Theory and Design for Mechanical Measurements
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 5.1P
To determine

The differences between an error and an uncertainty and the ways in which uncertainty can be estimated for a measured value.

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Explanation of Solution

An error is the difference between measured value and the actual value of the measured quantity. Since we do not know the exact value, or the true value is unknown, the error is estimated. This numerical estimation is called an uncertainty. Errors are regarded as the effects whereas uncertainties are the numbers which define the amount of errors. Errors are caused due to number reasons, but the uncertainty is a number which the amount of error from the true value.

Ways to estimate the uncertainty for a measured value:

Systematic Uncertainty: The error due to systematic uncertainty remains constant under fixed operating conditions. It might cause a high offset or a low offset in the determined estimate of the true value of the measured variable. Since the value of systematic error is constant, it difficult to estimate and to recognize its presence. The systematic error is represented by an interval, b. The value b is the estimate of the systematic standard uncertainty. The interval defined by the systematic uncertainty at the 95% probability level is written as ±B=±2b

  • Random Uncertainty: The probable range of the random error is estimated by random uncertainty.

The random uncertainty level is ±sx¯.



The degrees of freedom are, ν=N1.

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Chapter 5 Solutions

Theory and Design for Mechanical Measurements

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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