Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 5, Problem 5.42P
When disturbed, a floating buoy will bob up and down at frequency f. Assume that this frequency varies with buoy mass m, waterline diameter d, and the specific weight
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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 5 Solutions
Fluid Mechanics
Ch. 5 - Prob. 5.1PCh. 5 - A prototype automobile is designed for cold...Ch. 5 - P5.3 The transfer of energy by viscous dissipation...Ch. 5 - When tested in water at 20°C flowing at 2 m/s, an...Ch. 5 - P5.5 An automobile has a characteristic length and...Ch. 5 - P5.6 The disk-gap-band parachute in the...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - The Richardson number, Ri, which correlates the...Ch. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - The Stokes number, St, used in particle dynamics...Ch. 5 - Prob. 5.13PCh. 5 - Flow in a pipe is often measured with an orifice...Ch. 5 - The wall shear stress T in a boundary layer is...Ch. 5 - P5.16 Convection heat transfer data are often...Ch. 5 - If you disturb a tank of length L and water depth...Ch. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - As will be discussed in Chap. 11, the power P...Ch. 5 - The period T of vibration of a beam is a function...Ch. 5 - Prob. 5.24PCh. 5 - The thrust F of a propeller is generally thought...Ch. 5 - A pendulum has an oscillation period T which is...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - P5.29 When fluid in a pipe is accelerated linearly...Ch. 5 - Prob. 5.30PCh. 5 - P5.31 The pressure drop per unit length in...Ch. 5 - A weir is an obstruction in a channel flow that...Ch. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - A certain axial flow turbine has an output torque...Ch. 5 - When disturbed, a floating buoy will bob up and...Ch. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - P5.45 A model differential equation, for chemical...Ch. 5 - P5.46 If a vertical wall at temperature Tw is...Ch. 5 - The differential equation for small-amplitude...Ch. 5 - Prob. 5.48PCh. 5 - P5.48 A smooth steel (SG = 7.86) sphere is...Ch. 5 - Prob. 5.50PCh. 5 - Prob. 5.51PCh. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - P5.56 Flow past a long cylinder of square...Ch. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Prob. 5.59PCh. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - The Keystone Pipeline in the Chapter 6 opener...Ch. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - Prob. 5.66PCh. 5 - Prob. 5.67PCh. 5 - For the rotating-cylinder function of Prob. P5.20,...Ch. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - The pressure drop in a venturi meter (Fig. P3.128)...Ch. 5 - Prob. 5.72PCh. 5 - Prob. 5.73PCh. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - Prob. 5.77PCh. 5 - Prob. 5.78PCh. 5 - Prob. 5.79PCh. 5 - Prob. 5.80PCh. 5 - Prob. 5.81PCh. 5 - A one-fiftieth-scale model of a military airplane...Ch. 5 - Prob. 5.83PCh. 5 - Prob. 5.84PCh. 5 - *P5.85 As shown in Example 5.3, pump performance...Ch. 5 - Prob. 5.86PCh. 5 - Prob. 5.87PCh. 5 - Prob. 5.88PCh. 5 - P5.89 Wall friction Tw, for turbulent flow at...Ch. 5 - Prob. 5.90PCh. 5 - Prob. 5.91PCh. 5 - Prob. 5.1WPCh. 5 - Prob. 5.2WPCh. 5 - Prob. 5.3WPCh. 5 - Prob. 5.4WPCh. 5 - Prob. 5.5WPCh. 5 - Prob. 5.6WPCh. 5 - Prob. 5.7WPCh. 5 - Prob. 5.8WPCh. 5 - Prob. 5.9WPCh. 5 - Prob. 5.10WPCh. 5 - Given the parameters U,L,g,, that affect a certain...Ch. 5 - Prob. 5.2FEEPCh. 5 - Prob. 5.3FEEPCh. 5 - Prob. 5.4FEEPCh. 5 - Prob. 5.5FEEPCh. 5 - Prob. 5.6FEEPCh. 5 - Prob. 5.7FEEPCh. 5 - Prob. 5.8FEEPCh. 5 - In supersonic wind tunnel testing, if different...Ch. 5 - Prob. 5.10FEEPCh. 5 - Prob. 5.11FEEPCh. 5 - Prob. 5.12FEEPCh. 5 - Prob. 5.1CPCh. 5 - Prob. 5.2CPCh. 5 - Prob. 5.3CPCh. 5 - Prob. 5.4CPCh. 5 - Does an automobile radio antenna vibrate in...Ch. 5 - Prob. 5.1DPCh. 5 - Prob. 5.2DP
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