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138 CHAPTER 10 1960 Guide the greatly reduced relative humidities experienced in hrmsea in extreme cold weather, when cold outdoor air enters the house and is heated. remain more or less stationary and will increase the conduc tivity largely by sdding to the path available for heat flow. On this basis, the effect of moisture on heat flow can be ac WATER (N BUILDING MATERIALS counted for quite simply by the use of suitable coefficients of conductivity in the usual beat-flow equations. The data The surfaces of most common materials have an affinity presented in Chapter 9 on moist soils are of this type. for water molecules. Molecular forces of attraction will hold Evidence to date indicates, however, that in porous ma water molecules to the surface, but decrease very rapidly terials partially saturated with water there is likely to be a with increase in distance of molecular proportions. The film migration of moisture to the cold side under the influence of thickness and therefore the amount of water held in equilib tire temperature gradient. This can occur by a process of rium with the surrounding atmosphere is roughly proportional evaporation, vapor flow, and condensation within the ma to relative humidity. Surface films of water molecules, at low terial, a substantial amount of heat being transferred as humidities, may be only one molecule thick; at moderate latent heat of the vapor, particularly in the case of open humidities poly-molecular films may be established, while fibrous materials. The transmission of heat through moist at humidities very close to 100 percent, the film* become so materials becomes complex whenever conditions are such as thick, relatively, that small pores may become filled and to produce any appreciable migration of the moisture, and, larger capillaries may be partially filled At saturation condi consequently, calculations by the usual heat-flow theory alone, tions all voids in the material may be completely fiiwi are an approximation. Some materials such as silica gel, alumina and most natural it The usual approach to the calculation of moisture migra fibrous materials present very large effective surfaces to the tion has been to consider the flow as hydraulic, under the water molecules, so that the amount of water on the influence of hydrostatic forces when the materials are satu effective surface in these materials may be relatively large, rated, and as a vapor flow produced by vapor pressure dif even at moderate humidities. These are said to be hygroscopic. ferences in unsaturated materials. These simple concepts Other materials, such as most metals, not penetrated by the might be adequate were it not for the fact that there are inter water molecules, present relatively small surfaces and so may actions between water molecules and the material through take only minute quantities of water, except when wetted which they are passing, as already mentioned. Further com directly by liquid. plications may be introduced by the presence of salts and Substances having a great affinity for water, and their use electrical potentials. as debumidifying agents, are described in Chapter 42. Data It is now recognised that the migration of moisture under on the moisture contents of various common materials in conditions of partial saturation in a material having an affin equilibrium with the atmosphere at various relative humidities ity for water actually occurs as a kind of series-parallel flow are given in Table 2 of Chapter 50, and equilibrium moisture of vapor and liquid, with the liquid phase having more nd content is further discussed in Chapter 53 on Industrial more influence as tire moisture content, or the degree of satura Drying Systems. tion, increases. Hie two kinds of flow cannot be separated Significant dimensional changes take place in many ma once they are closely coupled everywhere along the flow path terials used in buildings, with change in moisture content. by evaporation and condensation. Enough is already known The best known are those which take place in wood, of the to indicate that the isothermal or constant temperature case order of 0.1, 2, and 4 percent in the longitudinal, radial and of vapor flow under a vapor-pressure gradient is much more tangential directions, respectively, oa a change from air dry manageable than the cases in which there are both tempera at 12 to 15 percent moisture content to oven dry conditions. ture and vapor-pressure gradients. Cases of combined heat Most wood-fiber products, including papers, will exhibit mois and moisture flow are now known to be extremely complicated ture expansion consistent with the basic wood properties to a and it is quite clear that when both are occurring, neither degree dependent on the fiber orientation and arrangement. one can be adequately dealt with independently of the other. Data on wood are available in publications on wood tech No adequate way of handling the general case theoretically nology. Almost all plant and animal fibers experience ap has yet been found, despite efforts being in many preciable moisture changes with changing relative humidity laboratories. The bibliography at the end of this chapter and undergo substantial dimensional changes of the oam* includes some of the more important papers cm thi? subject. order as thoee in wood. Less generally recognised are the di A relatively simple equation for the calculation of water- mensional changes that can occur in masonry materfrla as a vapor flow based upon the concept of vapor pressure ahm* result of changes in moisture content. as the driving force, has been in use for a number of years. Water is either an essential or a contributory factor in al It can be applied without great difficulty to cases where uni most all cases of breakdown of building resulting form temperatures or only small temperature gradients exist, from chemical changes such as the rusting of steel, physical and to cases of low or moderate relative humidity. It changes such as the spalling of masoniy by frost action, or been shown to be useful in other cases, provided that the biological processes such as the rotting of wood. The control proper values representative of the conditions to which it is of water in building constructions may be necessary to ensure being applied can be found for the flow coefficient to be used adequate service from the materials involved. in the calculations. The complications inherent in the 'com Condensation of water vapor, although not the only inwms bined mechanisms of heat and moisture flow are not ade by which wetting may be brought about, is nevertheless a quately covered by the variables used in the equation, but most insidious one, particularly in respect to freere-thaw appear in the determination of suitable values of the flow breakdown, since from its nature it is most likely to occur at coefficient, which, however, may vary greatly for any one points of low temperature at which there may later be risk of material, depending on the conditions of flow. freesing while the material remains in a saturated condition. Moisture in building materials may have a marked effect VAPOR TRANSMISSION THROUGH MATERIALS upon the transmission of beat through them. It has been com monly assumed that moisture when present in a material will The equation presently used in calculating water-vapor transmission through materials is based on a form of Fick's Moisture in Building Construction 139 L&w, and is as follows*. dp w dx (1) where u> *= weight of vapor transmitted through a unit area in unit time. p -- vapor pressure, x -= distance along the Sow path, and hence: d--p =* vapor pressure grad..ien.t. dz p -- permeability. The close parallel with Fourier's equation for heat flow will be noted. The actual transmission of vapor through a ma terial is extremely complex, so that the coefficient, 4, is not a simple one but is actually a function of relative humidity and temperature, and may vary along the flow path through tile material in question.' Integrating Equation 1 from' x 0 to z = l and from pi to p, and rearranging, the following is obtained: in a unit of grains-inches per (square foot) (hour) (inch of mercury vapor pressure difference). Whenever it is convenient to deal with a material of a stated or implied thickness other than the unit thickness to which 4 or 4 refer, use may be made of the permeance co efficient Af, where M = fi/l. The designation perm for the unit of permeance is now widely used, and is a convenient substitute for the unit, 1 grain per (square foot) (hour) (inch of mercury vapor pressure difference).* The corresponding unit of permeability is perm-inch, since it is the permeance of unit thickness. The corresponding flow equation is: W -= MAOAp (6) Resistance to vapor flow provided by a sheet, or board is the reciprocal of the permeance, and correspondingly, the over-all vapor resistance of an assembly (like a wall) of ma terials in series is the sum of the resistances of its component parts. Hie over-all permeance of the assembly may be found from the permeances of the individual components4* * in a manner paralleling that used in calculating the over-all co efficient of thermal conductivity from the individual con ductances: where l length of flow path (or thickness of material). If Equation 1 had been integrated, assuming the coefficient 4 to be independent of vapor pressure (and temperature) along the flow path, Equation 4 would have been obtained, but with 4 replaced by 4. The coefficient is therefore an average permeability coefficient applicable to the varying conditions along the flow path of length l, while the coefficient 4 is the spot or differential permeability. Equation 4 may be rewritten and units assigned: This simple theory for vapor flow, as in the case of the cor responding simple beat-flow theory, awnim**! conditions of unidirectional, steady-state flow. Useful calculations can be made for an assembly or sub-assembly for which the inflow and outflow of vapor are equal (a condition at which no con densation occurs) if a permeance applicable to actual condi tions can be assigned to each component part. Over-all per meances, vapor pressures and vapor flow can be calculated, and in conjunction with thermal calculations, relative hu midities can be determined, and the imminence of condensa tion predicted. (See Example I, and fig. 2. See also Chapter 13, Cooling Load, for use of vapor-flow calculations.) Exam-ole t: A wood frame wall is exposed to indoor conditions 70 F and 50 percent relative humidity (0-37 in. Hg vapor pres sure) and outdoor conditions 0 F and 80 percent relative PCASTER MINERAL WOOL SMCATKMQ ON LATH BETWEEN STUOS PAPER a SJOUM * VT -- fkAa ~ (5) where, W = total weight of vapor transmitted, grains. A -- area of cross-section of the flow path, square feet. 9 " time during which the transmission occurred, hours. Ap -- difference of vapor pressure between ends of the flow path,'inches of mercury. i =* length of flow path, (or thickness of specimen), inches. The baric units given are those now favored by the build ing industry. The permeability 4 or 4 is therefore expressed Fig. 2 .... Temperatures and Vapor Pressures under Vapor Flow Conditions in the Insulated Frame Wall of Example 1.