Area, derived units expression

Derive an expression for the radiant heat transfer rate per unit area between two large parallel planes of emissivities e and en and at absolute temperatures T and 73 respectively. 

A soluble gas is absorbed into a liquid with which it undergoes a second-order irreversible reaction. The process reaches a steady-state with the surface concentration of reacting material remaining constant at (.2ij and the depth of penetration of the reactant being small compared with the depth of liquid which can be regarded as infinite in extent. Derive the basic differential equation for the process and from this derive an expression for the concentration and mass transfer rate (moles per unit area and unit time) as a function of depth below the surface. Assume that mass transfer is by molecular diffusion. 

MackorJ used the model outlined in Example 13.6 to derive the expression AGR = NkBT( — d/L) for the repulsion per unit area of particles carrying N rods of length L when the surfaces are separated by a distance d. Assuming this repulsion equals the van der Waals attraction when the particle separation is 1.5 nm, calculate the effective Hamaker constant in this system if L = 2.5 nm. Select a reasonable value for Win this calculation and justify your choice. 

Consider laminar forced convective flow over a flat plate at whose surface the heat transfer rate per unit area, qw is constant. Assuming a Prandtl number of 1, use the integral equation method to derive an expression for the variation of surface temperature. Assume two-dimensional flow. 

A plane wall of thickness 2L has an internal heat generation which varies according to q = q0 cos ax, where q0 is the heat generated per unit volume at the center of the wall (x = 0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area. 

The International System (SI) of the Units rests upon seven base units and two supplementary units as shown in Table A-l. From the base units, derived units can be obtained to express various quantities such as area, power, force, etc. Some of these have special names as listed in Table A-2. Multiples and submultiples are obtained by using prefixes as shown in Table A-3. 

To derive equations for mass transport we introduce the quantity f, which we define as the mass flux density of species i, expressed in units of mass per unit area per unit time. Given fj, we express the rate of change of total mass inside volume V as equal to the rate of mass flux into the volume ... 

Darcy s law has been used to derive an expression which reflects not only the effect of a change in elevation, but also provides a means for estimating changes in air rate resulting from changes in vacuum level and cake thickness (or cake weight per unit area). In order for this relationship to hold for changes in vacuum and cake thickness, it must be assumed that both cakes nave the same specific resistance. 

All other formulae can be derived based upon the above definition. For example. A, which is the surface area per unit mass of crystal, can be expressed as... 

Derive an expression for the rate at which the particles of a polydisperse aerosol settle on a horizontal plate from a stagnant gas. Dimensions arc number per unit time per unit area. Assume that Stokes law holds for the terminal settling velocity, and express your answer in terms of the appropriate moments. 

A certain chemical species is adsorbed by the particles of an aerosol. The mass adsorbed is proportional to the surface area of the particle. Derive an expression for the distribution of the species with respect to particle size expre.ssed as mass of the species per unit volume of gas in the size range u to u + ttv. Express your answer in terms of it and n(tt). Define any constants you introduce. 

The ceU density (N) is defined as the number of cells or channels per unit of cross-sectional area perpendicular to the axis of the channel. This is usually expressed in units of cells per square inch, and abbreviated cpsi. The open frontal area (OFA) is equal to the open area of an individual channel multiphed by the cell density and is usually expressed as a percent. The geometric surface area (GSA) of a cellular structure is derived by establishing the surface area per unit length of an individual channel that is then multiphed by the cell density. This represents a surface area per unit volume and is expressed as cm /cm, m /hter, or some other appropriate set of units. The total surface area (TSA) of a structure is then the geometric surface area multiphed by the volume (V) of the structure under consideration. 

The rate expressions of Section 14.2.1 are for the most part not particularly well suited for direct application to phenomenological wear and require further treatment to adapt them to specific experimental procedures for measuring wear. In the case of Eqn 14-22a, which was originally derived on the basis of unit apparent conjunction area [9], q is the volume of material removed per unit apparent area in unit time and the expression has the dimension 1/i. therefore is... 

Employing nucleation theory it is possible to derive an expression for the rate of formation of critical size nuclei per unit surface area per unit time. A complete derivation can be found in Ohara and Reid (1973). A simplified version of the rate expression follows. 

To derive an expression for nucleation rate per particle we use a procedure analogous to that for homogeneous nucleation discussed in the previous section. The main difference is that, instead of calculating a nucleation rate per unit volume, we calculate a rate per unit area of foreign substrate and then introduce the surface area of the particle, assumed to have homogeneous properties, to calculate the nucleation rate per particle. For a spherical particle of radius R cm the result is... 

The name pascal, Pa, is given to this combination. You will learn more about pressure in the chapter "Gases. Prefixes can also be added to express derived units. For example, area can be expressed in cm, square centimeters, or mm, square millimeters. 

A pressure of 1 mm Hg is also called 1 torr to honor Torricelli for his invention of the barometer. The average atmospheric pressure at sea level at 0°C is 760 mm Hg. Pressures are often measured in units of atmospheres. One atmosphere of pressure (atm) is defined as being exactly equivaient to 760 mm Hg. In SI, pressure is expressed in derived units called pascals. The unit is named for Blaise Pascal, a French mathematician and philosopher who studied pressure during the seventeenth century. One pascai (Pa) is defined as the pressure exerted by a force of one newton (1 N) acting on an area of one square meter. In many cases, it is more convenient to express pressure in kilopascals (kPa). The standard atmosphere (1 atm) is equal to 1.013 25 x 10 Pa, or 101.325 kPa. Several pressure units and common uses for them are summarized in Figure 1.5. 

The determination of the interface surface area S, using equation (8-11), requires the measurement of the scattering intensity in absolute units. However, applying equations (8-11) and (8-12), another expression for the surface area per unit volume can be derived ... 

The adsorption capacity of a surface with respect to molecules of a given species is characterized by the total number N of molecules of the particular species retained by unit surface area under the conditions of equilibrium with the gas phase under the given external conditions (i.e., at a given pressure P and temperature T). An expression for N as a function of rf, rr, and 7j+ will be derived in Section II. 

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