Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 8, Problem 8.54PP
Water at
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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
Applied Fluid Mechanics (7th Edition)
Ch. 8 - A 4-in-ductile iron pipe carries 0.20ft3/s of...Ch. 8 - Calculate the minimum velocity of flow in ft/s of...Ch. 8 - Calculate the maximum volume flow rate of fuel oil...Ch. 8 - Calculate the Reynolds number for the flow of each...Ch. 8 - Determine the smallest metric hydraulic copper...Ch. 8 - In an existing installation, SAE 10 oil (sg = 0.89...Ch. 8 - From the data in Appendix C, we can see that...Ch. 8 - Compute the Reynolds number for the flow of 325...Ch. 8 - Benzene (sg = 0.86 ) at 60c C is flowing at 25...Ch. 8 - Hot water at 80 C is flowing to a dishwasher at a...
Ch. 8 - A major water main is an 18 -in ductile iron pipe....Ch. 8 - ]8.12 An engine crankcase contains SAE 10 motor...Ch. 8 - Repeat Problem 8.12 for an oil temperature of 160...Ch. 8 - At approximately what volume flow rate will propyl...Ch. 8 - SAE 30 oil (sg = 0.89 ) is flowing at 45 L/min...Ch. 8 - Repeat Problem 8.15 for an oil temperature of 160...Ch. 8 - Repeat Problem 8.15, except the tube is 50 mm...Ch. 8 - Repeat Problem 8.17 for an oil temperature of 0 C.Ch. 8 - The lubrication system for a punch press delivers...Ch. 8 - After the press has run for some time, the...Ch. 8 - A system is being designed to carry 500 gal/min of...Ch. 8 - The range of Reynolds numbers between 2000 and...Ch. 8 - The water line described in Problem 8.22was a cold...Ch. 8 - In a dairy, milk at 100 F is reported to have a...Ch. 8 - In a soft-drink bottling plant, the concentrated...Ch. 8 - ]8.26 A certain jet fuel has a kinematic viscosity...Ch. 8 - Crude oil is flowing vertically downward through...Ch. 8 - Water at 75 C is flowing in a standard hydraulic...Ch. 8 - Fuel oil is flowing in a 4 -in Schedule 40 steel...Ch. 8 - A 3-in Schedule 40 steel pipe is 5000 ft long and...Ch. 8 - Benzene at 60 C is flowing in a DN 25 Schedule 80...Ch. 8 - As a test to determine the effective wall...Ch. 8 - Water at F flows from a storage tank through ft...Ch. 8 - A water main is an 18 -in-diameter concrete...Ch. 8 - Figure 8.12shows a portion of a fire protection...Ch. 8 - A submersible deep-well pump delivers 745 gal/h of...Ch. 8 - On a farm, water at 60 F is delivered from a...Ch. 8 - Figure 8.15 shows a system for delivering lawn...Ch. 8 - A pipeline transporting crude oil (sg = 0.93 ) at...Ch. 8 - For the pipeline described in Problem 8.39,...Ch. 8 - Water at 10 C flows at the rate of 900 L/min from...Ch. 8 - For the system shown in Fig. 8.17, compute the...Ch. 8 - Fuel oil (sg = 0.94 ) is being delivered to a...Ch. 8 - Figure 8.18 shows a system used to spray polluted...Ch. 8 - In a chemical processing system, the flow of...Ch. 8 - Water at 60 F is being pumped from a stream to a...Ch. 8 - For the pump described in Problem 8.46, if the...Ch. 8 - Gasoline at 50 F flows from point A to point B...Ch. 8 - Figure 8.20 shows a pump recirculating 300 gal/min...Ch. 8 - Linseed oil at 25 C flows at 3.65 in a standard...Ch. 8 - Glycerin at 25 C flows through a straight...Ch. 8 - Water at 75 C flows in a standard hydraulic copper...Ch. 8 - Benzene (sg = 0.88 ) at 60 C, flows in a DN 25...Ch. 8 - Water at 80 F flows in a 6 -in coated ductile iron...Ch. 8 - Water at 50 F flows at 15.0 ft3/s in a concrete...Ch. 8 - Water at 60 F flows at 1500 gal/min in a 10 -in...Ch. 8 - ]8.57 A liquid fertilizer solution (sg = 1.10 )...Ch. 8 - Crude oil (sg = 0.93 ) at 100 C flows at a rate of...Ch. 8 - Water at 65 C flows in a DN 40 Schedule 40 steel...Ch. 8 - Propyl alcohol flows in a standard hydraulic...Ch. 8 - ]3.61 Water at 70 F flows in a 12 -in-diameter...Ch. 8 - Heavy fuel oil at 77 F flows in a 6 -in Schedule...Ch. 8 - Water flows at a rate of 1.50ft3/s through 550 ft...Ch. 8 - Compute the energy loss as water flows in a...Ch. 8 - ]8.65 A water main is an 18 -in-diameter concrete...Ch. 8 - A fire protection system includes 1500 ft of 10...Ch. 8 - ]8.67 A standard hydraulic copper tube, 120 mm...Ch. 8 - Compute the energy loss as 2.0ft3/s of water flows...Ch. 8 - It is desired to flow 2.0ft3/s of water through...Ch. 8 - Specify a suitable size of new, clean Schedule 40...Ch. 8 - For the pipe selected in Problem 8.70, compute the...Ch. 8 - Compare the head loss that would result from the...Ch. 8 - In Problem 6.107, a theoretical flow rate of water...Ch. 8 - A pipeline is needed to transport medium fuel oil...Ch. 8 - Medium fuel oil at 25 C is to be pumped at a flow...Ch. 8 - A tremendous amount of study has gone into the...Ch. 8 - In a given installation, it is determined that the...Ch. 8 - "Laminar" fountains have become quite popular due...Ch. 8 - Use PIPE-FLO to model a straight horizontal run of...
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- Auto Controls A union feedback control system has the following open loop transfer function where k>0 is a variable proportional gain i. for K = 1 , derive the exact magnitude and phase expressions of G(jw). ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities. iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin) iv. what happens to the gain margin and Phase margin when you increase the value of K?you You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus NO COPIED SOLUTIONSarrow_forwardThe 120 kg wheel has a radius of gyration of 0.7 m. A force P with a magnitude of 50 N is applied at the edge of the wheel as seen in the diagram. The coefficient of static friction is 0.3, and the coefficient of kinetic friction is 0.25. Find the acceleration and angular acceleration of the wheel.arrow_forwardAuto Controls Using MATLAB , find the magnitude and phase plot of the compensators NO COPIED SOLUTIONSarrow_forward
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