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 5.40P
The power usage of a DC strip heater can be determined in cither of two ways: (1) Heater resistance and voltage drop can be measured simultaneously and power computed, or (2) heater voltage drop and current can be measured simultaneously and power computed. Instrument manufacturer specifications are listed (assume 95% level):
| Instrument | Resolution | Uncertainty (% reading) |
| Ohmmeter | 1 Q | 0.5% |
| Ammeter | 0.5 A | 1% |
| Voltmeter | 1 V | 0.5% |
For loads of 10 W, 1 kW, and 10 kW, determine the best method based on an appropriate uncertainty analysis. Assume nominal values as necessary for resistance, current, and voltage.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
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
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.
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
- To 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_forwardThe actual value of pressure differential for flow across a venturimeter is 60 mm WC. The measured values using a pressure sensor are; Confidence level 95% mm WC 59.8,59.2,59.7,60.2,60.3,60.1,60.5 Estimate Bias uncertainty (1) Precision uncertainty (2) Total uncertainty (3)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_forward
- The shear modulus, G, of an alloy can be determined by measuring the angular twist, θ,resulting from a torque applied to a cylindrical rod made from the alloy. For a rod of radius Rand a torque applied at a length L from a fixed end, the modulus is found by G=2LT/pR4θ.Examine the effect of the relative uncertainty of each measured variable on the shearmodulus. If during test planning all of the uncertainties are estimated to be 1%, what is theuncertainty in G?arrow_forwardPressure 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_forwardA 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.arrow_forward
- The 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_forwardn a certain dynamic measurement application the input(x) – output(y) relationship is given by y=1+(1+x)e^(-x) With what uncertainty must x be determined to yield a relative uncertainty of ±5 percent for y at a value of x = 2,4arrow_forwardA 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 dc Output: 0-5Vdc Range: 0-5 cm The transducer output is to be indicated on a voltmeter 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. Assume 95% confidence. The displacement transducer above is used in measuring the displacement of a body impacted by a mass. Twenty measurements are made, which yield Determine a best estimate for the mass displacement at 95% probability based on all available information.arrow_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 dc Output: 0-5Vdc Range: 0-5 cm The transducer output is to be indicated on a voltmeter 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. Assume 95% confidence. The displacement transducer above is used in measuring the displacement of a body impacted by a mass. Twenty measurements are made, which yield X= 17.20mm Sx= 1.70mm Determine a best estimate for the mass displacement at 95% probability based on all available information.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_forwardThe heat transfer between a solid body and a fluid medium is determined by the equation Q=h·A·(Ts-Tf). Here; Q is the amount of heat transferred, h is the heat transfer coefficient, A is the heat transfer surface area, Ts is the temperature of the surface and Tf is the temperature of the fluid. These parameters were measured as h=250±1.75 W/m2ºC, A=20±0.75 m2, Ts =100±0.75ºC and Tf =25±0.75ºC, including error levels. What is the total uncertainty in the amount of heat transferred, in ±%? a. 3.98 b. 4.07 c. 2.73 d. 2.95 e. 3.88arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY