Thin Circular

Rupture Disks A rupture disk is a device designed to function by the bursting of a pressure-retaining disk (Fig. 26-15). This assembly consists of a thin, circular membrane usually made of metal, plastic, or graphite that is firmly clamped in a disk holder. When the process reaches the bursting pressure of the disk, the disk ruptures and releases the pressure. Rupture disks can be installed alone or in combination with other types of devices. Once blown, rupture disks do not reseat thus, the entire contents of the upstream process equipment will be vented. Rupture disks are commonly used in series (upstream) with a relief valve to prevent corrosive fluids from contacting the metal parts of the valve. In addition, this combination is a reclosing system. 

The torsion-tube test described by Whitney, Pagano, and Pipes [2-14] involves a thin circular tube subjected to a torque, T, at the ends as in Figure 2-29. The tube is made of multiple laminae with their fiber directions aligned either all parallel to the tube axis or all circumferentially. Reasonable assurance of a constant stress state through the tube thickness exists if the tube is only a few laminae thick. However, then serious end-grip difficulties can arise because of the flimsy nature of the tube. Usually, the thickness of the tube ends must be built up by bonding on additional layers to introduce the load so that failure occurs in the central uniformly stressed portion of the tube (recall the test specimen criteria). Torsion tubes are expensive to fabricate and require relatively sophisticated instrumentation. If the shearing strain y 2 is measured under shear stress t.,2, then... 

Because there is a large literature, we restrict ourselves to an interesting example, useful for understanding the axial support of thin mirrors. Consider a thin circular plate of radius a and thickness h, with elastic constant E and Poissons ratio v. Let this plate be axially loaded by gravity and assume we will support this plate against this load by N supports. This is shown in Fig. 2. 

When a jet fire impinges on an object, its shape may be very distorted compared to the free-field shapes modeled. If the jet fire impinges perpendicularly on a flat object such as a fire-wall or deck, it will produce a thin circular flame over the object s surface. 

Triaxial tests usually involve more elaborate testing equipment and more precise measuring techniques than those normally used for uniaxial and biaxial measurements. In the poker chip test (33, 59) the faces of a thin circular disc are bonded to rigid plates (Figure 18). The speci-... 

It may be noticed that some of the filters discussed are operated continuously and some are not. For example, the rapid sand filter, the slow sand filter, the pressure filter, and the rotary vacuum filter are all operated continuously. The plate-and-frame press is operated as a batch. Thus, filters may also be classified as continuous and discontinuous. Only the plate-and-frame press is discussed in this chapter as a representation of the discontinuous type, but others are used, such as the shell-and-leaf filters and the cartridge filters. The first operates in a mode that a leaf assembly is inserted into a shell while operating and retracted out from the shell when it is time to remove the cake. The second looks like a cartridge in outward appearance with the filter medium inside it. The medium could be thin circular plates or disks stacked on top of each other. The clearance between disks serves to filter out the solids. 

Because of the logarithmic term the drag changes but slowly with the ratio of major to minor axes. A thin circular disc of diameter a, thickness h, will have both a horizontal (m ) and a vertical velocity (mJ component of velocity (Figure 6.2), where ... 

A more realistic approximate theory for the SECM with a tip shaped as a cone or spherical segment was presented in Ref. 9. The surface of the nonplanar tip electrode was considered to be a series of thin circular strips, each of which is parallel to the planar substrate. The diffusional flux to each strip was calculated using approximate equations for a disk-shaped tip over a conductive or an insulating substrate. The normalized current to the nonplanar tip was obtained by integrating the current over the entire tip surface. Two families of working curves for conical tips over conductive (Fig. 8A) and insulating substrates (Fig. 8B) illustrate the effect of the tip geometry. 

For thin circular cylinders of length l and radius a, one has 47 2 47ri 47r2... 

The case x -> oo (that is, a -> 0 and b = const) corresponds to diffusion to the surface of a thin circular disk of radius b perpendicular to a uniform translational Stokes flow. 

A thin circular-disk earring 5.00 cm in diameter is plated... 

Isothermal Annulus. Smythe [95] obtained the solution for the capacitance of a thin circular annulus. The solutions were recast [135] into the following dimensionless thermal spreading resistance expressions ... 

J. H. Blackwell, Transient Heat Flow from a Thin Circular Disk Small-Time Solution, Journal of the Australian Mathematical Society, Vol. XIV, pp. 433-442,1972. 

E. J. Normington and J. H. Blackwell, Transient Heat Flow From Constant Temperature Spheroids and the Thin Circular Disk, Quarterly Journal of Mechanics and Applied Mathematics Vol. 17, pp. 65-72,1964. 

In a dilute suspension of thin circular disks of radius R, the contributions by individual particles scattering independently can be derived in a manner similar to that for thin rods, but here we will simply present the result (see Kratky and Porod11 for the derivation) ... 

Figure 5.3 The Debye function, Equation (5.31), for a random coil chain is plotted and compared with the independent scattering intensity function for a thin rod and a thin circular disk.

In spite of the simplicity of the model of the thin circular ring, the frequency response of the induced current contains some general features which are inherent to much more complicated cases as will be demonstrated in later chapters. 

A volume V of a liquid of density p and surface tension a is contained between two parallel, concentric circular disks that are oriented horizontally and separated from each other by a distance a. A thin circular capillary tube of radius a is connected to the upper disk at its center and oriented vertically. The liquid level in the tube measured upward from the center of the space between the disks (all) to the meniscus is H (the meniscus height itself is taken to be small). The distance the liquid extends radially outward between the disks, measured from the centerline of the... 

Thin circular sheet of radius r Normal to the plate through the 1 2... 

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