Part 23

The difference in B. t. u. in a pound of steam at the boiler pressure and after passing the orifice is the heat available for evaporating the moisture content and superheating the steam. Therefore,

H - h = xL + 0.47(t{2} - t{1})

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.

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,

X = x - x_{1}

H - h - 0.47(t{2} - t{1}) H - h - 0.47(T - t_{1}) = --------------------------- - ----------------------- L L

0.47(T - t_{2}) = --------------- (6) L

As T and t{2} are taken with the same thermometer under the same set of conditions, any error in the reading of the thermometers will be approximately the same for the temperatures T and t{2} and the above method therefore corrects for both the radiation and thermometer errors. The theoretical readings for dry steam, where there are no losses due to radiation, are obtainable from formula (5) by letting x = 0 and solving for t{2}. The difference between the theoretical reading and the normal reading for no moisture will be the thermometer and radiation correction to be applied in order that the correct reading of t{2} may be obtained.

For any calorimeter within the range of its ordinary use, such a thermometer and radiation correction taken from one normal reading is approximately correct for any conditions with the same or a duplicate thermometer.

The percentage of moisture in the steam, corrected for thermometer error and radiation and the correction to be applied to the particular calorimeter used, would be determined as follows: Assume a gauge pressure in the trial to be 180 pounds and the thermometer reading to be 295 degrees. A normal reading, taken in the manner described, gives a value of T = 303 degrees; then, the percentage of moisture corrected for thermometer error and radiation is,

0.47(303 - 295) x = ---------------- 845.0

= 0.45 per cent.

The theoretical reading for dry steam will be,

1197.7 - 1150.4 - 0.47(t_{2} - 212) 0 = ------------------------------------ 845.0

t_{2} = 313 degrees.

The thermometer and radiation correction to be applied to the instrument used, therefore over the ordinary range of pressure is

Correction = 313 - 303 = 10 degrees