When steam pa.s.ses through an orifice from a higher to a lower pressure, as is the case with the throttling calorimeter, no external work has to be done in overcoming a resistance. Hence, if there is no loss from radiation, the quant.i.ty of heat in the steam will be exactly the same after pa.s.sing the orifice as before pa.s.sing. If the higher steam pressure is 160 pounds gauge and the lower pressure that of the atmosphere, the total heat in a pound of dry steam at the former pressure is 1195.9 B. t. u. and at the latter pressure 1150.4 B. t. u., a difference of 45.4 B. t. u. As this heat will still exist in the steam at the lower pressure, since there is no external work done, its effect must be to superheat the steam. a.s.suming the specific heat of superheated steam to be 0.47, each pound pa.s.sing through will be superheated 45.4/0.47 = 96.6 degrees. If, however, the steam had contained one per cent of moisture, it would have contained less heat units per pound than if it were dry. Since the latent heat of steam at 160 pounds gauge pressure is 852.8 B. t. u., it follows that the one per cent of moisture would have required 8.5 B. t. u. to evaporate it, leaving only 45.4 - 8.5 = 36.9 B. t. u. available for superheating; hence, the superheat would be 36.9/0.47 = 78.5 degrees, as against 96.6 degrees for dry steam. In a similar manner, the degree of superheat for other percentages of moisture may be determined. The action of the throttling calorimeter is based upon the foregoing facts, as shown below.
Let H = total heat of one pound of steam at boiler pressure, L = latent heat of steam at boiler pressure, h = total heat of steam at reduced pressure after pa.s.sing orifice, t_{1} = temperature of saturated steam at the reduced pressure, t_{2} = temperature of steam after expanding through the orifice in the disc, 0.47 = the specific heat of saturated steam at atmospheric pressure, x = proportion by weight of moisture in steam.
The difference in B. t. u. in a pound of steam at the boiler pressure and after pa.s.sing 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: a.s.sume 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 pa.s.sed 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: a.s.sume 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
The chart may be used in the determination of the correct reading of moisture percentage and the permanent radiation correction for the instrument used without computation as follows: a.s.sume the same trial pressure, feed temperature and normal reading as above. If the normal reading is found to be 303 degrees, the correction for thermometer and radiation will be the theoretical reading for dry steam as found from the chart, less this normal reading, or 10 degrees correction. The correct temperature for the trial in question is, therefore, 305 degrees. The moisture corresponding to this temperature and 180 pounds gauge pressure will be found from the chart to be 0.45 per cent.
[Ill.u.s.tration: Fig. 16. Compact Throttling Calorimeter]
There are many forms of throttling calorimeter, all of which work upon the same principle. The simplest one is probably that shown in Fig. 14.
An extremely convenient and compact design is shown in Fig. 16. This calorimeter consists of two concentric metal cylinders screwed to a cap containing a thermometer well. The steam pressure is measured by a gauge placed in the supply pipe or other convenient location. Steam pa.s.ses through the orifice A and expands to atmospheric pressure, its temperature at this pressure being measured by a thermometer placed in the cup C. To prevent as far as possible radiation losses, the annular s.p.a.ce between the two cylinders is used as a jacket, steam being supplied to this s.p.a.ce through the hole B.
The limits of moisture within which the throttling calorimeter will work are, at sea level, from 2.88 per cent at 50 pounds gauge pressure and 7.17 per cent moisture at 250 pounds pressure.
Separating Calorimeter--The separating calorimeter mechanically separates the entrained water from the steam and collects it in a reservoir, where its amount is either indicated by a gauge gla.s.s or is drained off and weighed. Fig. 17 shows a calorimeter of this type. The steam pa.s.ses out of the calorimeter through an orifice of known size so that its total amount can be calculated or it can be weighed. A gauge is ordinarily provided with this type of calorimeter, which shows the pressure in its inner chamber and the flow of steam for a given period, this latter scale being graduated by trial.
The instrument, like a throttling calorimeter, should be well insulated to prevent losses from radiation.
While theoretically the separating calorimeter is not limited in capacity, it is well in cases where the percentage of moisture present in the steam is known to be high, to attach a throttling calorimeter to its exhaust. This, in effect, is the using of the separating calorimeter as a small separator between the sampling nozzle and the throttling instrument, and is necessary to insure the determination of the full percentage of moisture in the steam. The sum of the percentages shown by the two instruments is the moisture content of the steam.
The steam pa.s.sing through a separating calorimeter may be calculated by Napier"s formula, the size of the orifice being known. There are objections to such a calculation, however, in that it is difficult to accurately determine the areas of such small orifices. Further, small orifices have a tendency to become partly closed by sediment that may be carried by the steam. The more accurate method of determining the amount of steam pa.s.sing through the instrument is as follows:
[Ill.u.s.tration: Fig. 17. Separating Calorimeter]
A hose should be attached to the separator outlet leading to a vessel of water on a platform scale graduated to 1/100 of a pound. The steam outlet should be connected to another vessel of water resting on a second scale. In each case, the weight of each vessel and its contents should be noted. When ready for an observation, the instrument should be blown out thoroughly so that there will be no water within the separator. The separator drip should then be closed and the steam hose inserted into the vessel of water at the same instant. When the separator has acc.u.mulated a sufficient quant.i.ty of water, the valve of the instrument should be closed and the hose removed from the vessel of water. The separator should be emptied into the vessel on its scale. The final weight of each vessel and its contents are to be noted and the differences between the final and original weights will represent the weight of moisture collected by the separator and the weight of steam from which the moisture has been taken. The proportion of moisture can then be calculated from the following formula:
100 w x = ----- (7) W - w
Where x = per cent moisture in steam, W = weight of steam condensed, w = weight of moisture as taken out by the separating calorimeter.
Sampling Nipple--The principle source of error in steam calorimeter determinations is the failure to obtain an average sample of the steam delivered by the boiler and it is extremely doubtful whether such a sample is ever obtained. The two governing features in the obtaining of such a sample are the type of sampling nozzle used and its location.
The American Society of Mechanical Engineers recommends a sampling nozzle made of one-half inch iron pipe closed at the inner end and the interior portion perforated with not less than twenty one-eighth inch holes equally distributed from end to end and preferably drilled in irregular or spiral rows, with the first hole not less than one-half inch from the wall of the pipe. Many engineers object to the use of a perforated sampling nipple because it ordinarily indicates a higher percentage of moisture than is actually present in the steam. This is due to the fact that if the perforations come close to the inner surface of the pipe, the moisture, which in many instances clings to this surface, will flow into the calorimeter and cause a large error. Where a perforated nipple is used, in general it may be said that the perforations should be at least one inch from the inner pipe surface.
A sampling nipple, open at the inner end and unperforated, undoubtedly gives as accurate a measure as can be obtained of the moisture in the steam pa.s.sing that end. It would appear that a satisfactory method of obtaining an average sample of the steam would result from the use of an open end unperforated nipple pa.s.sing through a stuffing box which would allow the end to be placed at any point across the diameter of the steam pipe.
Incidental to a test of a 15,000 K. W. steam engine turbine unit, Mr.
H. G. Stott and Mr. R. G. S. Pigott, finding no experimental data bearing on the subject of low pressure steam quality determinations, made a investigation of the subject and the sampling nozzle ill.u.s.trated in Fig. 18 was developed. In speaking of sampling nozzles in the determination of the moisture content of low pressure steam, Mr. Pigott says, "the ordinary standard perforated pipe sampler is absolutely worthless in giving a true sample and it is vital that the sample be abstracted from the main without changing its direction or velocity until it is safely within the sample pipe and entirely isolated from the rest of the steam."
[Ill.u.s.tration: Fig. 18. Stott and Pigott Sampling Nozzle]