2 edition of **Reflectors, infinite cylinders, intersecting cylinders and criticality** found in the catalog.

Reflectors, infinite cylinders, intersecting cylinders and criticality

J. T Thomas

- 146 Want to read
- 38 Currently reading

Published
**1978**
by Dept. of Energy, [Office of Energy Technology], Oak Ridge National Laboratory, for sale by the National Technical Information Service in Oak Ridge, Tenn, Springfield, Va
.

Written in English

- Criticality (Nuclear engineering),
- Nuclear engineering

**Edition Notes**

Statement | J. L. Thomas |

Series | ORNL/CSD/TM ; 57 |

Contributions | Oak Ridge National Laboratory |

The Physical Object | |
---|---|

Pagination | viii, 40 p. : |

Number of Pages | 40 |

ID Numbers | |

Open Library | OL14881264M |

I want to derive a formula for the area of the intersection of two rigth cylinders with different radii. To get an idea I attached a sketch. Volume of Intersection of cylinders (different radii) Ask Question Asked 5 years, 2 months ago. Infinite endurance. Other Parts of the Index: Part 2 of 4 Part 3 of 4 Part 4 of 4. Periodicals and Special Collections Los Alamos Science-- magazine Dateline Los Alamos-- magazine Los Alamos Reflections-- monthly publication for employees and retirees Los Alamos: Beginning of an Era-- historical report (and Trinity color photo) Los Alamos 50 th Anniversary-- historical articles and photos.

Beryllium oxide as well can be used as a reflector in the low power research reactor. Its density is higher than the density of the Be reflector (Ding and Kloosterman, ). Table 1 shows the physical characteristics of different types of reflectors usually used in the low power research reactors (U.S. Atomic Energy Commission, ).Cited by: 4. Ray intersection usually starts with a faster check against the bounding box of the cylinder, before you do the more expensive check against the cylinder geometry. Either way, it boils down to a line-plane intersection test (since the cylinder is comprised of a bunch of polygons, which are themselves bounded planes).

As seen in Figure , the intersection of a plane with an infinite cylinder can be a single line, two lines, a circle, or an ellipse. The first three of these are special cases that occur only when the plane and cylinder are at one of two special angles relative to one another, and so the ellipse may be considered to be the typical case. 1. Homework Statement: Find surface area of part of cylinder x^2 + z^2 = 1 that is inside the cylinder x^2 + y^2 = 2ay and also in the positive octant (x \\geq 0, y \\geq 0, z \\geq 0). Assume a > 0. Homework Equations x^2 + z^2 = 1 x^2 + y^2 = 2ay (x \\geq 0.

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@article{osti_, title = {Reflectors, infinite cylinders, intersecting cylinders and criticality}, author = {Thomas, J T}, abstractNote = {Calculations of the effective neutron multiplication factor of critical and subcritical infinitely long cylinders of aqueous solutions of fissile materials for various configurations of Reflectors and concrete reflectors are presented.

The results provide a basis for investigating the criticality of intersecting pipes with similar : J.T. Thomas. Reflectors, Infinite Cylinders, Intersecting Cylinders, and Nuclear Criticality J. Thomas Oak Ridge National Laboratory, Computet Sciences Division, P 0 Box X, Oak Ridge, Tennessee 3 Received Octo Accepted March 2 7, I9 However, formatting rules can vary widely between applications and fields of interest or study.

The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or. Reflectors, Infinite Cylinders, Intersecting Cylinders, and Nuclear Criticality J.

Thomas Oak Ridge National Laboratory, Computer Sciences Division, P. Box X, Oak Ridge, Tennessee Received Octo Accepted March 2 7, Calculations of the effective neutron multiplication factor of critical and subcritical infinitely long cylinders of aqueous solutions of fissile materials for various configurations of water and concrete reflectors are presented.

The results provide a basis for investigating the criticality of intersecting pipes with similar reflectors. the bottom of the solution in the infinite cylinders cylinders was cm above the floor of the reflector tank, thereby providing an effectively infinite bottom water reflector.

Calibration with water prior to installation in the system indicated that the inside diameter was not Size: 8MB. In Studies in Mathematics and Its Applications, The Equations.

The Taylor problem is the study of the flow of a viscous incompressible liquid in a doman of ℛ 3 bounded by two infinite cylinders of radius r 1 and r 2 (r 2 > r 1 > 0), having the same vertical axis.

The inner cylinder is rotating with an angular velocity α, while the other is at rest. g(U)/cm3) and the critical masses of water-reflected cylinders containing the same material. Since the buckling of the cylinder is a function of both height and diameter, this is a parametric problem with a series of solutions.

Figure 42 of Ref. 5 gives the critical mass of a water-reflected sphere of this material as approximately Size: KB. It is of three semitransparent orthogonal intersecting cylinders coloured red, green, and blue. The following shows the intersection solid of these three cylinders in plan, and two elevations as well as an isometric view.

The volume of the intersection is 8 (2 - sqrt(2)) r 3, where r is the radius of the cylinder. What is the volume of the. Thomas, “Reflectors, Infinite Cylinders, Intersecting Cylinders, and Nuclear Criticality,” Nuclear Science and Engineering, 67, ().

Lloyd, C. Richey, E. Clayton, and D. Skeen, “Criticality Studies with Plutonium Solutions”, Nuclear Science and Engineering, 25, (). W = U V. Points in the cylinder are parameterized by X(;t) = C+ (scos)U+ (ssin)V+ tW; 2[0;2ˇ);0 s r;jtj h=2 (1) The projections of a cylinder onto a line are determined solely by the cylinder wall, not the end disks.

The choice of U and V is arbitrary. Intersection queries between cylinders should be independent of. Right Circular Cylinder Reactor. Interpretation of Criticality Condition.

Optimum Geometries. Reflected Reactor Reflected Slab Reactor. Reflector Savings. Reflected Spherical, Cylindrical, and Rectangular Parallelepiped Cores.

Homogenization of a. A new form for the critical equation of a slab with an infinite reflector is derived. One speed transport theory is employed and we also make use of a little-known transformation first developed by Wallace (Wallace, P.R., by: 2 Representation of an In nite Cylinder The cylinder axis contains the point C and has unit-length direction D.

The cylinder consists of those points at a distance rfrom the cylinder axis. An algebraic equation that represents the cylinder is derived as follows. To project out the D portion of a vector V, you compute V0 = V (DTV)D = IV D(DTV. Books at Amazon. The Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch.

Here you'll find current best sellers in books, new releases in books, deals in books, Kindle eBooks, Audible audiobooks, and so much more. Results are given for experimental determinations of the critical parameters for aqueous solutions of UO 2 (NO 3) 2. By transformation of the geometric parameter, critical dimensions have been obtained for reactors in the shape of a sphere, an infinite cylinder and an infinite plane : B.G.

Dubovskii, A.V. Kamaev, F.M. Kuznetsov, G.M. Vladykov, G.A. Popov, Yu.D. Palamarchuk. Volume of 3 intersecting Cylinders Thread starter davidjoey; Start date ; #1 davidjoey. 1 0. Homework Statement I am trying to find the volume of three intersecting cylinders that intersect at right angles given that the radius is 5.

I have found many sites that state just the answer, but I am after the proof for it. To handle this finite length cylinder, solve Equation 41 above. This gives, at most, two values of these t 1 and t ate z 1 and z 2 using Equation 24 (z 1 = z E + t 1 z D and z 2 = z E + t 2 z D) and then check ver intersection point passes this test and, if both pass the test, has the smallest non-negative value of t, is the closest intersection point of the ray with.

RADIATION HEAT TRANSFER I n Chap we considered the fundamental aspects of radiation and the radiation properties of surfaces. We are now in a position to consider radiation exchange between two or more surfaces, which is the primary quantity of interest in most radiation problems.

Let (x-c1)^2 + (y-c2)^2 = d^2 be the equation for the cylinder. Substitute x from the line equation into the cylinder equation.

You can solve for y using the quadratic equation. You can have 0 solutions (cylinder and line does not intersect), 1 solution or 2 solutions. Substitute the value of y into the line equation to get x and z coordinates.

I know to intersect ray with cylinder I need to do two check, the first is with the body (with that I get an Infinite Cylinder), for this I assume circle in two dimensions, in the plane xz (x² + z² = r, where r is the radius) then I need check that Y coordinate is between 0 and height and finally I need to check if the intersection is in the.

I'm afraid this test is not % accurate. The problem arises if the infinite cylinder barely touch each other. In the projection to u3, the intersection would be close to the projected main axis of the cylinders.

However, the two rectangles would intersect in cases where there is no actual cylinder intersection.Nuclear Criticality Safety 42 Directed Self-Study reflectors. For example, the known radius of a critical sphere may be used to obtain the radius and length of a corresponding critical cylinder.

For an applied definition of buckling, see Ref. 4, pp. 7 and 8. calculational method (method). The mathematical equations, approximations, assumptions.