Document kDKoq76Vj4dJNDzOjkwRMv7zO

46 CHAPTER 3 1965 Guide AndData.BooV Table 7------ Calculated Diffusion Coefficients for Water-Air-at One Atmosphere Ump,F cm*/tec; -100 -- 50 - 40 - 30: - 20 0.130 ; 0.163 0.169 0.176 0.183 - 10 30 0.190 0.198 0.205 0.213 0.220 Temp, F 40 50 60 70 80 90- 100 110' 120 T30 cm3/tec 0.228 0.236 0.243 0.251 0.260 0.269 0.277 0.285 0.294 0:302 ' Tvmp, F 140 . 150 : 200 - 250 . 300 350 400 450 500 ent/rte 0.463 the finl dry-buib temperature of the moist air tuiu rate c. steam flow.required in lb per hE -' Solution: Fig.' 9 shows the schematic solution. By Table 3, theenthalpy oT.the steam h, ~ 1157.0 Bfci/lb water. Thus, from Equation 29,' the condition fine oh the'ASHRAE chart connecting Stated 1 and 2 must have a direction. AA '' ' ' Btu/lb water. .. , . ^ The condition One may be drawn through use of the &h/&.W, pro tractor. The procedure is as follows: On the protractor establish the' reference line by connecting ` the ori&n with the'.'value 6h/aW " 1157. Draw a second line parallel to the reference line and.through the state-point,of-the moist air. This second line is the condition line. State'2 is established at the intersection of the condition line with the horizontal line extended from the saturation curve at 55 F (te *><55 F). Thus, U 72.2 F. Vahiee of Wt and Wmay be read from the chart. The required steam flow is ,-.i . m* - m.{Wt - WO - (200)(60)(0.00920 - 0.00070) -- 102 lb steam/hr Absorption of Space Heat and Moisture Gains byMoist'Air <' i.fwj The problem'of air ooniditiamiiga space usually reduces to the 'determination of the quantity `of moist air that.must be supplied and,the necessary condition which it must.have,in order to-remove given amounts of energy, and water from the space aad'be withdrawn at a specified condition.' ' > * " Fig; 10 schematically shows a space with incident rates of energy and moisture gains. The quantity q, denotes the net Bum of all rates of heat gain upon the space, arising from transfers through*boundaries and from sources within the space. This heat gain involves addition of, energy alone and does not include energy' contributions due to-addition of water (or water'vapor). It is usually called the.sensible heat gain. The quantity denotes the net sum ofall rates of moisture gain upon the space arising from;transfers through boundaries and from sources .within the space. Each pound of moisture injectedinto the space adds an amount of energy equal to its specific enthalpy. Assuming steady-state conditions, the governing equations are, ,* ;* ;;.-f * ... i mjh + q, + (n<A) " wA* + ]T m. a m*Wt . + ;(*nAi.) - --.Ad (30) m. -.m.dF, - Wi) (31) It is to be noted that the left side of Equation 30 represents the total rate of energy addition to the space from all sources. By Equations 30 and 31 , , ht -- ht g + ("A) Wt-Wx~- * ' - according towhich: on tSe-ASHRAE chart andfor a given state cf^the withdrawn air, sail possible states (conditions) forthe supply .dir'must'tie on a straight line drawn'through the statepoiht of.the wiihdratonair and which has o direction `specified by the numerical value of fa + lAE^W- This freight line is called the condition line for the given problem. , rErxramrp*le 8a-: Moist ajuitr is wijthndarawna Iir_o_r_a_.&. 'room &t 80 ,F ldl~ryr_Srnl?b*,ttekm1perature aon?d''668? F tKnfmwfffniiml* wet-builub t-e---m---j--- tort Tlw sensible rate of heat gam for the space is 30,0O0 Bth SSo^nt'*7.^!m"*UroK!"'0, ! Ib per hricun, from tte occopute of t_h_e__a_p_a_c_e. Thu, umuouisHtuurev>-umiay/-1 hue Basssuummeead uee seaturmatedd`water--vvaapor at 90 F.' Moist air is mintrooduiiced ihnto the room'at a'dry-bulb temperature' of' 60' F. Find the required thermodynamic wet-bulb^temperature of the supplyair aitd-the required volume rate of Bow of the supply air. Solution: Fig. 11 shows the schematic 'solution. State 2 may be located on the'ASHBAE chart. From* Table 2, the specific enthalpy of the water vapor added is A, -- 1100.44 Btu/lb. From Equation 32 -. Oh `30,000 -f (10)(1I00.44) rtv a Arr 10 ------------ - 4100 Btu/lb water l fryiSwdroetrier' obfcO '.-'.c; WiththenA/hTTprotrsctcr;,-rtaMuih areference lineof direction OhJaW. - 4100 Btu/Ib water. Parallel to thisreference liiw, draw tt~ntr**gbt`1ine on'the chart.through State 2. The intersection of this Ime with the GO F dry-bulb temperature line is 8tate 1. Thus, ,,-Ad 56.4'F. sltemate fand approximately correct)'procedure in estab lishing the condition line is to uoe the sensible-total heat'ratio - ' *----*>* 'Afc/A-W. npftln TV>. /niwitih. 30,000 - - 0.732 . 6Mr~,i. + E.Cm-h.) "30)000 .+, (10)0100.44) ......... It may be observed that' 0.732 on the protractor coincides closely with AA/AfP * 4100 Bu/lb.water. -The flow rate ofdry air may be calculatedfrom either *frrfitwn 30 w 3I.`From Equation 30' ' ! i-"101.5 Ib'dry air/ihin , ^ At Statoi, si - 13.29 cu ft/lb dry air. Thus Supply volume ' nwei " (101.5) (13.29)' -- 1349 cfm) transport PROpemES of moist air For certain scientific and experimental work, particularly in the field of heat transfer, a number of other properties of moist air are important. These are generally classified as Transport Properties and include: Diffusion Coefficient, Viscosity, Thermal Conductivity and Thermal Diffusion Factor. A recent paper" derives these properties by calcula tion. Table 7 and Figs. 12 and 13 summarize the author's results on the first three properties listed above. It will be noted from the indicated boundaries of Charts 1, 2 and 3 that the viscosity varies little from that of dry air at normal atmospheric pressure, and the thermal conductivity is essen tially identical. "" . Conversion between mol fraction of water and humidity ratio may be accomplished by means of Equation 33. W - .822 (^--) (33) LETTER SYMBOLS USED IN CHAPTER 3 p - degree of saturation WfWn 4 * relative humidity, dimensionless. A Coefficient in Equation 3, given by Table 5, eu ft per pound dry air. B Coefficient in Equation 5, given by Table 5, Btu per pound dry air. C Coefficient in Equation 7, given by Table 5, Btu per (pound dry air) (Fahrenheit degree absolute). - Denthalpy deviation, Btu per pound dry air. . h -- enthalpy of moist air, Btu per pound dry air. i enthalpy correction term given by Equation 5 and to be added to Equation 4 for temperatures above 150 F, Btu per pound dry air. K w specific enthalpy of dry air, Btu per pound. h-- A, -- K, Btu per pound dry air. A/ specific enthalpy of saturated liquid water, Btu per pound. A/ * A, -- hf, Btu per pound. A, * specific enthalpy of saturated water vapor, Btu per pound. A, -- enthalpy of moist air at saturation, Btu per pound dry air. A,* -- enthalpy of moist air at saturation at thermodynamic wet-bulb temperature, Btu per pound dry air. 47 A, -- -specific enthalpy,of water vapor, Btu per pound: A* - specific enthalpy of condensed water (liquid or solid) at a pressure of 29-921 in. Hg., Btu per pound. A " specific enthalpy of water (any phase) added to or re moved from moist air in a process, Btu per pound. .: m -- mass flow of dry air, pounds per unit timie.' m " mass flow of water (any phsse), pounds per unit timA. < n. -- mob of dry air. n* * molfl of water vapor. - p -- total pressure of moist air, inches Hg or pounds per , ..square inch. - - '= : Pm -- partial pressure of dry air, inches Hg or pounds per square inch. p. -- reference pressure of 29.921 inches Hg in definition of U. 8. Standard Atmosphere. p, -- vapor pressure of water in moist air at saturation, inches Hg or pounds per square inch. Differs from the'satura- -,v. .. tion pressure of pure water, because of presence of the - air. - . . p.~ partial preasure'of water vapor in moist air, inches Hg or pounds per square inch. p-- ~ pressure of saturated pure water, inches Hg or pounds per square inch. q -- rate of heat addition (or withdrawal), Btu per unit time. q, m rate of addition (or withdrawal) of sensible heat, Btu per unit time. R - universal gas constant, 1544 foot-pounds per (Fahren heit degree absolute) (mol). R. a gas constant for dry air, 53.35 foot-pounds per (Fahren heit degree absolute) (pound). > entropy of moist air, Btu per (pound dry air) (Fahren heit degree absolute). } entropy correction term given by Equation 7 and to be added to Equation 6, Btu per (pound dry air) (Fahrenheit degree absolute). I " entropy correction term given by Equation 8 and to be added to Equation 6, Btu per (pound dry air) (Fahrenheit degree absolute). -- specific entropy ol dry air, Btu per (pound) (Fahrenheit degree absolute). Btu per (pound dry air) (Fahrenheit degree absolute). Sf -- specific entropy of saturated liquid water, Btu per (pound) (Fahrenheit degree absolute). /, = t, -- /, Btu per (pound) (Fahrenheit degree absolute), t, -- specific entropy of saturated water vapor, Btu per (pound) (Fahrenheit degree absolute). = specific entropy of condensed water (liquid or solid) at a pressure of 29.921 inches Hg, Btu per (pound) (Fahren heit degree absolute). t a dry-bulb temperature of moist air, Fahrenheit degrees. td " dew-point temperature of moist air, Fahrenheit degrees, t* * thermodynamic wet-bulb temperature of moist air,^- Fahrenheit degrees. T absolute temperature, Fahrenheit degrees. T, " reference temperature of 518.67 Fahrenheit degrees absolute in definition of U. S. Standard Atmosphere. e volume of moist air, cubic feet per pound dry air. 9 a volume correction term given by Equation 3 and to be added to Equation 2 for temperatures above 150 F, cubic feet per pound dry air. Os a specific*volume of dry air, cubic feet per pound, o- a v, -- cubic feet per pound dry air. */ a specific volume of saturated liquid water, cubic feet per pound. Of, a ct -- 0/, cubic feet per pound.