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3DK - PRISM
3DK - PRISM

... The computed points x1 and x2 will be identical only if the two neighboring triangles are coplanar. Even in the case when l1 and l2 do not actually intersect, an equation can be formed by forcing the two points x1 and x2 to be identical. 3DK – September 15, 2000 ...
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... separate one variable z (say) from the other variables. After separating variable z, equation is directly integrable. Satisfaction of condition of integrability is must in each problem. Students are advised to try the same in each question, and then go ahead as follows: Example 1: Solve (x - y) dx – ...
Grade 4, Benchmark 4(Chapters 7 and 8)
Grade 4, Benchmark 4(Chapters 7 and 8)

... c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. d. Solve word problems involving addition and subtraction of fractions referr ...
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... For the second step (from x = 0.05 to 0.1),  x1,i 1   2.819795 2.800187   5.619981   5.443885  x ...
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Computation of power from an array of wave energy converters

... Figure 3. Comparison of added mass and damping coefficients for l=5b between NEMOH and eigenfunction expansion. Variation of q factor Finally we apply the formula of power absorption (equations 911) to investigate the q factor for two different spacing, l=5b and l=10b, in figure 4. We also include t ...
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Sure Shot Questions for XII Maths - Kendriya Vidyalaya BSF, Dabla

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... 2. A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 2 labour hours for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximu ...
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... applying perturbations to models, for which a previous solution has been calculated. Two mathematical formulations of RPT have emerged: Hamiltonian formulation and Lagrangian formulation. In both, a similar procedure is adopted. A ray is traced through a reference medium cell by cell for which an an ...
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appendix `d`
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... Rs. 5760 to invest and has space for at most 20 items. An electronic sewing machine costs him Rs. 360 and a manually operated sewing machine Rs. 240. He can sell an electronic machine at a profit of Rs. 22 and manually operated machine at a profit of Rs. 18. Assuming that he can sell all the items t ...
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... FIG. 4. (Color online) Example of computed flow profiles in the axisymmetric tube at various cross sections. The Stokeslet strengths are first computed based on velocity boundary conditions on the surface of the tube. Then, the instantaneous flow at various cross sections is computed and displayed h ...
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... Familiar real-world contexts must be used in tasks.  All values, including variables, are whole numbers  Tasks must not include more than 1 variable  Allowable multiplication notation: 3x, 3·x & ...
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... In this time of a down economy, falling national ranking in test scores for math and science, and an ever increasing dropout rate of American students from degrees in the fields of mathematics, engineering, and computer science, there is an overwhelming movement to restructure the way in which STEM ...
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... However, even in the more general case when the two masses are of similar size, we shall show that the problem can be reduced to a ”Kepler” problem. Although most problems in celestial mechanics involve more than two bodies, many problems of practical interest can be accurately solved by just looki ...
Dispersion of Discontinuous Periodic Waves - Math-UMN
Dispersion of Discontinuous Periodic Waves - Math-UMN

... numerical experiments with step function initial data strongly indicate that the dispersive quantization/fractalization effect is present in the periodic boundary value problems for both the integrable nonlinear Korteweg–deVries and Schrödinger equations, as well as non-integrable models of a simil ...
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Computational fluid dynamics



Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests.
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