Right cylinder

Hearth. The induction melting coil is almost always round and in the form of a right cylinder. It is highly desirable that the refractory lining within the coil be uniform in thickness, so most hearths are cylindrical whether they hold a few kg or 59 t. There are a few instances of a smaller coil being attached to the bottom of a larger hearth, so the hearth could be modified to suit a particular requirement (10). Oval cods have been budt and operated satisfactordy, but they are rare. 

For shorter penetration the use of p emitting isotopes is widely made applying much the same absorption law for p radiation as for y rays, with a minor modification. An alternative procedure used by Kingety and Paladino for the study of diffusion in AI2O3 employs two right cylinders, one only containing the radioactive Al isotopic species which emits relatively low energy ( ,nax = 0.511 MeV) p particles. 

The measurement of oxygen diffusion is usually made by the use of as die labelling isotope. If a gas containing an initial concentration C, of in O , and Co is the initial conceiiuation of in a right cylinder oxide sample of thickness 21, and a is the ratio of oxygen atoms in the original gas phase compared widi that in the solid, dieii after a time t, when the concentration in the gas phase is C/... 

Apply this reasoning to the system is Figure 40.11. If the input piston is pushed down a distance of 1 inch, the volume in the left cylinder will decrease by 2in. At the same time, the volume in the right cylinder will increase by 2in. Since the diameter of the right cylinder cannot change, the piston must move upward to allow the volume to increase. The piston will move a distance equal to the volume increase divided by the surface area of the piston. In this example, the piston will move one-tenth of an inch (2 in /20 in ). 

FIGURE 3.3. Comparison of Critical Temperatures for Frank-Kamenetskii and Semenov Models (Right Cylinder Configuration). 

Runaway will occur when the calculated delta (8) exceeds the critical delta (8cr) which depends on the shape of the reaction mixture 0.88 for a plane slab, 2.00 for an infinite cylinder, 2.78 for a right cylinder with 1/d equal to 1, and 3.32 for a sphere. Bowes [133] provides formulas for calculation of 8cr for other geometric shapes and structures. In this model, heat is lost by conduction through the material to the edge, where the heat loss rate is infinite relative to the conduction rate. In this model, there is a maximum temperature in the center as shown in Figure 3.20 Case B. 

Thomas [209] describes the effect of Biot number on the critical 8 in calculations of runaway temperatures. Biot numbers for right cylinders with various 1/d ratios are available. 

The theoretical calculations of the phase volume of the sorbent are facilitated by considering the fiber to be a right cylinder. The dimensions of the fused silica fiber are accurately known so that the volume of the fused silica core can be subtracted from the total volume of the fiber to yield the phase volume of the sorbent. 

Schematic representations of ideal catalyst pellet geometries, (a) Infinite slab, (b) Infinite right cylinder, (c) Sphere.

Table 2.4 Square radii of gyration of rigid objects uniform thin disc of radius R, uniform sphere of radius R, thin rod of length L, and uniform right cylinder of radius R and length L...

Calculate the radius of gyration of a uniform right cylinder of radius R and length L. 

The ASTM test describes in detail the apparatus for measuring compressive properties, preparation of test specimens, conditioning, and procedures. The standard test specimen is recommended to be in the form of a right cylinder or prism whose length... 

III. To find the equation of the surface of a right cylinder. Let one side of a rectangle rotate about Oz as axis. Any point on the outer edge will describe the circumference of a circle. 

The equation of a right cylinder is thus independent of z. This means that z may have any value whatever assigned to it. 

The standard method for compressive tests are listed in Table 12.3. For example, the ISO Standard 604 allows four types of test specimens 1) the right square prism, 2) the right rectangular prism, 3) the right cylinder and 4) the right circular crown tube. The test specifies for each of these test specimens, the load-bearing surfaces be parallel to each other within 0.1% of the height of the test piece. 

The flow is into the tank at a constant rate given by the density of the fluid and its volumetric flow rate. The mass in the tank at any time is the product of the density and the fluid volume. Notice that as the level of the fluid increases, so too does its width. Viewed from the top, the area of the liquid surface grows as a function of time. This is the main difference between this "tank" and that of a right cylinder standing on end. In that case the surface of the liquid viewed from above remains constant, so that the volume is only a function of the level. To summarize what we have so far ... 

The tendency of expls to self-heat is an important indication of a serious stability problem. Studies of this phenomenon are performed by maintaining progressively larger r idar shapes of the expl or the proplnt (for example, right cylinders, cubes or spheres) at elevated temps until deflagration occurs (Refs 19 82). The progress of the self-heating is followed with inserted thermocouples. The critical sizes at... 

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