Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.46P
To determine
Tension force in each bolt?
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Example-1:
l
D
A uniform rotor of length 0.6 m and diameter 0.4 m is made of steel (density 7810 kg/m³)
is supported by identical short bearings of stiffness 1 MN/m in the horizontal and vertical
directions. If the distance between the bearings is 0.7 m, determine the natural frequencies
and plot whirl speed map.
Solution:
B
find the laplace transform for the
flowing function
2(1-e)
Ans. F(s)=-
S
12)
k
0
Ans. F(s)=
k
s(1+e)
0 a
2a 3a 4a
13)
2+
Ans. F(s)=
1
s(1+e")
3
14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
Chapter 8 Solutions
Fluid Mechanics
Ch. 8 - Prob. 8.1PCh. 8 - The steady plane flow in Fig. P8.2 has the polar...Ch. 8 - P8.3 Using cartesian coordinates, show that each...Ch. 8 - P8.4 Is the function 1/r a legitimate velocity...Ch. 8 - Prob. 8.5PCh. 8 - An incompressible plane flow has the velocity...Ch. 8 - Prob. 8.7PCh. 8 - For the velocity distribution u=By,=+Bx , evaluate...Ch. 8 - Prob. 8.9PCh. 8 - Prob. 8.10P
Ch. 8 - Prob. 8.11PCh. 8 - Prob. 8.12PCh. 8 - P8.13 Starting at the stagnation point in Fig....Ch. 8 - P8.14 A tornado may be modeled as the circulating...Ch. 8 - Hurricane Sandy, which hit the New Jersey coast on...Ch. 8 - Prob. 8.16PCh. 8 - P8.17 Find the position (x, y) on the upper...Ch. 8 - Prob. 8.18PCh. 8 - Prob. 8.19PCh. 8 - Plot the streamlines of the flow due to a line...Ch. 8 - P8.21 At point A in Fig. P8.21 is a clockwise line...Ch. 8 - P8.22 Consider inviscid stagnation flow, (see...Ch. 8 - P8.23 Sources of strength m = 10 m2/s are placed...Ch. 8 - P8.24 Line sources of equal strength m = Ua, where...Ch. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Prob. 8.27PCh. 8 - Sources of equal strength m are placed at the four...Ch. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - A Rankine half-body is formed as shown in Fig....Ch. 8 - Prob. 8.32PCh. 8 - P8.33 Sketch the streamlines, especially the body...Ch. 8 - Prob. 8.34PCh. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - Prob. 8.37PCh. 8 - Consider potential flow of a uniform stream in the...Ch. 8 - A large Rankine oval, with a = 1 m and h = 1 m, is...Ch. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Prob. 8.42PCh. 8 - P8.43 Water at 20°C flows past a 1-rn-diameter...Ch. 8 - Prob. 8.44PCh. 8 - Prob. 8.45PCh. 8 - P8.46 A cylinder is formed by bolting two...Ch. 8 - Prob. 8.47PCh. 8 - Prob. 8.48PCh. 8 - Prob. 8.49PCh. 8 - It is desired to simulate flow past a...Ch. 8 - Prob. 8.51PCh. 8 -
P8.52 The Flettner rotor sailboat in Fig. E8.3...Ch. 8 - P8.52 The Flettner rotor sailboat in Fig. E8.3 has...Ch. 8 - Prob. 8.54PCh. 8 - Prob. 8.55PCh. 8 - Prob. 8.56PCh. 8 - Prob. 8.57PCh. 8 - Prob. 8.58PCh. 8 - Prob. 8.59PCh. 8 - Prob. 8.60PCh. 8 - Prob. 8.61PCh. 8 - Prob. 8.62PCh. 8 - The superposition in Prob. P8.62 leads to...Ch. 8 - Consider the polar-coordinate stream function...Ch. 8 - Prob. 8.65PCh. 8 - Prob. 8.66PCh. 8 - Prob. 8.67PCh. 8 - Prob. 8.68PCh. 8 - Prob. 8.69PCh. 8 - Prob. 8.70PCh. 8 - Prob. 8.71PCh. 8 - Prob. 8.72PCh. 8 - Prob. 8.73PCh. 8 - Prob. 8.74PCh. 8 - Prob. 8.75PCh. 8 - Prob. 8.76PCh. 8 - Prob. 8.77PCh. 8 - Prob. 8.78PCh. 8 - Prob. 8.79PCh. 8 - Prob. 8.80PCh. 8 - Prob. 8.81PCh. 8 - Prob. 8.82PCh. 8 - Prob. 8.83PCh. 8 - Prob. 8.84PCh. 8 - Prob. 8.85PCh. 8 - Prob. 8.86PCh. 8 - Prob. 8.87PCh. 8 - Prob. 8.88PCh. 8 - Prob. 8.89PCh. 8 - NASA is developing a swing-wing airplane called...Ch. 8 - Prob. 8.91PCh. 8 - Prob. 8.92PCh. 8 - Prob. 8.93PCh. 8 - Prob. 8.94PCh. 8 - Prob. 8.95PCh. 8 - Prob. 8.96PCh. 8 - Prob. 8.97PCh. 8 - Prob. 8.98PCh. 8 - Prob. 8.99PCh. 8 - Prob. 8.100PCh. 8 - Prob. 8.101PCh. 8 - Prob. 8.102PCh. 8 - Prob. 8.103PCh. 8 - Prob. 8.104PCh. 8 - Prob. 8.105PCh. 8 - Prob. 8.106PCh. 8 - Prob. 8.107PCh. 8 - P8.108 Consider two-dimensional potential flow...Ch. 8 - Prob. 8.109PCh. 8 - Prob. 8.110PCh. 8 - Prob. 8.111PCh. 8 - Prob. 8.112PCh. 8 - Prob. 8.113PCh. 8 - Prob. 8.114PCh. 8 - Prob. 8.115PCh. 8 - Prob. 8.1WPCh. 8 - Prob. 8.2WPCh. 8 - Prob. 8.3WPCh. 8 - Prob. 8.4WPCh. 8 - Prob. 8.5WPCh. 8 - Prob. 8.6WPCh. 8 - Prob. 8.7WPCh. 8 - Prob. 8.1CPCh. 8 - Prob. 8.2CPCh. 8 - Prob. 8.3CPCh. 8 - Prob. 8.4CPCh. 8 - Prob. 8.5CPCh. 8 - Prob. 8.6CPCh. 8 - Prob. 8.7CPCh. 8 - Prob. 8.1DPCh. 8 - Prob. 8.2DPCh. 8 - Prob. 8.3DP
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