Projected area

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

The choice of parameter used in the determination of size distribution should include consideration of the information needed in the interpretation of the data. For example, in the case of a manufacturer of paint pigment, the size parameter that best describes the hiding power (performance of the pigment) is the projected area of particles. A powdered catalyst manufacturer is primarily concerned with surface-area equivalence. 

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed dkection (29) Feret diameter, the projected length with respect to a reference dkection (30) and the diameter of equivalent surface area, the diameter of a ckcle the area of which is equivalent to the projected area of the particle in question (3). 

This unit, most recentiy defined by the 16th CGPM in 1979, replaced the candle and, later, the new candle and a definition of the candela based on the luminous intensity of a specified projected area of a blackbody emitter at the temperature of freezing platinum. 

Hardness is determined by measuring the penetration (depth or area) when a harder material, such as diamond, is pushed into the surface of the material of interest under a specified load. Tme hardness is defined as the force divided by the projected area. Vickers hardness tests, which employ a pyramid-shaped indentor, are frequently used to characterize ceramics however, Vickers hardness calculations normally employ total surface area rather than projected area (43). Measurements are made on the diamond impression shown in Figure 6. Vickers hardness is calculated using... 

Pxampk 2. A smooth spherical body of projected area Al moves through a fluid of density p and viscosity p with speed O. The total drag 8 encountered by the sphere is to be determined. Clearly, the total drag 8 is a function of O, Al, p, and p. As before, mass length /, and time t are chosen as the reference dimensions. From Table 1 the dimensional matrix is (eq. 23) ... 

A = projected area perpendicular to the flow p = fluid density V = free-stream fluid velocity... 

For a cylinder, = 1.7. For a vibrating cylinder, the effective projected area exceeds, but is always less than twice, the actual cylinder projected area (Rouse, Engineering Hydraulics, Wiley, New York, 1950). 

A Projected area m q Average volumetric flow rate mVs... 

AP is the pressure drop, cm of water Pg is the gas density, g/cm Ap is the total projected area of an entire row of baffles in the direction of inlet gas flow, cm" and At is the duct cross-sectional area, cm". The value jd is a drag coefficient for gas flow past inclined flat plates taken from Fig. 14-113, while L/ is the actual gas velocity, cm/s, which is related to the superficial gas velocity by U = L/g/cos 0. It must be noted that the angle of incidence 0 for the second and successive rows of baffles is twice the angle of incidence for the first row. Most of Calverts work was with 30° baffles, but the method correlates well with other data on 45° bafiles. 

The area that is theoretically available for separation is equal to the sum of the projected areas or all channels on the horizontal plane. Figure 18-88 shows the horizontally projected area A, of a single channel in a clarifier of unit width. If X is the uniform distance between plates (measured perpendicularly to the plate surface), the clarifier will contain sin Ci/X channels per unit length and an effective collection area per unit clarifier length of A, sin O/X, where Ot is the angle of inclination of the plates to the horizontal. It follows that the total horizontally projected plate area per unit volume of sludge in the clarifier Aj is... 

Microscope Methods In microscope methods of size analysis, direct measurements are made on enlarged images of the particles. In the simplest technique, linear measurements of particles are made by using a cahbrated scale on top of the particle image. Alternatively, the projected areas of the particles can be compared to areas of circles. 

FIG. 20-5 Statistical (Martin s and Feret s) and projected area diameters for an irregular particle. 

A Projected area of fragment, breach area, or fragment cross-sectional... 

Nx = / nowhere Ix is the radiation flux, n is the number of gas molecules in the path of the beam per cm of projected area, and a is the cross-section of absorption. Alternatively, the absorption coefficient, is defined drrough the Beer-Lambert equation... 

This consists of loading a pointed diamond or a hardened steel ball and pressing it into the surface of the material to be examined. The further into the material the indenter (as it is called) sinks, the softer is the material and the lower its yield strength. The true hardness is defined as the load (F) divided by the projected area of the indent, A. (The Vickers hardness, H , unfortunately was, and still is, defined as F divided by the total surface area of the indent. Tables are available to relate H to Ff .)... 

The bearing health can be best described by plotting a ZNjP versus coefficient of friction curve. Figure 13-10 shows such a curve where Z is the lubricant viscosity in centipoise, N the rpm of the journal, and P is the projected area unit loading. 

Indentation has been used for over 100 years to determine hardness of materials [8J. For a given indenter geometry (e.g. spherical or pyramidal), hardness is determined by the ratio of the applied load to the projected area of contact, which was determined optically after indentation. For low loads and contacts with small dimensionality (e.g. when indenting thin films or composites), a new way to determine the contact size was needed. Depth-sensing nanoindentation [2] was developed to eliminate the need to visualize the indents, and resulted in the added capability of measuring properties like elastic modulus and creep. 

The result is a modified Euler number. You can prove to yourself that the pressure drop over the particle can be obtained by accounting for the projected area of the particle through particle size, S, in the denominator. Thus, by application of dimensional analysis to the force balance expression, a relationship between the dimensionless complexes of the Euler and Reynolds numbers, we obtain ... 

This is a simple convenient expression for estimating the clamping force required for the disc. The same expression may also be used for more complex shapes where the projected area may be approximated as a circle. It will also give sufficiently accurate estimates for a square plate when the radius, R, in Fig. 4.41(a) is taken as half of the diagonal. 

An alternative way of looking at this equation is that the clamping pressure, based on the projected area of the moulding, is given by... 

In practice the clamping pressure will also depend on the geometry of the cavity. In particular the flow ratio (flow length/channel lateral dimension) is important. Fig. 4.42 illustrates typical variations in the Mean Effective Pressure in the cavity for different thicknesses and flow ratios. The data used here is typical for easy flow materials such as polyethylene, polypropylene and polystyrene. To calculate the clamp force, simply multiply the appropriate Mean Effective Pressure by the projected area of the moulding. In practice it is... 

In this case the runner system will be almost totally in the shadow of the projected area of the cavities and so they can be ignored. 

Since the reactants have a low viscosity, the injection pressures are relatively low in the RIM process. Thus, comparing a conventional injection moulding machine with a RIM machine having the same clamp force, the RIM machine could produce a moulding with a much greater projected area (typically about 10 times greater). Therefore the RIM process is particularly suitable for large... 

Exclnsion/contamination zone Project area where contamination of any kind is believed to exist or does exist. Sometimes referred to as a hot area. ... 

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