EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 10, Problem 6P
Use LU decomposition to determine the matrix inverse for the following system. Do not use a pivoting strategy, and check your results by verifying that
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A prototype automobile is designed to travel at 65 km/hr. A model of this design is tested in a wind tunnel with identical standard sea-
level air properties at a 1:5 scale. The measured model drag is 529 N, enforcing dynamic similarity. Determine (a) the drag force on the
prototype and (b) the power required to overcome this drag. See the equation
Vm
m
=
D
V Dm
(a) Dp = i
(b) Pp = i
N
hp
A new blimp will move at 6 m/s in 20°C air, and we want to predict the drag force. Using a 1: 14-scale model in water at 20°C and
measuring a 2500-N drag force on the model, determine (a) the required water velocity, (b) the drag on the prototype blimp and, (c) the
power that will be required to propel it through the air.
(a) Vm = i
(b) Dp = i
(c) Pp = i
m/s
N
W
Drag measurements were taken for a sphere, with a diameter of 5 cm, moving at 3.7 m/s in water at 20°C. The resulting drag on the
sphere was 10 N. For a balloon with 1-m diameter rising in air with standard temperature and pressure, determine (a) the velocity if
Reynolds number similarity is enforced and (b) the drag force if the drag coefficient in the equation below is the dependent pi term.
li ε pVI
D
1
= CD = Q
μ
(a) Vp = i
(b) Dp = i
m/s
N
Chapter 10 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 10 - 10.1 Use the rules of matrix multiplication to...Ch. 10 - 10.2 (a) Use naive Gauss elimination to decompose...Ch. 10 - 10.3 (a) Solve the following system of equations...Ch. 10 - 10.4 Solve the following system of equations using...Ch. 10 - Determine the total flops as a function of the...Ch. 10 - Use LU decomposition to determine the matrix...Ch. 10 - 10.7 Perform Crout decomposition on
Then,...Ch. 10 - The following system of equations is designed to...Ch. 10 - 10.9 Solve the following set of equations with LU...Ch. 10 - 10.10 (a) Determine the LU decomposition without...
Ch. 10 - Use the following LU decomposition to (a) compute...Ch. 10 - Determine Ae,A1,andAfor [A]=[82109131516] Scale...Ch. 10 - 10.13 Determine the Frobenius and the row-sum...Ch. 10 - 10.14 A matrix is defined as
Using the...Ch. 10 - 10.15 (a) Determine the condition number for the...Ch. 10 - 10.16 Determine the condition number based on the...Ch. 10 - Besides the Hilbert matrix, there are other...Ch. 10 - 10.18 Develop a user-friendly program for LU...Ch. 10 - Develop a user-friendly program for LU...Ch. 10 - Use iterative refinement techniques to improve...Ch. 10 - 10.21 Consider vectors:
Vector is...Ch. 10 - 10.22 Consider the following vectors:
Where is...Ch. 10 - 10.23 Let the function be defined on the interval ...Ch. 10 - 10.24 (a) Create a Hilbert matrix. This will be...Ch. 10 - Polynomial interpolation consists of determining...
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