EBK FLUID MECHANICS: FUNDAMENTALS AND A
4th Edition
ISBN: 8220103676205
Author: CENGEL
Publisher: YUZU
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Chapter 15, Problem 45CP
To determine
To discuss:
The advantages of left-right symmetry in case of potential flow.
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Use Triple Integral to solve the problem.
The exercise concerns the Gauss-Legendre integration method for integrals of the form that is in the picture i uploaded
with the difference that the integration will not be done at the N+1 specific points (or Gauss nodes: x_0, x_1, …, x_N) as tabulated in your book, but at N+1 points placed arbitrarily (but in monotonically increasing order) in the interval [-1, 1]. If f(x) is a polynomial of degree K, what is the largest value of K (expressed, obviously, as a function of N) for which the integral I is calculated exactly. Provide a convincing numerical demonstration of your answer for N=3 (choosing your own values for x_0, x_1, x_2, x_3).
(3) For the given boundary value problem, the exact solution is
given as = 3x - 7y. (a) Based on the exact solution, find
the values on all sides, (b) discretize the domain into 16
elements and 15 evenly spaced nodes. Run poisson.m and
check if the finite element approximation and exact solution
matches, (c) plot the D values from step (b) using topo.m.
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Side 3
Side 1
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(4) The temperature distribution in a flat slab needs to be studied under the conditions shown i
the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I
all cases assume the upper and lower boundaries are insulated. Assume that the units of length
energy, and temperature for the values shown are consistent with a unit value for the coefficier
of thermal conductivity.
Boundary Temperatures
6
Case
A
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Chapter 15 Solutions
EBK FLUID MECHANICS: FUNDAMENTALS AND A
Ch. 15 - A CFD code is used to solve a two-dimensional (x...Ch. 15 - Write a brief (a few sentences) definition and...Ch. 15 - What is the difference between a node and an...Ch. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 6CPCh. 15 - Prob. 7CPCh. 15 - Write a brief (a few sentences) discussion about...Ch. 15 - Prob. 9CPCh. 15 - Prob. 10CP
Ch. 15 - Prob. 11CPCh. 15 - Prob. 13CPCh. 15 - Prob. 14CPCh. 15 - Prob. 15CPCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - For each statement, choose whether the statement...Ch. 15 - Prob. 45CPCh. 15 - Gerry creates the computational domain sketched in...Ch. 15 - Think about modem high-speed, large-memory...Ch. 15 - What is the difference between mulugridding and...Ch. 15 - Suppose you have a fair) comp1c geometry and a CFD...Ch. 15 - Generate a computational domain and grid, and...
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- examples, by conering them mer and then trying to draw the paral law, and thiking about how the sine and conine laws re sed to d the mknowns Then before solhing any of the problems, try and sntve some of the Fundamental Problems given on the next page. The solutiuns und answers to these are given in the back of the boik. Doing this throuphout the book will help immensely in developing your problem-solving skills 1%19 |. A 1:-1 lec.2.pdf 2.3 VECTOR ADDITION OF FORCES 27 FUNDAMENTAL PROBLEMS* F2-1. Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis F2-4. Resolve the 30-lb force into components along the r and raves, and determine the magnitude of each of these components 30 Ib ŽAN 6KN 12-1 F2-4 12-2. Two forces act on the hook. Determine the magnitade F2-5. The foroe = 450 Ih acts on the frame. Resolve this force into eomponents acting along members AB and AC, and determine the magnitude of each component. of the…arrow_forward. The packing rings in a distillation tower are in the shape of a torus (doughnut) as shown in Fig. 8-13. The outside diameter of the ring is to be 20 mm, and the values of D and D2 are sought that yield maximum surface area where the area = 7?D,D2. Structure the problem as a constrained optimization and solve by the method of Lagrange multipliers. D212 D2 FIGURE 8-13arrow_forwardFor the two-dimensional computational domain of Fig, with the given node distribution, sketch a simple structured grid using four-sided cells and sketch a simple unstructured polyhedral grid using at least one of each: 3-sided, 4-sided, and 5-sided cells. Try to avoid large skewness. Compare the cell count for each case and discuss your results.arrow_forward
- i need the answer quicklyarrow_forward2. As shown in the right figure, write out your solution strategy, including model, meshing(at least 2Nim with 4 elements), boundary conditions, and element type and shape functions, also write out the nodal force formula. Do not require computing. 2Nim 2m 2marrow_forwardTopics Discussed: Static of Rigid Bodies, Force Vector, Addition of a System of Coplanar Forces, Cartesian Vector Please re-compute and re-solve the given, This is my answer. But I also want to see your expert answer if we land in the same solutions and answers. Please show your complete solution. Thank you.arrow_forward
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