Transactions

536 TRANSACTIONS OF TH E A.S.M.E. AUGUST, 1941
T i m e L a g o p I n d u s t r ia l M e r c u r y -i n -G l a s s T h e r m o m e t e r s
The protecting well for the glass bulb usually has a diameter of
*/« to 7/» in- and, if the space between bulb and well is properly
filled with mercury, the time lag should be between 3 and 4 sec
in well-agitated water. The separable socket with tapered fit approximately
doubles the time lag; figures of 7.5 to 8.5 sec have
been observed in water. It should be noted that, due to the tapered
fit, the time lag is only slightly more than doubled; whereas,
F i g . 8
F i g . 9
C h a n g e o f T i m e L a g i n A i r f o r V a r i o u s S p e e d s o f A i r
P a s t t h e B u l b
T im e L a g a s F u n c t i o n o f B u l b D i a m e t e r i n Q u i e t A ir
in case of the thermometers with straight bulbs described in the
previous section, the socket increases the time lag 3 to 4 times in
water.
The time lag in oil for the bare-stem thermometer is 15 to 20
sec; for the separable socket, 35 to 45 sec.
Fig. 8, based upon data in the Bureau of Standards paper,
shows the change of time lag with changing air speed past the
bulb of a mercury-in-glass thermometer. The rapid change in
time lag between zero and 1 fps air speed indicates that time-lag
figures for thermometer bulbs in quiet air will be extremely unreliable,
as any slight change in air drafts may double or halve
the time lag. Therefore, if we wish to control the time lag, we
must control the air speed. For instance, if we are required to
measure at a maximum rate of temperature change of 1 deg in
60 sec, and cannot allow an error of more than 1 deg, the time lag
cannot be more than 60 sec. According to Fig. 8, we will need a
minimum air speed of 3 fps for this particular thermometer. Fig.
8 shows some data on bulbs in quiet air; the figures correspond to
the time lag of 190 sec for zero speed in Fig. 8. Time lags at
other speeds can be estimated by using the same proportions of
time lag for equal air speeds. For instance, at 20 fps, Fig. 8 shows
a time lag of 30 sec; at zero, 190 sec. Fig. 9 shows for a 3/ s-in.
mercury-in-steel bulb a time lag of about 500 sec. At 20 fps the
‘/s-in. bulb would have a time lag of 500 X 3% 9o = 79 sec. This
relation checks reasonably well with actual tests.
C o n c l u s io n
The preceding sections give the prospective user of a thermometer
sufficient material to determine its behavior under actual
service conditions for a definite time-lag figure. What this
behavior should be for a certain process must, of course, be determined
from the requirements of the process and the characteristics
of the process apparatus, and is entirely beyond the scope
of this paper.
Once the desired time lag has been determined, it is necessary
to include it in the purchasing specifications in a form which is
definite and permits easy checking by means generally available.
The author proposes the following as a standard form of time-lag
specification:
The time lag of the thermometer in (medium) at a uniform rate of
temperature rise must not exceed ( ) seconds.
The time lag is to be determined by transferring bulb at temperature
T„ into a (medium) bath at temperature and measuring the
time required for the indication to progress from T, to T , = Ti,
— 0.368(Ti — T,) with bulb at rest and bath stirred moderately. This
figure will be accepted as representing the time lag in (medium) at a
uniform rate of temperature rise.
Actual figures should be inserted for Ta, Tb, T„ and T,. By
using specifications of this form, there cannot be any argument as
to whether or not they have been fulfilled. Also, the figure given
for the time lag permits the prospective user to predetermine the
maximum deviations between actual and indicated temperatures
which he may encounter in his process, using the formulas given
in the section on “Uses of Time-Lag Constant L .”
For industrial-type mercury-in-glass thermometers, it may be
advisable to add that the bulb should be maintained at the
temperature T b for 30 min before performing the test. The expression
“stirred moderately” is somewhat vague, but has been
chosen because generally no special equipment is available by
which the stirring speed could be measured. When such equipment
is available, a definite speed of the liquid past the bulb may
be inserted, for instance, 1 fps, or a speed corresponding to
actual service conditions.
Frequently, it will not be possible to have the time-lag test
performed in the medium in which the thermometer is actually
used. In this case one of the mediums discussed previously with
temperature characteristics nearest to the actual medium can
be selected, or the figures for relations of time lags in different
mediums can be used. If the time lag is to be determined in air
or gas, the speed of the medium past the bulb in feet per second
should be inserted in the specification in place of the wording
“and bath stirred moderately.”
Appendix— 1
Those desiring to study further the theory of time lag should
obtain a reprint from the Bureau of Standards bulletin2 mentioned.
Some of the formulas are given herewith in more detail
than was justified in the main paper:
Ti = Original temperature of the thermometer bulb
Ti = Bulb temperature at time s
s = Time, sec
T„ — Original temperature of bath
T = Temperature of bath at time s
L = Time lag, sec
r = Rate of temperature rise, deg per sec
Newton’s law of cooling can be expressed as follows: The rate
of heat transfer is directly proportional to the difference of temperature
between two bodies, or