2

Instrumentation and Measurement Systems

Assignment No.1

Q1.(a) An instrument is calibrated in an environment at a temperature of 20C and the following output readings y are obtained for various input values x:

y13.126.239.352.465.578.6

x51015202530

Determine the measurement sensitivity, expressed as the ratio y/x.

(b) When the instrument is subsequently used in an environment at a temperature of 50C, the input/output characteristic changes to the following:

y14.729.444.158.873.588.2

x51015202530

Determine the new measurement sensitivity. Hence determine the sensitivity drift due to the change in ambient temperature of 30C.Q2. A load cell is calibrated in an environment at a temperature of 21C and has the following deflection/ load characteristic:

Load(kg)050100150200

Deflection(mm)0.01.02.03.04.0

When used in an environment at 35C, its characteristic changes to the following:

Load(kg)050100150200

Deflection(mm)0.21.32.43.54.6

(a) Determine the sensitivity at 21C and 35C.

(b) Calculate the total zero drift and sensitivity drift at 35C.

(c) Hence determine the zero drift and sensitivity drift coefficients (in units of m/C and (m per kg)/(C)).Q3. A science student was trying to determine power dissipated in the circuit for different resistance values within a specified tolerance, since he had only resistance values data available and an ammeter. He made the following observationsReading No.ResistanceCurrent

16534.651 mA

26604.52 mA

35805.172 mA

45955.03 mA

56035 mA

66005.03 mA

75835.1 mA

86434.68 mA

If a constant supply was used in the above experiment and intended value of the resistance for the experiment was 620 ohm.

Calculate

(a) The absolute error and the relative error of the above resistance. (b) If the 3rd reading was correct for the resistance used. Check the values of current measured and calculate errors, if any for each reading.

(c) Determine the mean power dissipated calculated by the student and the actual mean power dissipated by the resistances.

(d) What will be the deviation, standard deviation and variance of the actual power?

(e) Comment on the working of the student, giving possible reasons for the errors? Q4. A controlling spring is to be selected for the construction of a PMMC instrument. The constant of proportionality of the spring is 5.728835 X 10-6 N.m/rad. If the angle of test for the spring is 30 degrees and Six students were given the task to measure the torque with a torque meter. This is the values they achieved.

Reading No.Torque

Measured (N.m)

13.2 X 10-6

24 X 10-6

32.5 X 10-6

43 X 10-6

52.8 X 10-6

62.99999 X 10-6

Calculate

(a) Compute the arithmetic mean ( 1.5 mark)

(b) The standard deviation. (3.5 marks)

(c) The precision of the 2nd reading. (2.5 marks)

(d) In your opinion what is the correct value and which student has the correct reading? (2 marks)(e) What is the absolute error and relative error. (4 marks)(f) What is the probable error? (1.5 marks) Q.5 (a) The true value of voltage is 100 V. Value indicated by a measuring instrument are 104, 103, 105, 103 and 105 volts.

(i) Find the accuracy of the measurement.

(ii) The precision of the instrument.

(b) A voltmeter has a uniform scale with 100 divisions. The full scale reading is 5 V and 1/5 th of a division can be read. What is the resolution of the instrument?

(c)The dead zone in a pyrometer is 0.125% of the span. The instrument is calibrated for 800 to 1800C. What temperature change must occur before it is detected?

(d) An ammeter has a range of 0 to 30 A. The instrument gave the following readings:

Current flow (A)0510152025

Ammeter Reading1412142228

(i) Determine the static sensitivity of the instrument.

(ii) Determine the maximum non-linearity

(iii) Comment on the instrument with due reference to static characteristics of the instrument. Q6. A pressure measuring system consists of a piezoelectric transducer, a charge amplifier and a ultra-violet charge recorder; their sensitivities are 8.5 pC/bar, 0.004 V/pC and 20 mm/V respectively. Determine the deflection in mm for a pressure change of 25 bar. [Ans. 17 mm]Q7. A temperature sensing device can be modeled as a first order system with a time constant of 5 seconds. It is suddenly subjected to a step input of 30C - 160C. Calculate the temperature indicated by the device after 20 seconds after the start of the process. [Ans. 142.4 C]Q8. A thermometer initially at a temperature of 15C is suddenly plunged into a liquid bath maintained at 140C. After a time interval of 4 seconds, the thermometer indicated a temperature of 75C. Determine:

(a) The time constant for the thermometer. [Ans. = 6.12 sec](b) The indicated temperature after five time constant; comment upon this result. [Ans. 139.16 C]Q9. Determine the damping ratio; undamped natural frequency; damped natural frequency, static sensitivity and time constant for a second order system which follows the differential equation given as:

where qo and Ii are the output and input quantities respectively. [Ans. 0.2; 4.899 rad/s; 1.0; 0.2 s] Q10. An unmanned submarine is equipped with temperature and depth measuring these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth-measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, T0, is 20C and the temperature Tx at a depth of x metres is given by the relation:

Tx = T0 - 0.01x(a) If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 meters/ second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.

(b) What temperature does the submarine report at a depth of 1000 meters? [ Note: For answer to this question please check appendix 4 of Allan Morris]MTS-3614111013

_1434141992.unknown