EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 23, Problem 25P
You have to measure the flow rate of water through a small pipe. In order to do it, you place a bucket at the pipe's outlet and measure the volume in the bucket as a function of time as tabulated below. Estimate the flow rate at
| Time, s | 0 | 1 | 5 | 8 |
| Volume, cm3 | 0 | 1 | 8 | 16.4 |
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Consider y (t) — y" (t) − y' (t) + y(t) = 0
(a) Denote new variables x1(t) := y(t), x2(t) := y' (t), x3(t) = y"(t) and solve the following system
0
1
0
x1(t)
X' (t) =
0 1
X(t), X(t) =
x2(t)
-1
1
1
x3(t)
=
y(t)
y' (t)
y" (t)
(b) Use your solution to the system to find the solution to the original equation (verify!).
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Chapter 23 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9PCh. 23 - Develop a user-friendly program to apply a Romberg...
Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...
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