Hoopes

The principal use of AIF. is as a makeup ingredient in the molten cryoflte, Na.. AIF AI2O2, bath used in aluminum reduction cells in the HaH-Haroult process and in the electrolytic process for refining of aluminum metal in the Hoopes cell. A typical composition of the molten salt bath is 80—85%... 

Storage areas for maintenance, janitorial, and other service organizations must be provided. Safety items such as fire extinguishers, firehose cabinets, safety hoops on permanent ladders, guard rads, shielding for acid pumps, clearance for electric panel boards, etc, are needed. Manholes and cleanouts for sewer pipes within the facility as well as in the landscape and parking areas should be provided. 

When constmction is complete, the pipeline must be tested for leaks and strength before being put into service industry code specifies the test procedures. Water is the test fluid of choice for natural gas pipelines, and hydrostatic testing is often carried out beyond the yield strength in order to reHeve secondary stresses added during constmction or to ensure that all defects are found. Industry code limits on the hoop stress control the test pressures, which are also limited by location classification based on population. Hoop stress is calculated from the formula, S = PD/2t, where S is the hoop stress in kPa (psig) P is the internal pressure in kPa (psig), and D and T are the outside pipe diameter and nominal wall thickness, respectively, in mm (in.). 

Tank Shell. Another example of where thickness is set by minimums for fabricabihty but not for strength is in small-diameter tanks. For example, a water storage tank built using a steel of an allowable stress of 20,000 psi (138 mPa), 9 ft (3 m) in diameter by 21-ft (7-m) high, requires a shell thickness to resist hoop stress of only 0.023-in. (0.58-mm) thick. However, if built to API Standard 650, the shell would be fabricated at least 0.1875-in. (4.76-mm) thick. The code requires this thickness so that when fabrication, welding, and tolerances are considered, a tank of acceptable quaUty and appearance meeting the requirements of most services in most locations is provided. 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

Live and dead loads generate hoop forces in the area of the roof-to-sheU junction for a tank having a cone roof. For dead loads plus Hve loads, the roof-to-sheU junction is assumed to carry most of the tensile forces generated. The minimum area required is computed assuming that the membrane force transmitted to the roof-to-sheU junction varies with the sine of the angle of the roof ... 

For tank internal pressures that do not exceed the weight of the roof plates, most tanks have conical roofs because these are the simplest and most cost-effective. When the pressure is increased beyond the weight of the roof plates, the roof-to-sheU area goes into hoop compression. A small portion of the roof, the roof-to-sheU angle, and the top few centimeters of the sheU act as a compression ring to resist the unbalanced forces from internal pressure on the conical roof. The internal design pressure for this case may be... 

Reported by Westwater in Drew and Hoopes, Advances in Chemical Engineering, vol. I, Academic, New York, 1956, p. 15. 

Figure 9.2 Longitudinal stress-corrosion cracks in a heat exchanger tnbe the broad gap between the crack faces reveals that high-level residual hoop (circumferential) stresses from the tube-forming operation provided the stress component required for SCC.

The longitudinal orientation of these cracks reveals that hoop (circumferential) stresses caused by internal pressurization provided the necessary stresses. Ammonia was the specific corrodent involved. 

Although the coolant (river water) was at relatively low pressure, measurements revealed a residual hoop stress in the tube of approximately 9000 psi (62 MPa). The longitudinal rupture occurred as a result of these stresses after erosion had sufficiently reduced wall thickness. 

The hoop stress ct in the wall of a cylindrical pressure vessel containing gas at pressure p is given by... 

The hoop stress in the tube under the working pressure of 50 bar (5 MPa) is 5 MPa X 50 mm/5 mm = 50 MPa. Creep data indicate that, at 900°C and 50 MPa, the steel should fail after only 15 minutes or so. In all probability, then, the failure occurred by creep rupture during a short temperature excursion to at least 870°C. 

---