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is Cross-sectional Area Cross section (geometry) of control volume face, is Volume, is average value of source S over the control volume. It states that the difference between the diffusive flux Fick's laws of diffusion of ϕ {\displaystyle \phi } through the east and west faces of some volume corresponds to the change in the quantity ϕ ...
The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the xy-plane around the y-axis. Suppose the cross-section is defined by the graph of the positive function f(x) on the interval [a, b]. Then the formula for the volume will be: ()
The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily derived from the general transport equation for property Φ by deleting transient and convective terms [1]
For a given structure, the shear center is the point in space at which shear force could be applied without causing torsional deformation (e.g. twisting) of the cross-section of the structure. [4] The shear center is an imaginary point, but does not vary with the magnitude of the shear force - only the cross-section of the structure.
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
The two points tracing the cycloids are therefore at equal heights. The line through them is therefore horizontal (i.e. parallel to the two lines on which the circle rolls). Consequently each horizontal cross-section of the circle has the same length as the corresponding horizontal cross-section of the region bounded by the two arcs of cycloids.
The collision cross section per volume or collision cross section density is , and it is related to the mean free path by l = 1 2 C σ {\displaystyle l={\frac {1}{{\sqrt {2}}C\sigma }}} Combining the kinetic equations for molecular motion with the defining equation of shear viscosity gives the well known equation for shear viscosity for dilute ...
where ℓ is the mean free path, n is the number of target particles per unit volume, and σ is the effective cross-sectional area for collision. The area of the slab is L 2, and its volume is L 2 dx. The typical number of stopping atoms in the slab is the concentration n times the volume, i.e., n L 2 dx. The probability that a beam particle ...