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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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.
y
Side 3
Side 1
8.0
(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
C
D.
D.
00
LEGION
Side 4
z epis
. 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 8-13
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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