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
Videos
Textbook Question
Chapter 5, Problem 5.37P
The density of a metal composite is to be determined from the mass of a cylindrical ingot. The volume of the ingot is determined from diameter and length measurements. It is estimated that mass m can be determined to within 0.1 lbm using an available balance scale; length L can be determined to within 0.05 in. and diameter I) to within 0.0(X)5 in. Instrumentation for each variable has a known calibration systematic uncertainty of 1% of its reading. Estimate the design-stage uncertainty in the determination of the density. Which measurement contributes most to the uncertainty in the density? Which measurement method should be improved first if the uncertainty in density is unacceptable? Use the nominal values of m = 4.5 lbm. L = 6 in., and D = 4 in. (Note: 1 lbm = 0.4535 kg; 1 inch = 0.0254 m.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Materials of Interest: CuFeS, in a silica matrix, 1.5% Cu (4.3318% CuFeS,); Top Size = 1.5 cm; CuFeS, grain size = 0.01 cm Desired sampling accuracy: +0.02% Cu, certainty of 0.99 (2.576 standard deviations) CuFeS, specific gravity=4.2: Overall specific gravity 2.8 Broad size distribution. Determine the minimum sample weight (in grams) needed for testing.
The transducer specified in Table 1.1 is chosen to measurea nominal pressure of 500 cm H2O. The ambient temperature is expected to vary between 18 ∘C and 25 ∘C duringtests. Estimate the possible range (magnitude) of each listedelemental error affecting the measured pressure refering to the solution provided online,
Sensitivity error(eK)
= (±0.0025)(500 cm H2O)= ± 0.75 cm H2O
= ± 0.00375 V
how do you get 0.75?? shoud it not be 1.25?
according the answer, for sensitivity
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.
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...
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
- Pressure distribution measurements are made on a two-dimensional wing model placed in a wind tunnel. The difference between the static pressure sockets on the surface and the static pressure of the free stream is measured. 30 data is taken at each measurement point. The average of the values measured from one of the sockets near the trailing edge was calculated as 2.30 Pa, and the standard deviation was calculated as 2.65 Pa. After applying the Chauvenet criterion to these measurement values, it was decided to eliminate 3 measurements and the new mean value was found to be 2.18 Pa and the standard deviation was 2.42. It was verified that the unexcluded data fit the normal distribution curve. Data above how many Pa and below how many Pa were eliminated? Estimate how many data have negative value (?<0) after elimination.arrow_forwardCardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…arrow_forwardMeasurement in Engineering Question is image C) ? c) Determine a 95% confidence interval for Nu and report the value.arrow_forward
- PLS ANSWER ASAP. THANK YOU! The slope of the calibration curve is based on __________. a. calibration limit b. calibration sensitivity c. calibration detection d. calibration functionarrow_forwardTo measure the density of a stone, a digital scale and a beaker cup filled with water are used. The balance is used to measure the mass of the stone, while the beaker is used to measure the volume of the stone. It is known that the digital balance has a resolution of 0.1 g and that the beaker cup has a resolution of 5 ml. Repeated mass measurements return the following values: 250.0 g; 249.9 g; 250.3 g; 249.6g; 250.1 g; 249.7g; 250.4 g; 250.0 g; 248.8 g; 250.2 g The volume is measured only once. Placing the stone in the beaker, a volume of displaced water equal to 50 ml is measured. Using a k=2.5, check if the density of the stone is compatible or out of line with the value ρ = (4910 ± 65) kg.m-3 (a) none of the above (b) the values are compatible (c) missing data to perform the compatibility test (d) the values are discrepantarrow_forwardcompute the 95 confidence intervals for the inventory of a series of 12 replication of the simulation of a system, where the VERAGE INVENtory is 1000 units and sample standard deviation is 38arrow_forward
- A company makes electrical resistors. The perfect resistor has a value of 400 ohms. A sample of 2000 resistors was tested and found to have a mean of 391.5 ohms and a standard deviation of 22.5 ohms. Assuming a normal distribution:a. How many resistors in the sample will have more than 440 ohms of resistance?b. How many resistors in the sample will have less than 360 ohms of resistance? note: you can use the frequency distribution table picture I attached.arrow_forwardThe transducer specified in Table 1.1 is chosen to measurea nominal pressure of 500 cm H2O. The ambient temperature is expected to vary between 18 ∘C and 25 ∘C duringtests. Estimate the possible range (magnitude) of each listedelemental error affecting the measured pressure. How do I calculate the sensitivity error? The solution that was given: Sensitivity error(eK) = (±0.0025)(500 cm H2O)= ± 0.75 cm H2O = ± 0.00375 V My Question is, how do you obtain 0.75 since 0.0025 x 500 gives 1.25! please help. thanksarrow_forwardIn a yogurt filling line, the containers are filled with yogurt. The producer uses a scale with anaccuracy of 1,8 percent of its range of 9 kg to measure the mass of each container in order to calculate theuncertainty in mass of the containers. 19 containers are selected at random and measured. The averagemass is 2 kg, and the standard deviation of the measurements is calculated to be 0,89 kg. Calculate the total uncertainty of the average mass of the containers at a 95 % confidence level.arrow_forward
- The volume of water in commercially supplied fresh drinking water containers is approximately normally distributed with mean 70 liters and standard deviation 0.75 liters. Estimate the proportion of containers likely to contain a) in excess of 70.9 liters, b) at most 68.2 liters, c) less than 70.5 liters.arrow_forwardCalculate the individual uncertainties associated for measuring this velocity from the provide individual values given by the manufacture. Then determine the design stage instrument uncertainty. Which uncertainty (or which couple of uncertainties) is the most significant contributor? You attempt to determine the validity of a mass balance in your lab by repeatedly placing 100 g calibration weight on it. Fifteen readings were obtained with values of 101.2, 100.1, 99.8, 100.5, 101.1, 100, 100, 99.6, 101.5, 100.8, 100.9, 100.3, 99.8, 100.5, and 100.9 Estimate the bias error and the maximum precision error of the measurementsarrow_forwardThe processing of raw coal involves “washing,” in which coal ash (nonorganic, incombustible material) is removed. The article “Quantifying Sampling Precision for Coal Ash Using Gy’s Discrete Model of the Fundamental Error” (Journal of Coal Quality, 1989:33–39) provides data relating the percentage of ash to the volume of a coal particle. The average percentage of ash for six volumes of coal particles was measured. The data are as follows: Volume (cm3) 0.01 0.06 0.58 2.24 15.55 276.02 Percent ash 3.32 4.05 5.69 7.06 8.17 9.36 Using the most appropriate model, predict the percent ash for particles with a volume of 48 cm3. Round answer to three decimal places. * the answer i got was of 6.260 was wrongarrow_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
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY