H - h - 0.47(t_{2} - t_{1})
or x = --------------------------- (4)
L
Almost invariably the lower pressure is taken as that of the atmosphere.
Under such conditions, h = 1150.4 and t_{1} = 212 degrees. The formula
thus becomes:
H - 1150.4 - 0.47(t_{2} - 212)
x = ------------------------------ (5)
L
For practical work it is more convenient to dispense with the upper
thermometer in the calorimeter and to measure the pressure in the steam
main by an accurate steam pressure gauge.
A chart may be used for determining the value of x for approximate work
without the necessity for computation. Such a chart is shown in Fig. 15
and its use is as follows: Assume a gauge pressure of 180 pounds and a
thermometer reading of 295 degrees. The intersection of the vertical
line from the scale of temperatures as shown by the calorimeter
thermometer and the horizontal line from the scale of gauge pressures
will indicate directly the per cent of moisture in the steam as read
from the diagonal scale. In the present instance, this per cent is 1.0.
Sources of Error in the Apparatus--A slight error may arise from the
value, 0.47, used as the specific heat of superheated steam at
atmospheric pressure. This value, however is very nearly correct and any
error resulting from its use will be negligible.
There is ordinarily a larger source of error due to the fact that the
stem of the thermometer is not heated to its full length, to an initial
error in the thermometer and to radiation losses.
With an ordinary thermometer immersed in the well to the 100 degrees
mark, the error when registering 300 degrees would be about 3 degrees
and the true temperature be 303 degrees.[19]
The steam is evidently losing heat through radiation from the moment it
enters the sampling nipple. The heat available for evaporating moisture
and superheating steam after it has passed through the orifice into the
lower pressure will be diminished by just the amount lost through
radiation and the value of t_{2}, as shown by the calorimeter
thermometer, will, therefore, be lower than if there were no such loss.
The method of correcting for the thermometer and radiation error
recommended by the Power Test Committee of the American Society of
Mechanical Engineers is by referring the readings as found on the boiler
trial to a "normal" reading of the thermometer. This normal reading is
the reading of the lower calorimeter thermometer for dry saturated
steam, and should be determined by attaching the instrument to a
horizontal steam pipe in such a way that the sampling nozzle projects
upward to near the top of the pipe, there being no perforations in the
nozzle and the steam taken only through its open upper end. The test
should be made with the steam in a quiescent state and with the steam
pressure maintained as nearly as possible at the pressure observed in
the main trial, the calorimeter thermometer to be the same as was used
on the trial or one exactly similar.
With a normal reading thus obtained for a pressure approximately the
same as existed in the trial, the true percentage of moisture in the
steam, that is, with the proper correction made for radiation, may be
calculated as follows:
Let T denote the normal reading for the conditions existing in the
trial. The effect of radiation from the instrument as pointed out will
be to lower the temperature of the steam at the lower pressure. Let
x_{1} represent the proportion of water in the steam which will lower
its temperature an amount equal to the loss by radiation. Then,
H - h - 0.47(T - t_{1})
x_{1} = -----------------------
L
This amount of moisture, x_{1} was not in the steam originally but is
the result of condensation in the instrument through radiation. Hence,
the true amount of moisture in the steam represented by X is the
difference between the amount as determined in the trial and that
resulting from condensation, or,