Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 8, Problem 8.27P
A J-type thermocouple is calibrated against an RTD standard within ±0.01 °C (95%) between 0 °C and 200 °C. The output voltage is measured with a voltmeter having 0.001 mV resolution and less than 0.015 mV (95%) systematic uncertainty. The reference junction temperature is 0 °C. The calibration procedure yields the following results:
7rtd (°C) 0.00 20.50 40.00 60.43 80.25 100.65 emf(mV) 0.010 1.038 2.096 3.207 4.231 5.336
- Determine a polynomial to describe the relation between the temperature and thermocouple voltage.
- Estimate the uncertainty in temperature using this thermocouple and voltmeter.
- Suppose the thermocouple is connected to a digital temperature indicator having a resolution of 0.1 °C with 0.3 °C (95%) systematic uncertainty. Estimate the uncertainty in indicated temperature.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A temperature measurement system is composed of a sensor and a readout device. The readout device has a claimed accuracy of 0.6 °C with a resolution of 0.1 °C. The sensor has an off-the-shelf limit of error of 0.5 °C. Estimate a design-stage uncertainty in the temperature indicated by this combination.
A displacement transducer has the following specifications:
Linearity error:±0.25% reading
Drift:±0.05%/°C reading Sensitivity error: ±0.25% reading
Excitation: 10-25 V
Output: dc 0-5Vdc
Range: 0-5 cm
The transducer output is to be indicated on a voltme- ter having a stated accuracy of 0:1% reading with a resolution of 10 μV. The system is to be used at room temperature, which can vary by 10 °C. Estimate an uncertainty in a nominal displacement of 2 cm at the design stage. Assume 95% confidence.
2. Consider the voltmeter calibration data in Table 1. Plot the data using a suitable scale.
a) Specify the percent maximum hysteresis based on full-scale range.
b) Referring to increasing input calibration, determined the sensitivity and linearity errors.
Increasing input (mV)
Decreasing input (mV)
X
Y
Y
0.0
1.0
0.1
5.0
5.0
1.1
4.0
4.2
2.0
2.1
3.0
3.2
3.0
3.0
2.0
2.2
4.0
4.1
1.0
1.2
5.0
5.0
Table 1: Calibration results
0.0
0.2
We wish to measure a characteristic of a machined part whose nominal size is 50 mm at 20 °C. For this, two different instruments are used; an analog micrometer and a digital vernier caliper, both recently calibrated and with the same resolution (0.01 mm). The calibration certificate data of the analog micrometer and the digital vernier are shown in tables 5 and 6 respectively. In both cases the calibration uncertainty does not include the contribution of resolution uncertainty. Additionally, there are drift studies for both instruments and it is established that the drift of the micrometer is ± 0.002 mm while the drift of the vernier is ± 0.02 mm.
The same number of measurements were performed with both instruments to avoid repeatability biases under controlled environmental conditions. Table 7 shows the results of the measurements of both instruments. The temperature of the piece was monitored with a digital thermometer whose calibration uncertainty is 0.1 °C, which already includes…
Chapter 8 Solutions
Theory and Design for Mechanical Measurements
Ch. 8 - Prob. 8.1PCh. 8 - Fixed temperature points in the International...Ch. 8 - Answers to the following questions may be found in...Ch. 8 - Calculate the resistance of a platinum wire that...Ch. 8 - Plot the resistance of a platinum wire that is 5 m...Ch. 8 - An RTD forms one arm of a Wheatstone bridge, as...Ch. 8 - An RTD forms one arm (/?4) of a Wheatstone bridge,...Ch. 8 - Research and describe current state-of-the-art...Ch. 8 - Prob. 8.9PCh. 8 - 8.10 Estimate the required level of uncertainty in...
Ch. 8 - 8.11 A thermistor is placed in a 100 °C...Ch. 8 - Prob. 8.12PCh. 8 - Prob. 8.13PCh. 8 - The thermocouple circuit in Figure 8.45 represents...Ch. 8 - The thermocouple circuit in Figure 8.45 represents...Ch. 8 - The thermocouple circuit in Figure 8.45 is...Ch. 8 - 8.17 a. The thermocouple shown in Figure 8.46a...Ch. 8 - Prob. 8.18PCh. 8 - Prob. 8.19PCh. 8 - A temperature measurement requires an uncertainty...Ch. 8 - A temperature difference of 3.0 °C is measured...Ch. 8 - Complete the following table for a J-type...Ch. 8 - Complete the following table for a T-type...Ch. 8 - Prob. 8.24PCh. 8 - 8.25 You are employed as a heating, ventilating,...Ch. 8 - A J-type thermocouple for use at temperatures...Ch. 8 - A J-type thermocouple is calibrated against an RTD...Ch. 8 - A beaded thermocouple is placed in a duct in a...Ch. 8 - Consider a welded thermocouple bead that...Ch. 8 - Prob. 8.30PCh. 8 - Prob. 8.31PCh. 8 - Consider the typical construction of a sheathed...Ch. 8 - An iron-constantan thermocouple is placed in a...Ch. 8 - Figure 8.48 Schematic diagram for Problems 8.33,...Ch. 8 - Figure 8.48 Schematic diagram for Problems 8.33,...Ch. 8 - 8.36 In Example 8.5, an uncertainty value for Rf...Ch. 8 - The thermocouple circuit shown in Figure 8.49...Ch. 8 - Prob. 8.38PCh. 8 - 8.39 A thin-film heat flux sensor employs a K-type...Ch. 8 - A thin-film heat flux sensor has a sensitivity uV...Ch. 8 - 8.41 A T-type thermopile is used to measure...Ch. 8 - 8.42 A T-type thermocouple referenced to 0 °C is...Ch. 8 - A T-type thermocouple referenced to 0 °C develops...Ch. 8 - 8.44 A temperature measurement system consists of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A thermocouple is used to measure the temperature T1. The thermocouple reference junction labeled 2 is at a temperature of 20°C. The voltage output is measured using a potentiometer and found to be 4.686 mV. What is T1 in degrees RK: if the temperature values are not in the table, you have to use interpolation. Select one: O a. 98 O b. 118 O c. 105 O d. 108 Previous page Next pagearrow_forwardA thermocouple was used to measure the temperature. Over the range of temperatures expected in the experiment, a linear regression analysis was performed for the temperature as a function of voltage. The best-fit equation was T = (-0.008563 + 220*V), where V is the thermocouple voltage. The voltage was fed into a 11-bit A/D converter with a voltage range of -8 V to 8 V. Determine the measurement resolution (in °C) due to the ADC? O 0.851 None O 3.113 1.710 0.393 4.960 1.144 O 3.797arrow_forwardA J-type thermocouple is used to measure the unknown steady-state temperature of a liquid. The sensor outputs a voltage of 2.532 mV. Using Equation 2 and Table 1.2, determine the unknown temperature. Show all calculations and assume the thermocouple is referenced to 0 °C. T = a₁ + a₂V + · ...+ a₂V² a a₁ 0.000 000 1.978 425 x 10-² -2.001 204 x 10¹7 1.036 969 x 10-¹1 -2.549 687 x 10-16 3.585 153 x 10-21 -5.344 285 x 10.26 5.099 890 x 10:³1 Table 1.2 -J-type thermocouple polynomial coefficients over the range of 0°C to 760°C ± 0.04°C 8₂ a3 a4 (2) as as a7arrow_forward
- 4:07 3G l. Moodle A bbb2.du.edu.om EE ...Session (15-3- Said Grami O College of Engineering Vision for the Future Question 3 During a step function calibration, a first-order instrument is exposed to a step change of 200 units. 1- If after 1.5 s the instrument indicates 140 units, find the instrument time constant. 2- find the error in the indicated value after 2 s S. 3- Find the raise time at 90 % of the system. y(0)=0 units; K=1 unit/unit. Question 4 A first order instrument with a time constant of 2 seconds is to be used to measure a periodic input. If a dynamic error of ±2% can be tolerated, 1- determine the maximum frequency of periodic input that can be measured. 2- What is the associated time lag (in seconds) at that frequency? MECH374: Instrumentation and Measurement Said Grami Practicearrow_forward13. The presence of a defect in the material illustrated in the figure (http://aero.tu sofia.bg/~vlados/ae2test04.png) was determined using: 109 omniscan TEEN TEL 000 2419 IN EV O Eddy current testing. O Radiography testing. O visual testing. Ultrasonic testing. KAU 1919 0:4 45 Aarrow_forwardThe following resistance of a platinum resistance thermometer were measured at a range of temperature. Determine the measurement sensitivity of the instrument in milli Ohms/ oC. Resistance (mῼ) Tempreture (oC) 210k 110 217k 89 221k 68 228k 47arrow_forward
- O Estimate the MRR (in cc/sec) of an alloy containing 18% cobalt, 62% nickel and 20% chromium during ECM with current of 500 ampere. The density of the alloy is 8.28 g/cc. The following data is available. Metal Gram atomic weight Velency Cobalt 58.93 Nickel 58.71 2 Chromium 51.99 Assume Faraday's constant is 96500 coulombs/ mole.arrow_forwardConsider the voltmeter calibration data in the following table. Plot the data using a suitable scale. Specify the percent maximum hysteresis based on full-scale range. Increasing Input [mV] Decreasing Input [mV] Y Y 0.0 0.1 5.0 5.0 1.0 1.1 4.0 4.2 2.0 2.1 3.0 3.2 3.0 3.0 2.0 2.2 4.0 4.1 1.0 1.2 5.0 5.0 0.0 0.2arrow_forwardi. Derive the linear and quatratic approximation of the below resistance temperature readings(temperature from 40 °c to 80 °c). (. ii. find out the resistance of RTD at a temperature of 200°c using linear approximation? ( Temperature 40 45 50 55 60[TO] 65 70 75 80 Resistance ohm 115.239 120.521 167.096 254.966 384.13 554.587 766.34 1019.38 1313.724arrow_forward
- A displacement transducer has the following specifications: Linearity error:±0.25% reading Drift:±0.05%/°C reading Sensitivity error: ±0.25% reading Excitation: 10-25 V Output: dc 0-5Vdc Range: 0-5 cm The transducer output is to be indicated on a voltme- ter having a stated accuracy of 0:1% reading with a resolution of 10 μV. The system is to be used at room temperature, which can vary by 10 °C. Estimate an uncertainty in a nominal displacement of 2 cm at the design stage. Assume 95% confidence.arrow_forward1. A process manufacturing missile component parts is being controlled, with the performance characteristic being the tensile strength in pounds per square inch. Samples of size 4 each are taken every hour and 30 samples are reported as below: 30 30 30 45219.84, Σ-1Τι = 321.6, Σ i= 1$i = 110.5 (a) Find trial control limits for X and R charts. (b) Repeat part (a) for X and S charts.arrow_forwardA thermostat control with dial markings from 0 to 100 is used to regulate the temperature of an oil bath. A calibration plot on logarithmic coordinates of the temperature, T (°F), versus the dial setting, R, is a straight line that passes through the points (R1 = 20.0, Ti =110.0 °F) and (R2 = 40.0, T2 = 250.0 °F). (a) Derive an equation for T (°F) in terms of R. (b) Estimate the thermostat setting needed to obtain a temperature of 320°F.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
What is Metrology in Mechanical Engineering? | Terminologies & Measurement; Author: GaugeHow;https://www.youtube.com/watch?v=_KhMhFRehy8;License: Standard YouTube License, CC-BY