# Problems. Instrumentation

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1 Problems TFMT14 A Instrumentation B a) Which instrument is an active type of device? b) Indicate one main advantage of each type?

2 Example Detection range and accuracy specs. Calculate accuracy and relative error for I = ma in all possible ranges. Select the best range and answer why is the best? Write the display indication of each resolution. 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.

3 Example Sensitivity Example x y

4 Example S = Ω/ C Bias and sensitivity drift

5 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. temperature raise B Response order 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?

6 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 Example Accuracy characterization

7 Example 3.10 (a), from L02 and Morris Ch.3 Example Alternatively

8 Example 3.10 (b), from L02 and Morris Ch.3 Example 3.10 (c) α = 0.022/(10) 1/2 = α = 0.022/(1000) 1/2 = 0.022/(10x10 2 ) 1/2 = 0.022/10x(10) 1/2

9 Error of the mean Quality control of nine batches of milk produce have recorded the following concentrations of cholesterol in [mg/100ml] is 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 %

10 Example Random errors / Confidence interval z = D / σ z = (2.5-3) / 0.25 z = % 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.!

11 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.! 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?

12 Explain the concept of insertion error. Insertion error is a systematic error or a random error? Why? How to minimize insertion error? 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?

13 Example Error propagation S = (1.5V + 1.5V) ± e e = [(0.01x1.5) 2 + (0.01x1.5) 2 ] 1/2 = V 100x0.021/3 = ±0.7% Error propagation

14 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% Calibration/Traceability Explain the following concepts Calibration Calibration chain Traceability Working standard Process instrument

15 Example Reliability MTBF = days or = 365/12 faults = days Example Reliability MTBF = 100 * 20 / 9 = 222 days

16 Example Reliability Availabitiy R (5000) = exp ( / ) R = = 95% tm = MTBF = MTTF What is the difference between MTBF and MTTF?

17 Example System reliability F2 = 1 - R2 = 0.1 = F4 RT = R1*(1-F2 2 )*R3*(1-F4 2 )*R5 RT = 0.98 * (0.99) * 0.98 * (0.99) * 0.98 = 0.92 = 92% 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.!

18 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?

19 ADC 0.745V Which type of ADC represents the circuit? Explain how it works? Aliasing Explain the concept of aliasing Which is the minimum sampling frequency to prevent aliasing?

20 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

21 Example Null-type, d.c. bridge (Wheatstone bridge) R v is varied until the voltage measured across points BD is zero. R2 = R3. Ru Rv

22 Write the Ru value in terms of Rv, R1 and R2 when VAB = 0 A Rv R1 R2 V Ru B Example Deflection-type d.c. 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

23 If the nominal value of the resistor (Ru) representing a resistive sensor output is Ru = 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 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

24 Example Capacitive sensor Equivalent to C1 // C2 CT = C1 + C2 1 4 d = 1 mm w = 50 mm l = 50 mm 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 = x F/m

25 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 semicircle 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 RGAP = 2d/μAIRμoπr 2 RARMATURE = 2R/μARMATUREμo(h.2r) r = 5 mm h = 5 mm R = 20 mm d = 1 and 3 mm n = 500 6cm

26 Example R thermometer A Pt100 resistor (0.385 Ω/ C) is measured in a 2 wires connection using 100m leads (Cu 1 mm 2 area). What is the error due to the cables in C? A V cable cable 5 Ω(100 m) 5 Ω Pt Ω 10 Ω 10/ (0.385 ohms/ºc) ~26 C error Explain the advantage of 4 wires connection for Pt-100 measurement with voltmeter and ammeter

27 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 mv when the hot junction is immersed in a fluid. Which is the temperature of the fluid? Tfluid = 600 C 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 mv when the hot junction is immersed in a fluid. Which is the temperature of the fluid?!

28 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 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 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 1.5x10 3 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 m 3 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.

29 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.

30 R3 R3!

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