EBK APPLIED FLUID MECHANICS
7th Edition
ISBN: 8220100668340
Author: UNTENER
Publisher: PEARSON
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Textbook Question
Chapter 5, Problem 5.61PP
A boat is shown in Fig. 5.33(a). Its geometry at the water line is the same as the top surface. The hull is solid. Is the boat stable?
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Consider the bar, shown in Figure 1 that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
x=0.0
x=2.0
2.0m
10 kN
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x))
-) +1(x) = 0.
d.x
dx
What are the accompanying boundary conditions for this bar?
b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM
approximation over the element.
1
2
3
1
2
1m
1m
Figure 2: Mesh of 2 elements. Elements are numbered with underlines.
c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is,
AE
Uj
N;(x)l(x)dx
– Ng(0)f(0)
¥ [4]}]{{}}={{{}\(\\+} + {N(2)f(2) = N (0)5() },
(1)
0, respectively.
L
=
(2)
where f(2) and f(0) denote the boundary forces at positions x 2 and x
Evaluate…
answer please
amination)
Question 1
Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
10 kN
X
x=0.0
x=2.0
2.0m
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x)) + 1(x) = 0.
dx
dx
What are the accompanying boundary conditions for this bar?
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DII
F5
F6
F7
F8
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F3
F4
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20
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Chapter 5 Solutions
EBK APPLIED FLUID MECHANICS
Ch. 5 - The instrument package shown in Fig. 5.18 weighs...Ch. 5 - A 1.0 -m-diameter hollow sphere weighing 200 N is...Ch. 5 - A certain standard steel pipe has an outside...Ch. 5 - A cylindrical float has a 10 -in diameter and is...Ch. 5 - A buoy is a solid cylinder 0.3 m in diameter and...Ch. 5 - A float to be used as a level indicator is being...Ch. 5 - A concrete block with a specific weight of...Ch. 5 - Figure 5.19shows a pump partially submerged in oil...Ch. 5 - A steel cube 100mm on a side weighs 80N. We want...Ch. 5 - A cylindrical drum is 2 ft in diameter, 3 ft long,...
Ch. 5 - If the aluminum weights described in Problem 5.10...Ch. 5 - Figure 5.20 shows a cube floating in a fluid....Ch. 5 - A hydrometer is a device for indicating the...Ch. 5 - For the hydrometer designed in Problem 5.13 what...Ch. 5 - For the hydrometer designed in Problem 5.13 , what...Ch. 5 - A buoy is to support a cone-shaped instrument...Ch. 5 - A cube has side dimensions of 18.00 in. It is made...Ch. 5 - A cube has side dimensions of 18.00 in. It is made...Ch. 5 - A ship has a mass of 292 Mg. Compute the volume of...Ch. 5 - An iceberg has a specific weight of 8.72kN/m3....Ch. 5 - A cylindrical log has a diameter of 450 mm and a...Ch. 5 - The cylinder shown in Fig. 5.23 is made from a...Ch. 5 - If the cylinder from Problem 5.22 is placed in...Ch. 5 - A brass weight is to be attached to the bottom of...Ch. 5 - For the cylinder with the added brass (described...Ch. 5 - For the composite cylinder shown in Fig. 5.25 what...Ch. 5 - A vessel for a special experiment has a hollow...Ch. 5 - A light foam cup similar to a disposable coffee...Ch. 5 - A light foam cup similar to a disposable coffee...Ch. 5 - Repeat Problem 5.29, but consider that the steel...Ch. 5 - Figure 5.27 shows a raft made of four hollow drums...Ch. 5 - Figure 5.28 shows the construction of the platform...Ch. 5 - For the raft shown in Fig. 5.27, how much of the...Ch. 5 - For the raft and platform shown in Figs. 5.27 and...Ch. 5 - A float in an ocean harbor is made from a uniform...Ch. 5 - Describe how the situation described in Problem...Ch. 5 - A cube 6.00 in on a side is made from aluminum...Ch. 5 - Prob. 5.38PPCh. 5 - A cylindrical block of wood is 1.00 m in diameter...Ch. 5 - A container for an emergency beacon is a...Ch. 5 - The large platform shown in Fig. 5.29 carries...Ch. 5 - Will the cylindrical float described in Problem...Ch. 5 - Will the buoy described in Problem 5.5 be stable...Ch. 5 - Will the float described in Problem 5.6 be stable...Ch. 5 - A closed, hollow, empty drum has a diameter of...Ch. 5 - Figure 5.30 shows a river scow used to carry bulk...Ch. 5 - Prob. 5.47PPCh. 5 - For the vessel shown in Fig. 5.26and described in...Ch. 5 - For the foam cup described in Problem 5.28, will...Ch. 5 - Referring to Problem 5.29, assume that the steel...Ch. 5 - Referring to Problem 5.30, assume that the steel...Ch. 5 - Prob. 5.52PPCh. 5 - Will the cylinder together with the brass plate...Ch. 5 - A proposed design for a part of a seawall consists...Ch. 5 - A platform is being designed to support some water...Ch. 5 - Prob. 5.56PPCh. 5 - A barge is 60 ft long, 20 ft wide, and 8 ft deep....Ch. 5 - If the barge in Problem 5.57 is loaded with 240000...Ch. 5 - A piece of cork having a specific weight of...Ch. 5 - Figure 5.20 shows a cube floating in a fluid, (a)...Ch. 5 - A boat is shown in Fig. 5.33(a). Its geometry at...Ch. 5 - (a) If the cone shown in Fig. 5.34 is made of pine...Ch. 5 - Refer to Fig. 5.35. The vessel shown is to be used...Ch. 5 - Prob. 5.64PPCh. 5 - Wetsuits are prohibited in some triathlons due to...Ch. 5 - A cylinder that is 500 mm in diameter and 2.0 m...Ch. 5 - The diving bell shown in Fig. 5.2 weighs 72 kN and...Ch. 5 - Prob. 5.68PPCh. 5 - A scuba diver with wet suit, tank, and gear has a...Ch. 5 - Prob. 5.70PPCh. 5 - Does steel float? It has a specific gravity of...Ch. 5 - Prob. 5.72PPCh. 5 - An undersea camera (Figure 5.36 ) is to hang from...Ch. 5 - Work Problem 5.73 again, but this time the camera...Ch. 5 - Write a program for evaluating the stability of a...Ch. 5 - For any cylinder of a uniform density floating in...Ch. 5 - For the results found in Project 2, compute the...Ch. 5 - Write a program for evaluating the stability of a...Ch. 5 - Write a program for determining the stability of a...
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