2.5 Self-test questions
2.1 Explain what is meant by:
(a) active instruments
(b) passive instruments.
Give examples of each and discuss the
relative merits of these two classes of instruments.
2.2 Discuss the advantages and
disadvantages of null and deflection types of measuring instrument. What are
null types of instrument mainly used for and why?
2.3 Briefly define and explain all
the static characteristics of measuring instruments.
2.4 Explain the difference between
accuracy and precision in an instrument.
2.5 A tungsten/5%
rhenium–tungsten/26% rhenium thermocouple has an output e.m.f. as shown in the
following table when its hot (measuring) junction is at the temperatures shown.
Determine the sensitivity of measurement for the thermocouple in mV/°C.
2.6 Define sensitivity drift and zero
drift. What factors can cause sensitivity drift and zero drift in instrument
characteristics?
2.7 (a) An instrument is calibrated
in an environment at a temperature of 20°C and the following output readings y
are obtained for various input values x:
Determine the measurement sensitivity, expressed as the ratio y/x.
(b) When the instrument is
subsequently used in an environment at a temperature of 50°C, the input/output
characteristic changes to the following:
Determine the new measurement sensitivity. Hence determine the sensitivity drift due to the change in ambient temperature of 30°C.
2.8 A load cell is calibrated in an
environment at a temperature of 21°C and has the following deflection/load
characteristic:
When used in an environment at 35°C, its characteristic changes to the following:
(a) Determine the sensitivity at 21°C
and 35°C.
(b) Calculate the total zero drift
and sensitivity drift at 35°C.
(c) Hence determine the zero drift
and sensitivity drift coefficients (in units of µm/°C and (µm per kg)/(°C)).
2.9
An unmanned submarine is equipped
with temperature and depth measuring instruments and has radio equipment that
can transmit the output readings of 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[1]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 20°C 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 metres/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 metres?
2.10
Write down the general differential
equation describing the dynamic response of a second order measuring instrument
and state the expressions relating the static sensitivity, undamped natural
frequency and damping ratio to the parameters in this differential equation.
Sketch the instrument response for the cases of heavy damping, critical damping
and light damping, and state which of these is the usual target when a second
order instrument is being designed.
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