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This is a torispherical head also named Semi ellipsoidal head (According to DIN 28013). The radius of the dish is 80% of the diameter of the cylinder ( r 1 = 0.8 × D o {\displaystyle r_{1}=0.8\times Do} ).
In terms of the principal diameters A, B, C (where A = 2a, B = 2b, C = 2c), the volume is V = 1 6 π A B C {\displaystyle V={\tfrac {1}{6}}\pi ABC} . This equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal.
tτ = (tσ 2 − 1 ) 1/2. Hence it is easy to infer that if we assume σ || λ , where λ is a vector in a given position, the new real vector σ + τ will terminate on the surface of a double-sheeted and equilateral hyperboloid ; and that if, on the other hand, we assume τ || λ , then the locus of the extremity of the real vector σ + τ ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors. The same notation is used here for all faces and cell dimensions as in one dimensional analysis. When the above equation is formally integrated over the Control volume, we obtain
In the 2-dimensional case, if the density exists, each iso-density locus (the set of x 1,x 2 pairs all giving a particular value of ()) is an ellipse or a union of ellipses (hence the name elliptical distribution).
The hyperspherical model is the generalization of the spherical model to higher dimensions. The points of n-dimensional elliptic space are the pairs of unit vectors (x, −x) in R n+1, that is, pairs of antipodal points on the surface of the unit ball in (n + 1)-dimensional space (the n-dimensional hypersphere).
A disadvantage of these vessels is that greater diameters are more expensive, so that for example the most economic shape of a 1,000 litres (35 cu ft), 250 bars (3,600 psi) pressure vessel might be a diameter of 91.44 centimetres (36 in) and a length of 1.7018 metres (67 in) including the 2:1 semi-elliptical domed end caps.