Document 7MD3gx34RDkmG0kae09Y8m91g

128 CHAPTER 10 1959 Guide the greatly reduced relative humidities experienced in houses in extreme cold weather, when cold outdoor air enters the house and is heated. WATER IN BUILDING MATERIALS The surfaces of most common materials have an affinity, for water molecules. Molecular forces of attraction will hold, water molecules to the surface, but decrease very rapidly with increase in distance of molecular proportions. The film thickness and therefore the amount of water held in equilib rium with the surrounding atmosphere is roughly proportional to relative humidity. Surface films of water molecules, at low humidities, may be only one molecule thick; at moderate humidities poly-molecular films may be established, while at humidities very close to 100 percent, the films become so thick, relatively, that small pores may become filled and larger capillaries may be partially filled. At saturation condi tions all voids in the material may be completely filled. Some materials such as silica gel, alumina and most natural fibrous materials present very large effective surfaces to the water molecules, so that the amount of water held on the effective surface in these materials may be relatively large, even at moderate humidities. These are said to be hygroscopic. Other materials, such as most metals, not penetrated by the water molecules, present relatively small surfaces and so may take only minute quantities of water, except when wetted directly by liquid. Substances having a great affinity for water, and their use as dehumidifying agents, are described in Chapter 42. Data on tire moisture contents of various common materials in equilibrium with the atmosphere at various relative humidities are given in Table 2 of Chapter 50, and equilibrium moisture content is further discussed in Chapter 53 oh Industrial Drying Systems. Significant dimensional changes take place in many ma terials used in buildings, with change in moisture' content. The best known are those'which take place in wood, of the order of 0.1, 2, and 4 percent in the longitudinal, radial and tangential directions, respectively, on. a change from air dry at 12 to 15 percent moisture content to oven dry conditions. Most wood-fiber products, including papers, will exhibit mois ture expansion consistent with the basic wood properties to a degree dependent on the fiber orientation and arrangement. Data on wood are available in publications on wood tech nology. Almost all plant and animal fibers experience ap preciable moisture changes with changing relative humidity and undergo substantial dimensional changes of the same order as those in wood. Less generally recognised are the di mensional changes that ran occur in masonry materials as a result of changes in moisture content. Water is either an essential or a contributory factor in al most all cases of breakdown of building materials resulting from chemical changes such as the rusting of steel, physical changes such as the spalling of masonry by frost action, or biological processes such as the rotting of wood. The control of water in building constructions may be necessary to ensure adequate service from the materials involved. Condensation of water vapor, although not the only means by which wetting may be brought about, is nevertheless a roost insidious one, particularly in respect to freeze-thaw breakdown, since from its nature it is most likely to occur at points of low temperature at which there may later be risk of freezing while the material remains in a saturated condition. Moisture in building materials may have a marked effect upon the transmission of heat through them. It has been com monly assumed that moisture when present in a material will remain more or less stationary and will increase the conduc tivity largely by adding to the path available for heat flow. On this basis, the effect of moisture on heat flow can be ac counted for quite simply by the use of suitable coefficients of conductivity in the usual heat-flow equations. The data presented in Chapter 9 on moist soils are of tins type. ' Evidence to date indicates, however, that in porous ma terials partially saturated with water there is likely to be a migration of moisture to the cold side under the influence of the temperature gradient. This can occur by a process of evaporation, vapor flow, and condensation within the ma terial, a substantial amount of heat being transferred as latent heat of the vapor, particularly in the case of open fibrous materials. The transmission of heat through moist materials becomes complex whenever conditions are such as to produce any appreciable migration of the moisture, and, consequently, calculations by the usual heat-flow theory alone, are an approximation. The usual approach to the calculation of moisture migra tion has been to consider the flow as hydraulic, under the influence of hydrostatic forces when the materials are satu rated, and as a vapor flow produced by vapor pressure dif ferences in unsaturated materials. These simple concepts might be adequate were it not for the fact that there are inter actions between water molecules and the material through which they are passing, as already mentioned. Further com plications may be introduced by the presence of salts and electrical potentials. It is now recognized that the migration of moisture under conditions of partial saturation in a material having an affin ity for water actually occurs as a kind of series-parallel flow of vapor and liquid, with the liquid phase having more and more influence as the moisture content, or the degree of satura tion, increases. The two kinds of flow cannot be separated since they are closely coupled everywhere along the flow path by evaporation and condensation. Enough is already known to indicate that the isothermal or constant temperature case of yapor flow under a vapor-pressure gradient is much more manageable than the cases in which there are both tempera ture and vapor-pressure gradients. Cases of combined heat and moisture flow are now known to be extremely complicated and it is quite clear that when both are occurring, neither one ran be adequately dealt with independently of the other. . No adequate way of handling the general case theoretically has yet been found, despite efforts being made in many laboratories. The bibliography at the end of this chapter includes some of the more important papers on this subject. A relatively ample equation for the calculation of watervapor flow based upon the concept of vapor pressure alone as tiie driving force, has been in use for a number of years. It can be applied without great difficulty to cases where uni form temperatures or only small temperature gradients exist, and to cases of low or moderate relative humidity. It has also been shown to be useful in other cases, provided that the proper values representative of the conditions to which it is being applied can be found for the flow coefficient to be used in the calculations. The complications inherent in the com' bined mechanisms of heat and moisture flow are not ade quately covered by the variables used in the equation, but appear in the determination of suitable values of the flow coefficient, which, however, may vary greatly for any one material, depending on the conditions of flow. VAPOR TRANSMISSION THROUGH MATERIALS The equation presently used in calculating water-vapor transmission through materials is based on a form' of Fick's Moisture in Building Construction Law, and is as follows: dp dx (1) where w = weight of vapor transmitted through a unit area in unit time. p = vapor pressure. x " distance along the flow path, and hence: d--p " vapor pressure gradien.t. dx 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, p, is not a ample one but is actually a function of relative humidity and temperature, and may vary along the flow path through the material in question.* Integrating Equation 1 from x = 0 to x = l and from pi to pi, and rearranging, the following is obtained: 129 in a unit of grains-inches per (square foot) (hour) (inch of mercury vapor pressure difference). stated or implied thickness other than the unit thickness to which p or p refer, use may be made of the permeance co efficient M, where M = p/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 = hlAQAp (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. The over-all permeance of the assembly may be found from the permeances of the individual components4, * in a mannpr paralleling that used in calculating the over-all co efficient of thermal conductivity from the individual con ductances: 1 where l -- length of flow path (or thickness of material). If Equation 1 had been integrated, assuming the coefficient p to be independent of vapor pressure (and temperature) along the flow path, Equation 4 would have been obtained, but withji-replaced by p. The coefficients is therefore an average permeability coefficient applicable to the varying conditions along the flow path of length l, while the coefficient p is tiie spot or differential permeability. Equation 4 may be rewritten and units assigned: W-tA,* (5) This simple theory for vapor flow, as in the case of the cor responding simple heat-flow theory, assumes 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, *nH in conjunction with thermal calculations, relative hu midities ran be determined, and the imminence of condensa tion predicted. (See Example 1, and Fig. 2. See also Chapter 13, Cooling Load, for use of vapor-flow calculations.) Example t: A wood frame wall is exposed to indoor conditions 70 F ana 50 percent relative humidity (0.37 in. Hg vapor pres sure) and outdoor conditions 0 F and 80 percent relative PLASTER MINERAL WOOL SKEATHOM ON LATH BETWEEN STUDS PAPER A StOOM X where, W = total weight of vapor transmitted, grains. A -- area of cross-section of the flow path, square feet. $. -- time dyring 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 basic units given are those how favored by the build ing industry. The permeability p or p is therefore expressed Hg. 2 .... Temperatures and Vapor Pressures under' Vapor Row Conditions in the Insulated Frame Wall of Example 1.