent heat for the recess and mercantile establishment conditions:
The unit & # 8220 ; dozenss of infrigidation & # 8221 ; is a unit used to mensurate the sum of heat removed by a hair-raiser per unit clip, and is equal in value to 12000 BTU/hr. It is a refrigerating consequence equal to runing one ton of ice in 24 hours. Using the undermentioned equation expresses the heat burden calculated by either equation 12 or equation 13 in dozenss of infrigidation:
It is of import to cognize the heat burden of the chilling tower in order to measure its overall capacity to reject heat from the & # 8220 ; capacitor H2O & # 8221 ; , so that ( in this peculiar instance ) accurate computations can be made as to how much volume the air conditioning system can efficaciously chill. The heat burden should be a big figure, as the larger the heat burden, the larger the sum of heat that can be removed from the H2O per hr, and the more condenser H2O that can be pumped through to absorb the heat rejected from the heat pump.
RESULTS AND DATA ANALYSIS
Cooling Diagram
The chilling diagram for the Bryan Hall chilling tower as constructed from the natural informations listed in Appendix C is shown in figure 3. In developing this diagram, a counterflow premise was made, even though the tower exhibits a crossflow form. In presuming counterflow, air and H2O conditions are assumed to be changeless across any horizontal subdivision of the tower. This differs from crossflow towers since both air and H2O conditions vary vertically and horizontally in crossflow towers. Some mistakes result from these differences. For case, colder H2O can be obtained from a counterflow tower ( Burger, 1999 ) . Colder H2O would consequence both of the temperature and air runing lines. If temperature of H2O out was ice chest, the incline of the air runing line ( L/G ) and the drive force would besides be smaller, therefore increasing the figure of transportation units. Since in this instance the figure of transportation units for the counterflow tower would be larger than for a crossflow tower, utilizing the counterflow theory overestimates the tower features.
Figure 3. Counterflow chilling diagram for Bryan Hall Cooling Tower
On the chilling diagram, the H2O runing line exhibits a curving form that increases as temperature additions. As H2O falls vertically, it tends to travel towards colder air. The H2O approaches the wet-bulb temperature as a bound ( Baker and Shryock, 1961 ) . The impregnation line besides lies on the H2O runing line. This is true because it is assumed that at points on this line, a movie ( saturated with H2O vapour ) surrounds each H2O atom. If a atom is at conditions above this line, it exists as H2O. The H2O runing line displays the same behaviour as the impregnation line.
The air runing line on the chilling diagram exhibits a consecutive line. Air that moves through a subdivision ever moves towards hotter H2O and this can be seen in the chilling diagram ( figure 3 ) . The air approaches the hot H2O temperature as a bound. As the hot air enters the underside of the chilling tower, it wants to travel towards hotter H2O ( hot H2O is located at the top of the tower ) . This is why the air runing line goes from cold H2O temperature to hot H2O temperature.
The incline of the air runing line was used to cipher L/G and ( L/G ) soap. Equations 1 and 2 ( calculated in Appendix A ) , severally, were used to cipher these values and they are presented in Table 1:
Table 1. Consequences for L/G and ( L/G ) soap.
L/G.7738 Btu/lb? F
( L/G ) max 1.5344 Btu/lb? F
The L/G ratio is merely the ratio of the mass flow rates of H2O to air. The L/G ratio additions as the air flow rate lessenings and the drive force is decreased. Therefore, the NTU would be increased. This is non a desired state of affairs since the extent of the equipment that allows the transportation to come to equilibrium is big. Therefore it is more desirable to hold a low L/G ratio. A low ratio means the gas flow rate is much larger than the liquid flow rate. More heat can be transferred from the H2O to the air faster if the gas flow rate is larger.
The drive forces at the top and underside of the tower were calculated utilizing combining weight. 3 ( computations in appendix A ) . Table 2 summarizes the consequences of the drive forces:
Table 2: Drive Forces at top and underside of chilling tower.
Location Driving Force
Top 13.39 Btu/lb BDA
Bottom 9.44 Btu/lb BDA
The driving force additions when traveling from the underside of the chilling tower to the top of the chilling tower.
The chilling scope is the difference between recess hot H2O temperature and the mercantile establishment cold H2O temperature and the heat burden is fixed. It is better if the scope is low because so the L/G ratio will be little, which in bend means the needed coefficient ( NTU ) is little and public presentation of the tower is better. Therefore, a larger chilling scope means a smaller extent of equipment is needed for the transportation to come to equilibrium, which is desirable. The chilling tower attack is the difference between mercantile establishment cold H2O temperature and come ining air wet-bulb temperature. Size and efficiency of the tower hole attack.
Number of Transfer Unit of measurements
The figure of transportation units measures the size or the extent of the equipment that allows the transportation to come to equilibrium. It was calculated three different ways: 1 ) numerical appraisal ; 2 ) adiabatic premise based on mass transportation ; 3 ) adiabatic premise based on heat transportation. In order to work out the equations 4 and 5, the Hsat, recess and Tsat, recess were found ( the values are found in Appendix C ) . In the numerical appraisal, equations for the H2O runing line and air runing line ( both labeled in figure 3 ) were found utilizing arrested development analysis. Table 3 summarizes the consequences of NTU computations ( mention to appendix A for sample computations ) :
Table 3: Consequences for NTU computations.
Method NTU
Numeric Appraisal 1.895
Mass Transfer Basis.0117
Heat Transfer Basis -.2097
The numerical appraisal gives the most dependable value out of the three. In appraisal utilizing mass transportation, the Hairout was non able to be found. This is because the dry-bulb temperature of the air out was higher than the dry-bulb temperature coming in. And with the adiabatic humidification premise, it was non possible to happen Hairou. Having the mercantile establishment dry-bulb temperature higher than the inlet dry-bulb temperature besides led to error in appraisal of NTU utilizing heat transportation footing.
NTU is an of import value for the tower public presentation because it is a step of the degree-of-difficulty of the job ( Baker and Shryock, 1961 ) . It is better for NTU to be little. A smaller NTU means it is easier for the transportation to come to equilibrium.
Mentions
Al-Dahhan, Muthanna. ChE 374 Laboratory Manual: Experiments in Heat-Mass-
Momentum Transport. Washington University, 1997.
Baker, Donald, and Shryock, Howark. Journal of Heat Transfer. & # 8220 ; A comprehensive attack to the analysis of chilling tower performance. & # 8221 ; August, 1961
Hensley, J.C. , erectile dysfunction. Cooling Tower Fundamentals. The Marley Cooling Tower Co. 1982.
McCabe, W.L. , Smith, J.C. , and Harriott, P. Unit Operations of Chemical Engineering.
fifth edition. McGraw-Hill, 1993.
Perry, R. , Green, D. , and Maloney, J. Perry & # 8217 ; s Chemical Engineers & # 8217 ; Handbook. 6th
edition. McGraw-Hill, 1984.
Smith, J.M. , and Van Ness, H.C. Introduction to Chemical Engineering
Thermodynamicss. 4th edition. McGraw-Hill, 1987.
Welty, James R. , Wicks, Charles E. , and Wilson, Robert E. Fundamentals of Momentum,
Heat, and Mass Transfer. 3rd edition. John Wiley & A ; Sons, 1984.
Convert Crossflow to Counterflow & # 8211 ; National Engineer by Bob Burger
Bibliography
Al-Dahhan, Muthanna. ChE 374 Laboratory Manual: Experiments in Heat-Mass-
Momentum Transport. Washington University, 1997.
Baker, Donald, and Shryock, Howark. Journal of Heat Transfer. & # 8220 ; A comprehensive attack to the analysis of chilling tower performance. & # 8221 ; August, 1961
Hensley, J.C. , erectile dysfunction. Cooling Tower Fundamentals. The Marley Cooling Tower Co. 1982.
McCabe, W.L. , Smith, J.C. , and Harriott, P. Unit Operations of Chemical Engineering.
fifth edition. McGraw-Hill, 1993.
Perry, R. , Green, D. , and Maloney, J. Perry & # 8217 ; s Chemical Engineers & # 8217 ; Handbook. 6th
edition. McGraw-Hill, 1984.
Smith, J.M. , and Van Ness, H.C. Introduction to Chemical Engineering
Thermodynamicss. 4th edition. McGraw-Hill, 1987.
Welty, James R. , Wicks, Charles E. , and Wilson, Robert E. Fundamentals of Momentum,
Heat, and Mass Transfer. 3rd edition. John Wiley & A ; Sons, 1984.
