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Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

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2 Lecture 4. Measurement systems and static response

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3 Measuring systems and their components Essential systems in fluid mechanics experiment flowing fluids, flow-producing apparatus, test models etc.1. Physical system: 2. Measuring system: 3. Experimenter(s): sensors, electric and electronic circuits, data acquisition and processing devices, and software person(s) who plans, executes, and interprets the measurements Response of measuring system - relationship between values of an input and an output Inputs of measuring system 1. Desired inputs 2. Undesirable inputs a. interfering inputs b. modifying inputs - add noise to desired inputs - change response to desired inputs Example: hot-wire anemometer used to measure air jet flow from a nozzle to lab room - The draft of air produced by ventilation system in lab acts as interfering inputs. - The room temperature change acts as modifying inputs.

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4 Filtering, compensation, and output correction Filters- used to reduce or eliminate undesirable input effects - no-pass filters remove all fluctuations, permitting only a steady component - low-pass filters remove fluctuations with frequencies above a cut-off value - high-pass filters remove fluctuations with frequencies below a cut-off value - band-pass filters remove all fluctuations except those with frequencies within a certain band - band-reject filters remove all fluctuations with frequencies within a certain band Filters classified according to frequency range: Filters classified in terms of physical operation - electrical-electronic filters, applied to electric signals; - mechanical filters, designed to filter motion or force fluctuations, e.g. shock absorbers used to reduce vibration of an apparatus; - thermal filters, designed to remove temperature fluctuations, e.g. thermal insulation - electromagnetic filters, designed to remove the interfering effects of electric and magnetic fields - digital filters, applied to recorded signals

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R s1 Measuring gauge V0V0 Filtering, compensation, and output correction Compensation- introduce additional interfering or modifying inputs to partly or entirely cancel the original undesirable effects. Example: - sensitive to ambient-temperature fluctuationsBonded strain gauge V0V0 R s1 Measuring gauge R s2 Reference gauge Analytical correction- remove undesirable effects & errors from output according to knowledge of undesirable inputs & system responses 5

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6 Modes and functions of measuring system components Operation modes: Response modes: 1. Passive – output energy supplied by input 2. Active – output energy supplied by external excitation source Functions of measuring system components: 1. Sensing used to produce output 2. Convection and conditioning used to transform output to a form, amplitude, or both more suitable for observation or further processing - analogue, discrete (digital, binary, etc.), or hybrid 3. Transmission used to transfer signals or other information from one component to another 4. Processing and storage used display or store output

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7 Static response and static calibration Static system - constant or slowly varying input and output Static calibration: 1. Zero drift – parallel shift of primary calibration curve 2. Sensitivity drift – a change in the slope of the primary calibration curve - determine input-output relationship (calibration curve) with standard system - performed separated for each desired input - accuracy depends on that of instruments used as standard Effects of undesirable inputs: Static response 1. Theoretically determined by physical law e.g. liquid manometer for gas pressure difference measurement, Fig. (a) Hydrostatic law: 2. More commonly determined by static calibration, e.g. variable-reluctance pressure transducer, Fig. (b) calibrated with liquid manometer:

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8 Static response and static calibration Static performance characteristics: Static sensitivity Scale readability Span (input full-scale) Full-scale output Dynamic range Non-linearity Threshold Resolution Hysteresis - slope of input-output relationship - ratio of largest to smallest values of input - smallest input level for detectable output - difference between the output value corresponding to an input value reached from below and the output value corresponding to the same input value reached from above. Elastic hysteresis of an band Input - constant in linear system linear - range of input to be measured with acceptable accuracy span - range of output values measured from minimum to maximum input values - local sensitivity varies over input range in non-linear system non-linear - minimum change in output can be observed - smallest input change for detectable output change - maximum deviation of actual response from straight line determined by least-square fit of calibration measurements

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9 Normality test and removal of outliers Normality test - Used to assess randomness of repeat measurement values Rearrange a number of repeat values x i, i=1,2, ,N, so that x i x i+1 Compute percentage of repeat values that are not more than x i, i.e. Compute mean value and variance as Normalize the repeat values as Plot y i vs. x i * on probability graph paper as right Assess deviation of plotted points from the Gaussian line

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10 Normality tests and removal of outliers Outliers Spurious values due to (2) Temporary or intermittent undesirable input (1) human error, e.g. misreading of an instrument’s output Identified by application of Chauvenet’s criterion Value x i is a outlier if Linear least-square fit (LLSF) A set of calibration measurements: LLSF line equation:

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11 Homework - Questions and Problems: 1, 4 on page 41 - Read textbook 2.1-2.2 on page 19-31 - Due on 08/31

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