ProblemsTFMT14 Question Instrumentation A B a) Which instrument is an active type of device? b) Indicate one main advantage of each type? Example Detection range and accuracy specs. • Calculate accuracy and relative error for I = 2.458 mA in all possible ranges. • Select the best range and answer why is the best? • Write the display indication of each resolution. Question • Calculate accuracy and relative error for I = 4.03 mA in all possible ranges. • Select the best range and answer why is the best? • Write the display indication of each resolution. Example Sensitivity http://www.colby.edu/chemistry/PChem/scripts/lsfitpl.html Example xy Example S = 0.233 Ω/°C Question Bias and sensitivity drift Question Linearity / Non-linearity Estimate the sensitivity in the 0-100Pa range and calculate the non-linearity of the gas sensor response for a C2Cl4 partial pressure of 70 Pa. Question Response order temperature raise B heater current temperature raise A Too bioreactors, A and B, have been characterized and show first order responses to heating. If the only difference between the reactors is their size, which is the larger reactor A or B? Question Precision / Accuracy The figure shows the statistical characterization of two different instrument measuring the same real value. Answer: • Which instrument is more precise? • Which instrument is more accurate? • Which instrument we should choose? instr. A instr. B signal value real value Accuracy Example characterization Example 3.10 (a), from L02 and Morris Ch.3 http://www.shodor.org/interactivate/activities/Histogram/ Example Alternatively Example 3.10 (b), from L02 and Morris Ch.3 Example 3.10 (c) α = 0.022/(10)1/2 = 0.007 α = 0.022/(1000)1/2 = 0.022/(10x102)1/2 = 0.022/10x(10)1/2 Question Error of the mean Quality control of nine batches of milk produce have recorded the following concentrations of cholesterol in [mg/100ml] is 7.45 7.66 7.20 7.54 7.86 7.13 7.14 7.75 7.30 Assuming a normal distribution of measured values: a) Calculate the mean value and standard deviation. b) Calculate the error of the mean! Example Random errors / Confidence interval 86.6 % Example Random errors / Confidence interval z=D/σ z = (2.5 - 3) / 0.25 z = -2 97.7% Question For the milk quality control problem Calculate the random error of a single measurement, using the previous data as reference measurement set, for 90% confidence interval. Choose the correct following figure to calculate the error.! Question Indicate (shading the area) in the following figure the probability that corresponds to measure a concentration of glucose smaller than 7.30 mg/100ml milk. ! Indicate (shading the area) in the following figure the probability that corresponds to measure a concentration of glucose larger than 7.42 and smaller than 7.60 mg/ 100ml milk. ! Question In a milk production plant the cholesterol concentration in the milk production is expressed with a 90% confidence as previously calculated, and in the daily production 100 samples of 100ml are taken for quality control. a) If 9 batches show cholesterol concentrations 12 mg/ml, is the production OK? b) If 11 batches show cholesterol concentrations 8 mg/ml, is the production OK? c) If 24 batches have the value 7.8 mg/ml, is the production OK? Question • Explain the concept of insertion error. • Insertion error is a systematic error or a random error? • Why? • How to minimize insertion error? Question • Explain how to measure the internal resistance RA of the ammeter in parallel with the potentiometer. • Which parameters are fixed, and which at varied during the measurement? • Which ratio between the total I and IRA is set? Example Error propagation S = (1.5V + 1.5V) ± e e = [(0.01x1.5)2 + (0.01x1.5)2]1/2 = 0.021 V 100x0.021/3 = ±0.7% Question Error propagation Question Error propagation One parameter used for comparison of bioreactor performance is the power input (P/V) where the power numbers (Np) is a function of the Re number, d is the impeller diameter, [m] N is the agitation speed [rpm], ρ is the density [kg/m3] and V the working volume [m3]. Calculate the error in the P/V determination if: Np = 5 N = 10rpm ±1% d = 30 cm V = 0.5 m3 ± 3% ρ = 1000 kg/m3 ± 2% Question Calibration/Traceability Explain the following concepts Calibration Calibration chain Traceability Working standard Process instrument Example Reliability MTBF = 30.41 days or = 365/12 faults = 30.41 days Example Reliability MTBF = 100 * 20 / 9 = 222 days Example Reliability Availabitiy tm = MTBF = MTTF R (5000) = exp (- 5000 / 100000) R = 0.9512 = 95% Question What is the difference between MTBF and MTTF? Example System reliability F2 = 1 - R2 = 0.1 = F4 RT = R1*(1-F22)*R3*(1-F42)*R5 RT = 0.98 * (0.99) * 0.98 * (0.99) * 0.98 = 0.92 = 92% Question The performance of 10 identical measuring instruments is monitored over a 320-days period. If a total of 5 faults are recorded in this period: a) Calculate the mean-time-between-failures (MTBF). ! b) If the mean time to repair (MTTR) is 7 days, calculate the availability.! c) Calculate the probability that the instrument will fail in the first 100 days of use. d) Calculate the reliability R of the instrument for the first 100 days of use. e) If five identical instruments of reliability R (calculated in d) are connected according to the following figure, calculate the total reliability of the system.! Question Instrumentation circuits Both circuits enable voltage attenuation V0<V1 What is the advantage of the Op-Amp respect to the voltage divider? What is the main implication? Question ADC 0.745V Which type of ADC represents the circuit? Explain how it works? Question Aliasing Explain the concept of aliasing Which is the minimum sampling frequency to prevent aliasing? Question Given the following voltage waveform calculate: a) Mean voltage (Um).!! b) Rectified mean voltage (Urm).!! c) Root mean squared voltage (Urms).! d) Form factor.! ! e) Top factor.! f) Explain the physical meaning of the rms value U Example Arbitrary waveforms AC/DC values Question Null-type, d.c. bridge Example (Wheatstone bridge) •R is varied until the voltage measured v across points BD is zero. R2 = R3. Ru Rv Question Write the Ru value in terms of Rv, R1 and R2 when VAB = 0 A Rv R1 V Ru R2 B Deflection-type d.c. Example bridge • The variable resistance Rv is replaced by a fixed resistance R1 of the same value as the nominal value of the unknown resistance Ru If the nominal value of the resistor (Ru) representing a resistive sensor output is Ru = Question 110 ±1.2%, and the strain gauge pressure sensor operates in the 0-20 Pa range, with R1 = 100± 1%; R2 = 100±0.5% and R3 = 110±0.4% Calculate the value of the voltage source (Vi) necessary to limit the current through the strain gauge to 15 mA.! ! ! ! ! Calculate the bridge output (Vo) when a 12 Pa pressure is measured with a pressure sensor with a sensitivity of 0.2/Pa and the bridge is excited with Vi. Calculate the error of Vo R3 Vi Vo ! Question Explain the concept of oscilloscope bandwidth Explain the concept of oscilloscope raise time For a 100MHz bandwidth oscilloscope the rise time in the order of: a)seconds b) milliseconds c)microsenconds d)nanoseconds e)femtoseconds Example Capacitive sensor Equivalent to C1 // C2 ➙ CT = C 1 + C 2 1 4 d = 1 mm w = 50 mm l = 50 mm Question A variable dielectric capacitive displacement sensor consists of two square metal plates of side 2.5 cm, separated by a gap of 1.3 mm. A sheet of dielectric material 1.3 mm thick and of the same area as the plates can be slid between them as shown in the figure. Given that the dielectric constant of air is 1 and that of the dielectric material 2.4, calculate the capacitance of the sensor when the input displacement x = 0.0, 1.7, 3 and 5 cm. ε0 = 8.854 x 10−12 F/m Example Inductive sensors A variable reluctance sensor consists of a core, a variable air gap and an armature. The core is a steel rod of diameter 1 cm and relative permeability 100, bent to form a semi- circle of diameter 4 cm. A coil of 500 turns is wound onto the core. The armature is a steel plate of thickness 0.5 cm and relative permeability 100. Assuming the relative permeability of air = 1.0 and the permeability of free space = 4π × 10−7 H m−1, calculate the inductance of the sensor for air gaps of 1 mm and 3 mm. total flow reluctance RCORE = πR/μCOREμoπ(r)2 r = 5 mm h = 5 mm RGAP = 2d/μAIRμoπr2 R = 20 mm d = 1 and 3 mm RARMATURE = 2R/μARMATUREμo(h.2r) n = 500 Question 6cm Example R thermometer A Pt100 resistor (0.385 Ω/°C) is measured in a 2 wires connection using 100m leads (Cu 1 mm2 area). What is the error due to the cables in °C? cable 5 Ω(100 m) A Pt100 V 100 Ω cable 5 Ω 10 Ω ➱ 10/ (0.385 ohms/ºC) ➱ ~26°C error Question Explain the advantage of 4 wires connection for Pt-100 measurement with voltmeter and ammeter Example Thermocouples Suppose that the reference junction of a chromel–constantan thermocouple is maintained at a temperature of 80°C and the output e.m.f. measured is 40.102 mV when the hot junction is immersed in a fluid. Which is the temperature of the fluid? Tfluid = 600°C Question Suppose that the reference junction of a chromel–constantan thermocouple is maintained at a temperature of 55°C and the output e.m.f. measured is 68.244 mV when the hot junction is immersed in a fluid. Which is the temperature of the fluid? ! Question chromel chromel constantan constantan ! Suppose that the reference junction of a chromel–constantan thermocouple is maintained at a temperature of 0°C and the output e.m.f. measured is 68.244 mV when the hot junction is immersed in a fluid, but the instrument is connected to the thermocouple through extension wires and the connection is at 40°C. Which is the temperature of the fluid? An ultrasonic Doppler flowmeter is to be used to measure the volume flow rate of a Question slurry in a steel pipe of diameter 0.13 m. Two piezoelectric crystals, each having a natural frequency of 0.95 MHz, are positioned, a few millimetres apart, on the outside of the pipe to form an ultrasonic transmission link. The transmitting crystal directs an ultrasonic beam into the pipe so that the beam is moving in an opposite direction to the flow stream. The angle between the ultrasonic beam and the direction of flow is 57°. On average 18% of the ultrasonic power reaching each solid particle is scattered back in the direction of the receiving crystal. Assume that the slurry has the same density and sound velocity as water (c ≈ 1.5x103 ms−1) and a power attenuation coefficient of 1.0 m−1. a) Find the difference between the frequencies of the transmitted and received beams when the flow rate is 1.12 × 103 m3 h−1. b) If the frequencies are known with an error of 1.4% and pipe diameter with an error of 0.7%, calculate is the error in the determination of the volume flow rate. Question Chemical sensor characterization • Range • Sensitivity • Resolution • Time response • Recovery time • Linearity • Contamination a) From a real measurement of a CO sensor as shoe above explain how to extract: Range, Response, Linearity, Sensitivity, Noise level, Resolution, Response time, Recovery time and Reproducibility/contamination b) Explain the concept of selectivity c) Explain how to improve selectivity in chemical sensing. Question R3 R3 !