Instructor: Lichuan Gui lichuan-gui@uiowa lcgui

1. Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)Time & Location: 2:30P - 3:20P MWF 218 MLHOffice Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net

2. Lecture 4. Measurement systems and static response

3. Measuring systems and their components Essential systems in fluid mechanics experiment 1. Physical system: flowing fluids, flow-producing apparatus, test models etc. 2. Measuring system: sensors, electric and electronic circuits, data acquisition and processing devices, and software 3. Experimenter(s): person(s) who plans, executes, and interprets the measurements - relationship between values of an input and an output Response of measuring system Inputs of measuring system 1. Desired inputs 2. Undesirable inputs a. interfering inputs - add noise to desired inputs b. modifying 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.

4. Filtering, compensation, and output correction Filters - used to reduce or eliminate undesirable input effects Filters 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 band 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

5. 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 fluctuations Bonded strain gauge V0 Rs1 Measuring gauge Rs2 Reference gauge V0 Rs1 Measuring gauge Analytical correction - remove undesirable effects & errors from output according to knowledge of undesirable inputs & system responses

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

7. Static response and static calibration Static system - constant or slowly varying input and output Static response 1. Theoretically determined by physical lawe.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 standard Effects of undesirable inputs: 1. Zero drift – parallel shift of primary calibration curve 2. Sensitivitydrift – a change in the slope of the primary calibration curve

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

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

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

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