The Spherical Tank

The differential change in volume can be thought of in terms of an area times a differential level change  

This is similar to the equation that we encountered in the last problem for the semicylindrical trough  

We can proceed with the solution as follows. First, we show that by integration over h of the Trr dh gives us the proper expression for the volume  

Next we integrate the left-hand side over h and the right-hand side over time. The left-hand side has two integrals over level  

This last expression can now be solved for h as a function of time  

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In addition, dimensional analysis can be used in the design of scale experiments. For example, if a spherical storage tank of diameter dis to be constmcted, the problem is to determine windload at a velocity p. Equations 34 and 36 indicate that, once the drag coefficient Cg is known, the drag can be calculated from Cg immediately. But Cg is uniquely determined by the value of the Reynolds number Ke. Thus, a scale model can be set up to simulate the Reynolds number of the spherical tank. To this end, let a sphere of diameter tC be immersed in a fluid of density p and viscosity ]1 and towed at the speed of p o. Requiting that this model experiment have the same Reynolds number as the spherical storage tank gives... 

Fixed-Roof Tanks. The effect of internal pressure on plate structures, including tanks and pressure vessels, is important to tank design. If a flat plate is subjected to pressure on one side, it must be made quite thick to resist bending or deformation. A shallow cone-roof deck on a tank approximates a flat surface and is typically built of 3/ 16-in. (4.76-mm) thick steel (Fig. 4a). This is unable to withstand more than a few inches of water column pressure. The larger the tank, the more severe the effect of pressure on the structure. As pressure increases, the practicality of fabrication practice and costs force the tank builder to use shapes more suitable for internal pressure. The cylinder is an economic and easily fabricated shape for pressure containment. Indeed, almost all large tanks are cylindrical. The problem, however, is that the ends must be closed. The relatively flat roofs and bottoms or closures of tanks do not lend themselves to much internal pressure. As internal pressure increases, tank builders use roof domes or spheres. The spherical tank is the most economic shape for internal pressure storage in terms of required thickness, but it is generally more difficult to fabricate than a dome- or umbrella-roof tank because of its compound curvature. 

A spherical lank of diameler D = 2 m that is filled with liquid idtrogen at 100 K is kept in an evacuated cubic enclosure w hose sides are 3 m long. The emissivities of the spherical tank and the enclosure are e, 0.1 and = 0.8, respectively. If the temperature of the cubic enclosure is measured to be 240 K, detennine (he net rale of radiation beat transfer to the liquid nitrogen. Ar)swer 228 W... 

FIGURE 23.1 (a) This chemical plant in Texas produces several billion kilograms of polyvinyl chloride each year. The spherical tanks store gaseous raw material, (b) A pipefitting of polyvinyl chloride. 

The cylindrical tank failed on October 20, 1944, and released 147,000 ft of LNG. Much of the liquid vaporized, but some of it also overflowed the enclosed area and entered the surrounding storm sewers. As there were numerous ignition sources in the vicinity, the vapor-air mixtures ignited and produced flames that were reported to extend to a height of at least 2800 ft these also ignited the explosive mixtures within the sewers and weakened the uninsulated columns of one of the spherical tanks. The columns collapsed and spilled the contents of this tank about 20 min after the failure of the cylindrical tank. Fire damage extended over 1/4 mile from the cylindrical tank ... 

Choosing propylene tank of 2000 cubic as the research object, the leakage is 0.5% of the total, environment temperature is 283.15 K, fire dike covers 2800 m. Population density in the spherical tank area is 0.001/m. Casualties due to domino effect are as shown in Table 3. 

Liquefied ammonia is delivered in rail tankcars to Fisons Limited for storage in a 1,900 tonnes spherical tank at -6° C. Several hundred tonnes of liquefied ammonia could be released on land if either of the two storage tanks, at Shell UK Oil and at Fisons Limited failed. The consequences of f lilure of the Shell tank would be minimal, because a high concrete wall to contain the contents and limit the heat transfer and consequently the rate of evaporation of the liquid. Such protection has not been provided. Because of the storage under pressure there are numerous ways the tank could fail from material defect to missile. The spillage of 50 to 100 tonnes, could kill people if noi [imrnp( , evacuation. 

Spherical tanks fragmented into ten to twenty pieces, whereas cylindrical vessels fragmented into two pieces. Because cylinders at the storage site had been stored parallel to each other, their fragments were launched in specific directions (Figure 2.26). 

Pittman (1972) performed five experiments with titanium-alloy pressure vessels which were pressurized with nitrogen until they burst. Two cylindrical tanks burst at approximately 4 MPa, and three spherical tanks burst at approximately 55 MPa. The volume of the tanks ranged from 0.0067 m to 0.170 m. A few years later, Pittman (1976) reported on seven experiments with 0.028-m steel spheres that were pressurized to extremely high pressures with argon until they burst. Nominal burst pressures ranged from 100 MPa to 345 MPa. Experiments were performed just above ground surface. 

Generally, alkoxide-derived monodisperse oxide particles have been produced by batch processes on a beaker scale. However, on an industrial scale, the batch process is not suitable. Therefore, a continuous process is required for mass production. The stirred tank reactors (46) used in industrial process usually lead to the formation of spherical, oxide powders with a broad particle size distribution, because the residence time distribution in reactor is broad. It is necessary to design a novel apparatus for a continuous production system of monodispersed, spherical oxide particles. So far, the continuous production system of monodisperse particles by the forced hydrolysis... 

Natural gas is stored in large spherical tanks because this shape holds the greatest volume for a given amount of containment material. 

Figure 8.16 displays spherical tank cost for liquid storage ranging from 300 to 20,000 bbl. This cost curve may be extrapolated to over 30,000 bbl. Fabrication economics show cost minimized by installing multiple spherical tanks rather than going over 35,000 bbl per tank. Figure 8.16 gives the curve based on the maximum liquid volume con-... 

These spherical tanks are not insulated, since the stored liquids approach the ambient temperature in most countries. Also, insulation problems result from water moisture condensing on the metal walls under the insulation. 

Figure 8.16 is the complete modular LPG storage spherical tank cost, including piping, stairwells, platforms, instruments, controls, steel, foundation, and dike containment. Both material and labor are included in the Fig. 8.16 cost curve, installed and ready to commission. 

Air finfan overhead condensers. Table 8.34 gives the modular cost of the overhead condensers and product coolers. Since this plant is to be installed in Saudi Arabia, cooling tower water is not available. Also, cooling water is not necessary since the products will be stored in spherical tanks requiring 150 to 180°F cooling. This is easy to obtain, even in Saudi Arabia, with air finfan coolers. The square feet of surface area shown in Table 8.34 is the bare tube surface area of each cooler. Please note this is not the extended surface of the outside tube area, but rather the outside bare tube surface area in square feet. Figure 8.4 was used to find the base cost of these air coolers. 

A hydrostatic tank gauge applied to a pressurized, spherical tank. (Courtesy of The Foxboro Co.)... 

A catastrophic explosion and major fire occurred within a major refinery as operations prepared a system for valve maintenance. This refinery stored a flashing flammable fluid (isobutane with a boiling point of 11° F or —12° C) in two spherical tanks. The spheres connected to an alkylation unit via a 10-inch (25 cm) line. Operating line pressure was about 50 psig (345 kPa gauge) and one of the valves in this underground system was in an open pit. [9]... 

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