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For equilibrium, the resistive force must be equal to the force due to pressure.Therefore, 2 di pi = dit h 4 h = pidi 4t or h = piri 2t (39.23)

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Equation (3923) gives the relevant maximum stress in a spherical shell The expression for hoop stress for a thin h t cylindrical shell and that for a thin spherdi ical shell are similar This simple dePi h duction is of great importance in the design of pressure vessels because the thickness requirement for a spherical vessel of the same material strength and FIGURE 393 Spherical shell under internal thickness-to-diameter ratio is only onepressure half that required for a cylindrical shell The change in internal volume V of a spherical shell can be evaluated easily from consideration of volumetric strain and the original volume Volumetric strain is equal to the sum of three equal and mutually perpendicular strains The change in internal volume due to internal pressure is given by 3p d V = i i (1 )Vo (3924) 4Et 394.

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So, basically the emitter itself has a mini game loop going on Every time it gets updated, it needs to create some new particles and add them to its currently active particle list Then it goes through all the active particles and moves them or rotates them or whatever Then it needs to check to see whether any particles have reached the end of their life, and if so, it removes them from the active list Finally, it needs to make the data arrays from all the particle states Here are a few things to keep in mind: The particle system needs to be able to go through thousands of particles in a single frame, so you need to find efficient ways to handle all of the particles and keep them updated.

5 Vessels Subjected to Fluid Pressure During the process of pressurization of a vessel, the fluid used as the medium changes in volume as the pressure is increased, and this must be taken into account when determining the amount of fluid which must be pumped into a cylinder in order to increase the pressure level in the vessel by a specified amount The cylinder is considered initially full of fluid at atmospheric pressure The necessary change in volume of the pressurizing fluid is given by Vf = where K = bulk modulus of fluid p = pressure Vo = original volume The additional amount of fluid necessary to raise the pressure must take up the change in volume given by Eq (3925) together with the increase in internal volume of the cylinder.

The amount of additional fluid Va required to raise the cylinder pressure by p is given by Va = pdi pV [5 4 ]V + 4Et K (3926) pVo K (3925).

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It can be shown by similar analysis that the additional volume of fluid Va required to pressurize a spherical vessel is given by Va = 3pdi pV (1 )V + 4Et K (39.27)

The emitter may need to emit a few hundred particles every frame, possibly even a few thousand, so you also need to be very efficient about creating particles Allocing objects is a costly process, so you want to avoid it at all costs Hundreds of particles can expire at the same frame, so you need to also be clever about how you clean up your particles Memory cleanup is slow and can affect performance, so you need to be careful about releasing a zillion particles all at once Dynamically mallocing vertex array memory is expensive You want to avoid changing the size of your vertex data arrays How do you solve these problems When your particle emitter is first created, you will need to build a big reserve of prealloced particle objects.

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