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-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 meters is given by the relation:
Tx ¼ T0 0:01x
(a) If the submarine starts diving at time 0 and thereafter goes down at a velocity of
0.5 m/s, 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 m?