System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.30P
Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 19 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table.
Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.
Figure 1.4.7 An experiment to determine flow rate versus liquid height.
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Find the solution of the following Differential Equations
1) y" + y = 3x²
3)
"+2y+3y=27x
5) y"+y=6sin(x)
7) y"+4y+4y = 18 cosh(x)
9) (4)-5y"+4y = 10 cos(x)
11) y"+y=x²+x
13) y"-2y+y=e*
15) y+2y"-y'-2y=1-4x³
2) y"+2y' + y = x²
4) "+y=-30 sin(4x)
6) y"+4y+3y=sin(x)+2 cos(x)
8) y"-2y+2y= 2e* cos(x)
10) y+y-2y=3e*
12) y"-y=e*
14) y"+y+y=x+4x³ +12x²
16) y"-2y+2y=2e* cos(x)
The state of stress at a point is σ = -4.00 kpsi, σy = 16.00 kpsi, σ = -14.00 kpsi, Try = 11.00 kpsi,
Tyz = 8.000 kpsi, and T = -14.00 kpsi.
Determine the principal stresses.
The principal normal stress σ₁ is determined to be [
The principal normal stress σ2 is determined to be [
The principal normal stress σ3 is determined to be
kpsi.
kpsi.
The principal shear stress 71/2 is determined to be [
The principal shear stress 7½ is determined to be [
The principal shear stress T₁/, is determined to be [
kpsi.
kpsi.
kpsi.
kpsi.
Repeat Problem 28, except using a shaft that is rotatingand transmitting a torque of 150 N * m from the left bearing to the middle of the shaft. Also, there is a profile keyseat at the middle under the load.
(I want to understand this problem)
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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