Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 1, Problem 1.35P
The acceleration of a cart down a plane inclined at an angle a to horizontal can be determined by measuring the change in speed of the cart at two points, separated by a distance s, along the inclined plane. Suppose two photocells are fixed at the two points along the plane. Each photocell measures the time for the cart, which has a length L, to pass it. Identify the important variables in this test. List any assumptions that you feel are intrinsic to such a test. Suggest a concomitant approach. How would you interpret the data to answer the question?
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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
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
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 1 Solutions
Theory and Design for Mechanical Measurements
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Discuss how the resolution of the display scale of...Ch. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10P
Ch. 1 - State the purpose of using randomization methods...Ch. 1 - Provide an example of repetition and replication...Ch. 1 - Develop a test plan that might be used to estimate...Ch. 1 - Develop a test plan that might be used to evaluate...Ch. 1 - A race engine shop has just completed two engines...Ch. 1 - A thermodynamics model assumes that a particular...Ch. 1 - Regarding the Mars Climate Orbiter spacecraft...Ch. 1 - A large batch of carefully made machine shafts can...Ch. 1 - Suggest an approach or approaches to estimate the...Ch. 1 - Suggest a test matrix to evaluate the wear...Ch. 1 - Figure 1.15 Orifice flow meter setup used for...Ch. 1 - The sale of motor fuel is an essential business in...Ch. 1 - Using either the ASME 19.5 or ISO 5167 test...Ch. 1 - A simple thermocouple circuit is formed using two...Ch. 1 - 1.25 A linear variable displacement transducer...Ch. 1 - For the LVDT calibration of the previous problem,...Ch. 1 - A manufacturer wants to quantify the expected...Ch. 1 - Prob. 1.28PCh. 1 - As described in a preceding problem, the...Ch. 1 - Light gates may be used to measure the speed of...Ch. 1 - You estimate your car’s fuel use by recording...Ch. 1 - When discussing concomitant methods, we used the...Ch. 1 - Prob. 1.33PCh. 1 - For the strain gauge calibration of the previous...Ch. 1 - The acceleration of a cart down a plane inclined...Ch. 1 - In general, what is meant by the term “standard”?...Ch. 1 - A common scenario: An engineer has two pencil-...Ch. 1 - Explain the potential differences in the following...Ch. 1 - Research the following test standards and codes....Ch. 1 - A hotel chain based in the United States contracts...Ch. 1 - Test code ASTM 558-13 allows for the comparison of...Ch. 1 - Suggest a reasonable number of significant digits...Ch. 1 - Using spreadsheet software (such as Microsoft...Ch. 1 - Prob. 1.44PCh. 1 - Round the following numbers to 3 significant...Ch. 1 - Express the result, rounding to an appropriate num...Ch. 1 - Express the result by rounding to an appropriate...Ch. 1 - A car’s speed is determined by the time it takes...Ch. 1 - How much error could you tolerate in (1) book...Ch. 1 - Apply the guidelines to determine the number of...Ch. 1 - Using a tape measure having 1 mm graduations, the...Ch. 1 - Show how the following functions can be...Ch. 1 - Prob. 1.53PCh. 1 - For the calibration data of Table 1.5, determine...Ch. 1 - Prob. 1.55PCh. 1 - Each of the following equations can be represented...Ch. 1 - Plot y = 10e“° 5x volts on in semilog format (use...Ch. 1 - Prob. 1.58PCh. 1 - Prob. 1.59P
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