Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 5, Problem 5.42P
A thermocouple is a temperature sensor made of two electrical conductors each of different materials. The conductors are electrically connected at two points, called junctions, each junction exposed to a different temperature. The thermocouple generates a voltage relative to the temperature gradient between junctions. Table 8.6 lists values of voltage as a function of temperature relative to one junction maintained at 0 °C for a thermocouple made from joining an iron wire with a constantan (chrome- nickel) wire. Estimate the sensitivity of the wire at 1 (X) “C (one junction) relative to 0 °C (one junction).
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
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subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
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for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
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Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 5 Solutions
Theory and Design for Mechanical Measurements
Ch. 5 - Prob. 5.1PCh. 5 - Explain what is meant by the terms “true value,"...Ch. 5 - SJ An official Olympics timekeeper once stated,...Ch. 5 - A tachometer has an analog display dial graduated...Ch. 5 - An automobile speedometer is graduated in 5-mph...Ch. 5 - An engineer reads the height of a mercury...Ch. 5 - Prob. 5.8PCh. 5 - Two resistors arc to be combined to form an...Ch. 5 - An equipment catalog boasts that a pressure...Ch. 5 - The shear modulus, G, of an alloy can be...
Ch. 5 - Heat transfer from a rod of diameter D immersed in...Ch. 5 - Estimate the design-stage uncertainty in...Ch. 5 - Explain the critical dift'erence(s) between a...Ch. 5 - A displacement transducer has the following...Ch. 5 - Prob. 5.18PCh. 5 - For a thin-walled pressure vessel of diameter D...Ch. 5 - Suppose a measured normal stress contains three...Ch. 5 - Prob. 5.31PCh. 5 - The area of a flat, rectangular parcel of land is...Ch. 5 - Estimate the random standard uncertainty in the...Ch. 5 - Estimate the uncertainty at 95% confidence in the...Ch. 5 - One use for a GPS rangefinder is on the golf...Ch. 5 - A pressure measuring system outputs a voltage that...Ch. 5 - The density of a metal composite is to be...Ch. 5 - A temperature measurement system is calibrated...Ch. 5 - The power usage of a strip heater is to be...Ch. 5 - The power usage of a DC strip heater can be...Ch. 5 - A thermocouple is a temperature sensor made of two...Ch. 5 - Time variations in a signal require that the...Ch. 5 - A hand-held infrared thermometer from a well-...Ch. 5 - The pressure in a large vessel is to be maintained...Ch. 5 - The cooling of a thermometer (c.g., Exs. 3.3 and...Ch. 5 - A J-type thermocouple monitors the temperature of...Ch. 5 - The density of air must be known to within 0.5%....Ch. 5 - In pneumatic conveying, solid particles such as...Ch. 5 - A step test is run to determine the time constant...Ch. 5 - The acceleration of a cart down a plane inclined...Ch. 5 - The heat flux in a reaction is estimated by Q =...Ch. 5 - A comparative test uses the relationship R =...Ch. 5 - A sensitive material is to be contained within a...Ch. 5 - A geometric stress concentration factor, K,, is...Ch. 5 - In Problem 5.9, we assumed that the errors in die...
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