Instructor: Lichuan Gui lichuan-gui@uiowa.edu http://lcgui.net 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

Lecture 4. Measurement systems and static response

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 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 - 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.

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

Filtering, compensation, and output correction - introduce additional interfering or modifying inputs to partly or entirely cancel the original undesirable effects. Example: Bonded strain gauge - sensitive to ambient-temperature fluctuations Rs1 Measuring gauge V0 𝑅 𝑠1 =𝛼 ∆𝑇 𝑅 𝑠 +∆𝑅 𝑉= 𝑅 3 𝑅 1 + 𝑅 3 + 𝑅 𝑠1 𝑅 2 + 𝑅 𝑠1 ∙ 𝑉 0 V0 Rs1 Measuring gauge Rs2 Reference gauge 𝑅 𝑠2 =𝛼 ∆𝑇 𝑅 𝑠 𝑅 𝑠1 =𝛼 ∆𝑇 𝑅 𝑠 +∆𝑅 𝑉= 𝑅 3 𝑅 1 + 𝑅 3 + 𝑅 𝑠1 𝑅 𝑠2 + 𝑅 𝑠1 ∙ 𝑉 0 = 𝑅 3 𝑅 1 + 𝑅 3 + 𝛼∙ 𝑅 𝑠 +∆𝑅 𝛼∙ 𝑅 𝑠 +∆𝑅 +𝛼∙ 𝑅 𝑠 ∙ 𝑉 0 = 𝑅 3 𝑅 1 + 𝑅 3 + 𝑅 𝑠 +∆𝑅 2𝑅 𝑠 +∆𝑅 ∙ 𝑉 0 Analytical correction - remove undesirable effects & errors from output according to knowledge of undesirable inputs & system responses

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. 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 3. Transmission used to transfer signals or other information from one component to another 4. Processing and storage used display or store output

Static response and static calibration Static system - constant or slowly varying input and output 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: 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. Sensitivity drift – a change in the slope of the primary calibration curve

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

Normality test and removal of outliers - 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. 𝑦 𝑖 =100 𝑖−1 𝑁 % Compute mean value and variance as 𝜇 𝑥 = 1 𝑁 𝑖=1 𝑁 𝑥 𝑖 𝜎 𝑥 2 = 1 𝑁−1 𝑖=1 𝑁 𝑥 𝑖 − 𝜇 𝑥 2 Plot yi vs. xi* on probability graph paper as right Normalize the repeat values as 𝑥 𝑖 ∗ = 𝑥 𝑖 − 𝜇 𝑥 𝜎 𝑥 Assess deviation of plotted points from the Gaussian line

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 output Identified by application of Chauvenet’s criterion Value xi is a outlier if 𝜏∙ 𝜎 𝑥 ≤ 𝑥 𝑖 − 𝜇 𝑥 Linear least-square fit (LLSF) A set of calibration measurements: LLSF line equation:

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