Question 2 A fine scale thermocouple is used to measure compressor. Assume the m

Question

Question 2 A fine scale thermocouple is used to measure compressor. Assume the measurement system constant, 0.12 seconds. Measured values are temperature variation in a piston-type Temp. vs time responds 180 170 160 150 140 130 á 120 110 100 90 80 70 60 as a first-order system with time 0.12 seconds·Measuredvalues are shown on the graph. a) What is your best estimate of the actual temperature range in the compressor? b) If you wanted to have measured amplitude always within 3% of the true amplitude, what thermocouple time constant, , would be required? 0 0.1 0.2 03 04 0.5 06 07 0.8 0.9 1 Time (sec.)

Explanation / Answer

Given that the fine cale thermocouple is used to measure temperature variation piston tyoe compressor. The measurement system responds to first order system with the time constant = 0.12 seconds
The meaning is that the system takes 0.12 seconds to make the change in temperature of 63.2% of temperature variation(100) .
i.e the sysytem takes 0.12 second for the change in temperature of 63.2oF
To calculate the best estimatte of the actual temperature range we can observe the waveform where there is a immediate change in the temerature of 63.2oF .
The curve is slowly decreasing from 170oF to 106.8oF in the time change oif 0.1 seconds to 0.28 seconds
Hence we can say that the best estimate of actual temperature range in the compressor is 0.1s<t<0.28s
(b)
if the amplitude change is always 3% of the true amplitude i.e 0.03*100 = 3 oF Then we can calculate the time constant as time taken by the system to change the temperature of 97oF , hence from the graph we can say that the temerature from170 to temperature 73oF (change of 97oF) the total time taken = 0.1 to 0.32 seconds
therefore time constant = 0.32-1 = 0.22 seconds

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