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130 CHAPTER 10 1959 Guide humidity (0.03 id. Hg vapor pressure). The wall consists of painted plaster on gypsum lath on the inside over 2 X 4 instuds, mineral wool fill between studs, 1 in. wood exterior sheathing, paper, and pine lap siding. Check for possible condensation. To simplify the example, consider the paint, piaster, and lath as a single element having a permeance it = 1.0 perms and a thermal conductance C = 2.4, and the exterior sheathing, paper, siding, and paint as another single element for which if a 2.0 perms ana C " 0.50. From Table 1 the value for the permeability of mineral wool fill may be found as = 116 nn-inches. The thermal conductivity for mineral wool, = 0.27. Solution: In this particular wall, insulated, and with moder ate warm-side relative humidities, condensation is unlikely to occur until the sheathing is reached. To check directly for condensation on the warm side of the exterior sheathing (des ignated as plane X -- X in Fig. 2 for convenient reference) proceed as follows: Calculate according to the method of Chapter 9 the tempera ture at plane X -- XT This is found to be 9 F. The saturation vapor pressure at this temperature is 0.06 in Hg. If condensa tion is imminent or occurring at X -- X, the vapor pressure there will be 0.06 in. Hg. Calculate the permeance for the portion of the wall from the warm side to X -- X, and the vapor flow rate to X -- X as follows: Permeance of wall to X -- X -- ------- ^ *= 0.97 perms. L0 + 116 Vapor pressure drop to X -- X -- 0.37 -- 0.06 * 0.31 in. Hg. Vapor flow to X -- X => 0.97 X 0.31 = 0.30 grains per (sq ft) (hr). Calculate the vapor flow rate from X -- X to outdoors as follows: Permeance of wall from X -- X to outdoors -- 2.0 perms. Vapor pressure drop from X -- X to outdoors = 0.06 - 0.03 = 0.03 in. Hg. Vapor flow rate to outdoors = 2.0 X 0.03 -- 0.06 grains per (sqft)(hr). It is apparent that continuity of vapor flow is not possible, since at toe highest vapor pressure at X -- X permitted by the temperature, there is indicated a greater flow to plane X -- X than from it to outdoors. Condensation is indicated at a rate of 0.30 -- 0.06 = 0.24-grains per (sq ft) (hr). Whether this condensation rate will be serious must still be decided, since it might readily be absorbed by the sheathing during the condensation period without excessive wetting. When the temperature at X -- X is below freezing, as in this case, the condensation will be in the form of frost which may. accumulate until released over a short period upon a rise in outdoor temperature. Condensation will be reduced or avoided if the permeance of the warm side of the wall can be reduced so that the flow to X -- X is limited to 0.06 groins per (sq ft) (hr). Permeance required for this is " 0.19 perms or less. A more resistant paint film on the plaster, reducing the paint-plasterlath permeance to 0.19 perms would accomplish this. When the critical plane for condensation is unknown, or for a more informative, graphical representation of the situation throughout the wall, temperatures and vapor pressures may be calculated and plotted as in Fig. 2. The vapor pressures throughout the wall, for continuity of flow, are calculated in a manner similar to the temperatures; the external vapor pressures are given, and the vapor pressure drops across each element are taken in proportion to resistance to vapor flow. The curve for saturation vapor pressures at the various temperatures throughout the wall is also shown in Fig. 2 and is seen to fall below the curve for vapor pressures with con tinuity of flow, toward the outer portions of the wall. This indicates that with the given temperatures and vapor pres sures, continuity of flow is not possible and that condensation will occur. Condensation on the sheathing is indicated as a definite possibility, and the new vapor-pressure curve Mn be constructed for this condition, as shown. This new curve does not rise above the saturatiOD-vapor-pressure curve, thereby confirming that the critical plane for condensation was cor rectly assumed. With the vapor pressures thus established, the relative humidities maybe found, by reference to the saturation vapor pressures. The permeances originally assigned to the various elements may then be re-examined iq the light of the service conditions of temperatures and relative humidities indicated, and the analysis repeated, if necessary, using more appropriate permeance values. In a more detailed analysis, individual values might be assigned to the elements forming the outer portion of the wall which is here dealt with as a composite, homogeneous element. The transmission of water vapor as outlined is based on the assumption of a diffusion process. The possibility of vapor being transferred as part of a moving air stream has thus far been ignored, except in Example 1 in which it is implied that the air circulation on either side of the wall will be sufficient to eliminate surface-film resistances to vapor flow. Differences in total pressure of the air may result in a transfer of vapor with air, augmenting and at times over-riding the effects of the flow produced by vapor-pressure gradients alone. This can be particularly important in the transfer of vapor through cracks and pinholes or through air-permeable building con structions. Similar effects can be obtained with air-permeable materials themselves.* This means of vapor transfer is similar to that of transfer of heat by air leakage in and through building constructions, and requires, for purposes of calculation, information on the nature and amount of the air leakage. It will seldom be im portant in constructions without air spaces and having parged or plastered surfaces. It may, however, be an important means of vapor transfer through constructions lacking in air tightness, and may contribute to condensation difficulties, since the mechanism of condensation is not dependent upon the way in which the vapor is transferred. PERMEANCE AND TESTING ^The simplest method of finding the permeance of a speci men is to seal it over the top of a cup containing desiccant or water, placing it in a controlled atmosphere, and weighing it periodically. The steady rate of weight gain or loss is nor mally the water vapor transfer. When the cup contains a desiccant the procedure is called the dry-cup method and when the cup contains water, the wet-cup method. Usually the sur rounding atmosphere is held at 50 percent relative humidity, thus providing, in either method, substantially the same dif ference of vapor pressure, but the results obtained by the two methods for the same specimens are likely to be much differ ent, the weVcup method producing the higheT values. The relationship between these values can best be understood by reference to Fig. 3, which shows a typical variation of spot permeability with relative humidity at one particular tem perature (isothermal conditions) for a material such as wood. The vapor permeability is shown to vary only moderately at low humidities, but to increase at an increasing rate as higher humidities are reached. The dry-cup test of this material carried out with 0 percent relative humidity one' side and 50 percent on the other, will experience throughout its thickness, because of the variation in relative humidity, a variation in spot permeability. The average permeability , is by definition (Equation 3), given by ^Pl , and since at a fixed tem pi - Pi perature there is a linear relationship between vapor pressure and relative humidity, this expression can be seen to cor respond to the mean height of the area under the spot per- Moisture in Building Construction 131 Table 1___Permeance and Permeability of Materials to Water Vapor famenca Farm % tHt-KH* Mafhodj tof.t Motend Purnm- ance farm % Mrthodf faf.t Aib (still) Insulation Cellular glass Corkboard Corkboard Structural Insulating Board (vegetable, uncoated) Mineral Wool (unprotected) 120* 0.0" 2.1-2.6* 9.6* 20-60* 116* 92-73 75-0 100-45 40-x 100-30 b d d w t w Interiob Finish Plaster on wood lath Plaster on metal lath--X in. Plaster on plain gypsum lath (with studs) Gypsum wall board--plain-- H *o. Insulating wail board (un- coated)--14 in. 11 100-30 20 40-85 50 50-20 50-90 40-x w t V t "Paint--2 coats Asphaltic paint on plywood Aluminum in varnish on wood Enamels, brushed on smooth plaster Primers or Seeders on insulat ing wall board Various Primer* + 1 coat flat paint on plaster Flat paint (alone) on insulat ing wall board Water Emulsion on insulating wall board 0.4 0.3-0.5 0.5-1.5 0.9-2.1 1.6-3. 30.-85. `Paint--Exterior, 3 coats White lead <fc oil prepared ( tO.3-1.0 on wood siding White lead-zinc oxide & lin 0.9 seed oil on wood 100-30 95-0 92-0 40-x 40-x 40-x 40-x -- 50-0 95-0 w d b d d 4 Wood Sugar Pine >.4-6.4* various Plywood (Exterior type 3 ply 0.72 50- 5 D.F.), k in. 11 Plywood (Interior type 3 ply 1.86 50- 9 D.F.), X in. 8 Masonbt Concrete (1:2:4 Mix) 3.2* Concrete (8 in. cored block 2.4 8 wall, limestone agrgt.) 9 Brick wall--with mortar--4 in. 0.8 4 Tile wall--with mortar--4 in. 0.12 100-45 79-68 50-x 50-x tv 4 w t t t 4 13 13 11 4 10 10 15 Lb per 9 SOO tq ft *T"p cup "Building Papers and 8 Felts 12 Duplex sheet, asphalt lami 43 4 nae, aluminumfoil one side Saturated and coated felt 326 9 heavy roll roofing Kraft and asphalt laminae, 34 9 Reinforced 30-120-30 Insulation back up, asphalt- 31 9 sat., one side glossy Asphalt-saturated and coated 43 9 sheathing paper Asphalt-saturated sheathing 22 15-pound asphalt felt 70 15 15-pound tar felt 70 Single sheet Kraft, double 16 12 infused 6.002 0.176 14 0.05 0.24 14 0.3 1.8 14 0.4 0.6-4.2 14 0.3 0.6 14 3.3 20.2 1.0 4.0 30.8 5.6 14 * These boldfsen value* an permeability Description is a t Methods: d--dry *ukfe only, and does cap; w--cup; t- e_k_____lperstures; b--special cell; > J Reference*. No. 9 also inrlnde* BulUtxi 23 and 25 of the Engineering "----- mia Stain College meability curve, between the appropriate relative humidity limits. The average permeability as found for the dry-cup conditions should therefore have the value i. Similarly for the wet-cup test between 50 percent and 100 percent rela tive humidity, the value should'bej. It is not uncommon for these values for wood and wood-fiber materials to be in the ratio of 1 to 3, or higher. (See Table 1.) The average permeability for any other relative humidities at a particular temperature is given by the mean height of the area under the curve of spot permeability for the material at that temperature, between the appropriate limits of rela tive humidity. Only average permeabilities (or permeances) are measurable directly in practical tests. However, if several average permeabilities at different relative humidities are known, and can be plotted as for the wet-cup and dry-cup tests shown in Fig. 3, it is possible to construct, by trial and error, a spot permeability curve which will satisfy the condi tion that the average height of the curve between the ap propriate limits for each test must equal the value found in each test. Separate curves are required for each temperature so that a large number of permeance cup tests would be re quired to cover a range of conditions of both temperature and humidity. Experience to date shows that the effect of temperature is quite moderate and, for some purposes, differences in tempera ture at which tests are run may be ignored. Corrections for temperature have been made with some success in the case of certain materials by the use of an equation based on activa tion energy7 which states: * - (s) where, in appropriate units, -- permeability at T * . ft -- gas constant. -- activation energy. e -- Naperian base of logarithms " 2.718. T = absolute temperature. Applications of this equation may be limited to materials such as resins, rubbers, and polymers in which the water molecules enter and move through the molecular structure by a process known as activated diffusion; It may serve also as a useful approximation in other cases. By use of Equation 8, spot permeability curves for a variety of temperatures can be constructed from a curve for one tem perature, provided only that two tests at different tempera tures can be run, from which E, the activation energy, can be evaluated. In this way it becomes possible to describe the permeability of a material with reasonable completeness from