Horizontal Project

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... 

Buoyancy forces influence the trajectory of horizontally projected air jets or air jets supplied at some angle to the horizontal plane (Fig. 7.24). Most nonisothermal air jet studies were devoted to horizontally projected compact air jets. Based on the analytical studies, 42,77-80 trajectory axis of inclined jets can be described by a polynomial function... 

Koestel, A. 1955. Paths of horizontally projected heated and chilled air jets. Heating. Piping and Air Conditioning, July, pp. 221-226. 

The most sophisticated PERT diagrams are drawn on a time scale, with the horizontal projection of connecting arrows drawn to represent the amount of time required for their activity. In the process of diagramming to scale. 

It is clear that the above mode of computation suffers from the defect pointed out at the start of this section, in the discussion of the force proof of the Young equation (1). If the forces are supposed to cancel each other along a vertical, rather than a horizontal, projection, then the relation obtained... 

The Alpine pin disc mill shown in Figure 2.11 is a form of pin mill and consists of two vertical steel plates with horizontal projections on their near faces. One disc may be stationary whilst the other disc is rotated at high speed sometimes, the two discs may be rotated in opposite directions. The material is gravity fed in through a hopper or air conveyed to the centre of the discs, and is thrown outwards by centrifugal action and broken against of the projections before it is discharged to the outer body of the mill and... 

Fig. 2. The horizontal projection of three trajectories of the spherical pendulum with different initial horizontal velocities, increasing from left to right.

Fig. 7. The horizontal projection of the trajectories for the exact solution (the left curve) and the solution of the approximate equation of motion in terms of Mathieu functions (the right curve) iox n = I, k = 2.

The horizontal projection of the approximate motion for 1, A =2 is shown in Fig. 7 (the right curve), compared with the same curve from Fig. 2 for the exact motion (the left figure). 

Lamella settlers are gravity settlers that use a large number of inclined flat plates, closely packed, so that the distance between the plates is small. The gravitational action makes the cells move in the direction of the lower surface of the individual separating space between two plates. Once settled, the particles slide down in a layer towards the plate periphery and then into the sludge hopper. For the same required sedimentation area, lamella settlers are much more compact than vertical ones. Theoretically, their total sedimentation area is the sum of the horizontally projected areas of all plates. In practice, however, only 50% of this total area is effective [137]. The main problem with inclined settlers is that the cells tend to adhere to the plates. Special coating of the plate surface and vibration of the whole lamella pack may alleviate this problem. 

The goal of the lDV-model is to calculate the time-dependent continuous vertical concentration profile of a compound, Cw(z,t), where the depth coordinate z is the height above the deepest point of the lake (thus the vertical coordinate z is chosen as positive upward). Let us consider a horizontal layer of thickness Az confined by the cross sections at depthz and z + Az,A(z) and A(z + Az), respectively (Fig. 23.6). The volume of the layer, AF, can be approximated by A(z)Az, and the sediment contact area AA by [A(z + Az) - A(z)]. Note that bottom slopes of lakes are commonly so small that AA, the horizontal projection of the inclined sediment surface, is usually a good approximation for the real contact area between water and sediment surface. In... 

The operating curve is drawn similarly with horizontal projections from pairs of random points of intersection of the binodal curve by lines drawn through the difference point P. Construction of these curves also is explained with Figure 14.6. 

An early method to picture the three-dimensional properties of molecules was the use of Fischer projections. In Fisher projections, bonds are drawn either vertically or horizontally. Bonds which are vertical project into file space behind the plane of file paper (blackboard, computer screen). Bonds which are horizontal project into file space in front of file plane of the paper (blackboard, computer screen). 

Consider a crystal having a n-fold rotation axis, often simply referred to as an n-axis. In Fig. 9.1.5, OE, OE, OE" represent the horizontal projections of three vertical planes generated by successive rotations of 2n/ about the symmetry axis, which passes through point O. As reference axes, we adopt the n-axis, OE, and OE", and the latter two are assigned unit length. Next, we consider a plane E F which is drawn parallel to OE. The intercepts of E F on the three axes are oo, 1, and (sec 2n/ri)/2. The Miller indices of plane E F are therefore (0,1,2 cos 2n/n) which must be integers. Since cos 2n/n < 1, the only possible values of 2 cos 2n/n are 2, 1, and 0. Hence... 

Because of the unusual amount of dust deposited and because the dust came from an area that has received heavy annual treatment with pesticides for many years, a large sample was collected for analysis at an installation that had previously been used to collect rainfall. Essentially, the collection surface is one fourth of a galvanized iron roof with the gutter arranged to discharge roof runoff into a collection tank. The collection area is 1090 square feet calculated from a horizontal projection. The day after the storm, the roof surface was flushed with 110 liters of Cincinnati tap water, and the dust slurry was collected in a stainless steel tank. The roof surface had been cleansed before the dust was de-... 

Horizontal projection, with or without hole 4) Area, A, area with or without a hole... 

KgMg(804)2.41120, and K2SO4 occurs, is represented on Figs. 36 and 37 in the way described previously, as the point H, by drawing h, the vertical projection for the Mg804, and Hg, the horizontal projection for the K2SO4, above and below the temperature axis respectively. 

The diagram actually represents the horizontal projection of a solid figure. Any point on it may represent a number of soln. of different composition, but if perpendiculars are erected at the limiting points and given lengths proportional to the total number of mols. present in the sat. soln. to which these points correspond, and if the ends of these perpendiculars are properly connected, any... 

Figure 8. Zijderveld plots of representative samples from Red Chamber, Symbols as for Figure 7. For clarity, sample RC 12 is presented in the alternative orthogonal projection, with the vertical plane aligned east-west, and with north to the top on the horizontal projection.

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