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 5.55P
The heat flux in a reaction is estimated by Q = 5(T\ — FzJkJ/s. Two thermocouples are used to measure T\ and Ti. Each thermocouple hits a systematic uncertainty of 0.2 °C (95%). Based on a large sample of measurements, Ti = 180 °C, 7\ = 90°C, and the random standard uncertainty in each temperature measurement is 0.1 °C. Assume large degrees of freedom. Compare the uncertainty in heat flux if the thermocouple systematic errors are (a) uncorrelated and (b) correlated. Explain.
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Students have asked these similar questions
A handbook value for the thermal expansion
coefficient of a particular pure metal is a = 16.52 X
10-6 °C-1 and states that the possible error in this
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The heat transfer conducted through material is calculated from the equation:
Q = KX AXTD/L
Where K: Conductivity of material
A: Area of heat transfer
TD: Temperature difference across material
L: Thickness of material
A student measures the area, thickness and temperature difference and assumes that the error in conductivity is negligible. The
student also estimates the uncertainty range for each variable.
In estimating the maximum possible value of Q, the student should use the following formula:
A
B
Q max= K x A max x TD max / L max
Q max= K x A max x TD max / L nom
Q max= Q nominal + dQ/dLmin
Q max= K x A max x TD max / L min
QUESTION 1
You find that statistical uncertainty is your largest measurement uncertainty and that the V value is your largest propagated uncertainty. How can you try to improve both uncertainties in the simplest. but most effective way?
O use a new V instrument and a new DV instrument to collect more measurements at a wicer variety of V data points
O collect DV data for new IV data points
O use a new V instrument but the same DV instrument to collect the same numtber of measurements at a wicer variety of IV data points
o take more measurements for the DV value at the IV data points aiready collected and add more IV data points
O use a new DV instrument to take more DV measurements for the Ivdata points already collected and collect additional DV data for more IV data points not previcusly measured
o start over to collect the same number of DV measurements as before. but al a greater variety of IV data points than before
o take more measurements for the DV values at the IV data points…
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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