2 Lecture 4. Measurement systems and static response
3 Measuring systems and their components Essential systems in fluid mechanics experiment1. Physical system:flowing fluids, flow-producing apparatus, test models etc.2. Measuring system:sensors, electric and electronic circuits, data acquisition and processing devices, and software3. Experimenter(s):person(s) who plans, executes, and interprets the measurementsResponse of measuring system- relationship between values of an input and an outputInputs of measuring system1. Desired inputs2. Undesirable inputsa. interfering inputs- add noise to desired inputsb. modifying inputs- change response to desired inputsExample: 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.
4 Filtering, compensation, and output correction Filters- used to reduce or eliminate undesirable input effectsFilters classified according to frequency range:- 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 bandFilters 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
6 Modes and functions of measuring system components Operation modes:- analogue, discrete (digital, binary, etc.), or hybridResponse modes:1. Passive – output energy supplied by input2. Active – output energy supplied by external excitation sourceFunctions of measuring system components:1. Sensing used to produce output2. Convection and conditioning used to transform output to a form, amplitude, or both more suitable for observation or further processing3. Transmission used to transfer signals or other information from one component to another4. Processing and storage used display or store output
7 Static response and static calibration Static system- constant or slowly varying input and outputStatic response1. 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:Static calibration:- performed separated for each desired input- determine input-output relationship (calibration curve) with standard system- accuracy depends on that of instruments used as standardEffects of undesirable inputs:1. Zero drift – parallel shift of primary calibration curve2. Sensitivity drift – a change in the slope of the primary calibration curve
8 Static response and static calibration InputOutput- local sensitivity varies over input range in non-linear systemnon-linear- maximum deviation of actual response from straight line determined by least-square fit of calibration measurementsStatic performance characteristics:- range of input to be measured with acceptable accuracyspan- range of output values measured from minimum to maximum input valuesfull-scale outputStatic sensitivity- minimum change in output can be observed- slope of input-output relationship- smallest input change for detectable output change- constant in linear systemlinearScale readabilitySpan (input full-scale)Full-scale outputDynamic range- ratio of largest to smallest values of inputNon-linearityElastic hysteresis of an bandThreshold- smallest input level for detectable outputResolutionHysteresis- 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.
9 Normality test and removal of outliers - Used to assess randomness of repeat measurement valuesRearrange a number of repeat values xi, i=1,2,,N , so that xi xi+1Compute percentage of repeat values that are not more than xi , i.e.𝑦 𝑖 =100 𝑖−1 𝑁 %Compute mean value and variance as𝜇 𝑥 = 1 𝑁 𝑖=1 𝑁 𝑥 𝑖𝜎 𝑥 2 = 1 𝑁−1 𝑖=1 𝑁 𝑥 𝑖 − 𝜇 𝑥 2Plot yi vs. xi* on probability graph paper as rightNormalize the repeat values as𝑥 𝑖 ∗ = 𝑥 𝑖 − 𝜇 𝑥 𝜎 𝑥Assess deviation of plotted points from the Gaussian line
10 Normality tests and removal of outliers Spurious values due to(2) Temporary or intermittent undesirable input(1) human error, e.g. misreading of an instrument’s outputIdentified by application of Chauvenet’s criterionValue xi is a outlier if𝜏∙ 𝜎 𝑥 ≤ 𝑥 𝑖 − 𝜇 𝑥Linear least-square fit (LLSF)A set of calibration measurements:LLSF line equation:
11 Homework- Read textbook on page 19-31Questions and Problems: 1, 4 on page 41- Due on 08/31