Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 8.1, Problem 8.11P
The gas pipe line is supported every 20 ft by concrete piers and also lays on the ground. If there are rigid retainers at the piers that hold the pipe fixed, determine the longitudinal and hoop stress in the pipe if the temperature rises 60°F from the temperature at which it was installed. The gas within the pipe is at a pressure of 600 lb/in2. The pipe has an inner diameter of 20 in. and thickness of 0.25 in. The material is A-36 steel.
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You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (p = 0.001 kg m-1 s-1) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
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applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
y = +h
I
2h = 1 cm
x1
y = -h
u(y)
1 dP
2μ dx
-y² + Ay + B
moving plate
stationary plate
U
2
I2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
Question 1
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
1 dP
u(y)
=
2μ dx
-y² + Ay + B
y= +h
Ꮖ
2h=1 cm
1
x1
y = −h
moving plate
stationary plate
2
X2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
(a) By considering the appropriate boundary conditions, show that the constants take
the following forms:
U
U
1 dP
A =…
Question 2
You are an engineer working in the propulsion team for a supersonic civil transport
aircraft driven by a turbojet engine, where you have oversight of the design for the
engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can
operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are
asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of
14,000 m. For all parts of the question, you can assume that the flow path of air through
the engine has a circular cross section.
(a)
← intake
normal
shock
472 m/s
A B
(b)
50 m/s
H
472 m/s
B
engine
altitude: 14,000 m
exhaust nozzle
E
F
exit to
atmosphere
diameter: DE = 0.30 m
E
F
diameter: DF = 0.66 m
Figure Q2: Propulsion system for a supersonic aircraft.
a) When the aircraft is at an altitude of 14,000 m, use the International Standard
Atmosphere in the Module Data Book to state the local air pressure and tempera-
ture. Thus show that the aircraft speed…
Chapter 8 Solutions
Mechanics of Materials (10th Edition)
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Ch. 8.1 - The gas pipe line is supported every 20 ft by...Ch. 8.1 - A pressure-vessel head is fabricated by welding...Ch. 8.1 - An A-36-steel hoop has an inner diameter of 23.99...Ch. 8.1 - The ring, having the dimensions shown, is placed...Ch. 8.1 - The inner ring A has an inner radius r1 and outer...Ch. 8.1 - Two hemispheres having an inner radius of 2 ft and...Ch. 8.1 - In order to increase the strength of the pressure...Ch. 8.2 - Show the results on the left segment.Ch. 8.2 - Show the stress that each of these loads produce...Ch. 8.2 - Fundamental Problems F81. Determine the normal...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the magnitude of the load P that will...Ch. 8.2 - Determine the state of stress at point B. Show the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Show the results in a differential element at the...Ch. 8.2 - Determine the shortest distance d to the edge of...Ch. 8.2 - The plate has a thickness of 20 mm and P acts...Ch. 8.2 - Plot the distribution of normal stress acting...Ch. 8.2 - Also, plot the normal-stress distribution over the...Ch. 8.2 - If the allowable normal stress for the steel is...Ch. 8.2 - If the applied force P = 1.50 kip, determine the...Ch. 8.2 - Determine the maximum normal stress on the cross...Ch. 8.2 - If the wood has an allowable normal stress of...Ch. 8.2 - Determine the maximum normal stress along section...Ch. 8.2 - Sketch the stress distribution along section aa of...Ch. 8.2 - Sketch the normal-stress distribution acting over...Ch. 8.2 - Determine the state of stress at points A and B,...Ch. 8.2 - If the force of 100 N is applied to the handles,...Ch. 8.2 - Determine the stress components at point A on the...Ch. 8.2 - Determine the stress components at point B on the...Ch. 8.2 - Determine the normal stress developed at points A...Ch. 8.2 - Sketch the normal-stress distribution acting over...Ch. 8.2 - Determine the state of stress at points A and B,...Ch. 8.2 - Determine the state of stress at point A on the...Ch. 8.2 - Determine the state of stress at point B on the...Ch. 8.2 - Determine the state of stress acting at point D....Ch. 8.2 - Determine the state of stress acting at point E....Ch. 8.2 - If it is subjected to the force system shown,...Ch. 8.2 - Solve Prob.840 for point B.Ch. 8.2 - Determine the stress components acting on the...Ch. 8.2 - Determine the stress components acting on the...Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - Neglect the weight of the block.Ch. 8.2 - He is supported uniformly by two bars, each having...Ch. 8.2 - Determine the state of stress at point A, and show...Ch. 8.2 - Determine the state of stress at point B, and show...Ch. 8.2 - Determine the state of stress at point C, and show...Ch. 8.2 - Determine the maximum radius e at which the load P...Ch. 8.2 - Specify the region to which this load can be...Ch. 8.2 - Determine the smallest force P that can be applied...Ch. 8.2 - The coiled spring is subjected to a force P. If we...Ch. 8.2 - The pins at C and D are at the same location as...Ch. 8.2 - Determine the state of stress at point A, and show...Ch. 8.2 - Determine the state of stress at point B, and show...Ch. 8.2 - Determine the stress components at points A and B...Ch. 8.2 - Determine the stress components at points C and D...Ch. 8.2 - Determine the stress components in the support...Ch. 8.2 - Determine the stress components in the support...Ch. 8.2 - If the force at the ram on the clamp at D is P= 8...Ch. 8.2 - Determine the maximum ram force P that can be...Ch. 8.2 - and an outer radius of 3.00 in. If the face of the...Ch. 8.2 - for points E and F.Ch. 8.2 - Determine the stress components at points A and B...Ch. 8.2 - Solve Prob.8-65 for points C and D.Ch. 8.2 - Due to internal gearing, this causes the block to...Ch. 8.2 - Determine the state of stress at point A and show...Ch. 8.2 - Solve Prob.868 for point B.Ch. 8.2 - Determine the stress components at point A. Sketch...Ch. 8.2 - for the stress components at point B.Ch. 8.2 - Determine the state of stress at point A at...Ch. 8.2 - Determine the state of stress at point B at...Ch. 8 - If it supports a cable loading of 800 lb,...Ch. 8 - Determine the state of stress at point E on the...Ch. 8 - Determine the state of stress at point F on the...Ch. 8 - The suspender arm AE has a square cross-sectional...Ch. 8 - If the cross section of the femur at section aa...Ch. 8 - If it has a mass of 5 kg/m, determine the largest...Ch. 8 - and is used to support the vertical reactions of...Ch. 8 - and is used to support the vertical reactions of...
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