orifice; Pa and po are the pressures in the tubes A and B, pa being the larger, and r。 and r are the latent heats of vaporization, and La and the heats of the liquid corresponding; a is the part of one unit of weight of the fluid in the tube A which is dry steam, and 1 x is the part which is water mingled with the steam; x, is the corresponding quantity for the tube B; finally, σ is the volume of one unit of weight of water.

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It is assumed that neither tube gives heat to the steam or receives heat from it, and that the friction of the fluid on the sides. of the wall can be neglected. The heat is supposed to be given at the orifice, it is commonly assumed to be zero, in which case the flow is said to be adiabatic.

At and near the orifice eddies and irregular currents are likely to be of sufficient importance to prevent us from knowing the condition of the steain; consequently the properties Pa and Ро and a must pertain to the steam only at such a distance from the orifice that the flow is steady.

In these experiments the velocity wa was so small that it could be neglected. At the same time we may assume the flow to be adiabatic, and thus reduce equation (1) to

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=Xara — Xoro + La − b + A6 (Pa — Po) (2.)

The value of x must be determined by experiment. x, can then be determined by the equation:

which applies to any adiabatic change of a mixture of a liquid with its vapor. In this last equation Ta is the absolute temperature of the steam in the tube A, and T, that of the steam in the tube B. c is

the specific heat of water, and fedt

above that at freezing point.

is the entropy of the liquid

If the area of the cross-section of the tube be N, then the volume per second is

V = Nwo

and the weight per second G is obtained by dividing by the specific volume

in which u is the increase in volume of one unit of weight of water when it is entirely vaporized. Therefore

The tube used in these experiments was of brass 0.275 of an inch internal diameter and eight inches long. At the entrance end a plate, 1 inches in diameter, was driven on flush with the end of the tube, and the orifice was well rounded to avoid contraction. This tube was the tube B, and led from an iron pipe six inches in diameter and two feet long which corresponded to the tube A. The brass tube discharged into another iron pipe six inches in diameter and two feet long, which formed a chamber in which the steam came to rest, and from which it was led to a surface condenser..

The two pieces of six-inch pipe were capped on the outer ends, and had flanges on the inner ends, between which was a plate holding the experimental tube. The whole apparatus was lagged on the outside, and the plate holding the brass tube was covered on both sides with about four inches of asbestos to prevent the flow of heat from one part of the apparatus to the other.

Steam was led to the apparatus by a lagged pipe one inch in diameter, and away from it to the condenser by a pipe of the same size. Each of these pipes had a valve near the apparatus. The valve in the supply pipe was used merely to shut off the steam when the apparatus was not in use, and during an experiment it was wide open, so that the pressure in the tube A was full boiler pressure or nearly so. The valve in the exhaust pipe was manipulated to maintain the desired difference of pressure between the two parts of the apparatus. Each chamber of the apparatus was supplied with a good steam gauge, and with a thermometer in a long brass cup filled with oil. The gauges were compared with a mercury column in the laboratory, and the thermometers were calibrated, and their freezing and boiling points were determined. The exhaust steam was condensed in a small surface condenser and weighed in a tank.

The experiments were begun after the apparatus had been running steadily for some time and lasted about half an hour.

Steam for the experiments was drawn from the main steam pipe, and as the supply pipe had a drip near the apparatus which remained open during an experiment, it was assumed that the

quality of the steam was the same as that in the main pipe. A large number of experiments with different types of calorimeters gave 1 to two per cent. of moisture in the steam. Later experiments with a new type of calorimeter, described in a paper presented to this meeting, gave under normal conditions 1 to 1.5 per cent. of moisture. With a large difference of pressure the steam, after coming to rest in the chamber beyond the tube, was superheated, and by the method employed with the new calorimeter, the amount of moisture could be calculated, giving the same result.

The data and the calculated results of the experiments quoted here are taken from the graduation thesis of Mr. B. G. Buttolph, of the class of 1888, who deserves much credit for the careful and thorough manner in which he did his work.

As the more recent data were not available till the work was nearly complete, the moisture was assumed to be two per cent. in all the calculations. The error from this source is inconsiderable. The data and results of the experiments are given in the following table, and are plotted in the accompanying diagram (Fig. 10). The abscissæ are differences of pressures, and the ordinates the ratio of the actual flow to the calculated flow. The curve on the diagram is intended merely to show the degree of regularity of the experiments more readily.

The table will be readily understood from the headings. It should, however, be noted that the calculated flow per hour is 3,600 times that given by equation (4).

The ratio of the actual quantity to the calculated quantity, if the theory were entirely applicable to this case, should resemble the coefficient of flow for water through a short pipe, and should not

be greater than unity. The marked, though regular increase of this ratio with the increase of the difference of pressure, and the fact that, for the larger differences, this ratio is larger than one, shows conclusively that some of the assumptions are inadmissible.

It is not improbable that heat is given by the steam to the tube at the admission end, and regained by the steam towards the exit end. Such an interchange must influence both the condition of the steam at the orifice and the rate of flow. The well-known phenomena of cylinder condensation and reevaporation in steam engines show that such an action may be energetic. It is also possible that the length of the tube is not sufficient to ensure a steady flow.

It is noticeable that the weight of steam discharged by the tube has a maximum, which is for a difference of pressure of about thirty-five pounds by the equation, and for a difference of pressure of about fifty-five pounds by experiment.

Some earlier experiments of this year are not recorded on

account of discrepancies due to the imperfection of the methods, and for the same reason experiments of two preceding years are excluded.

In such a series of experiments the superior pressure should be the same for all of the experiments. Some of the irregularity of the results may be chargeable to the fact that the boiler pressure was not the same on different days.

DISCUSSION.

Prof. Jas. E. Denton.-I have only just noticed that there is quite a discrepancy between these experiments regarding the flow of steam and those which I have examined, and if they are exact they upset the theory regarding the flow of steam. We have believed that there is a maximum flow of steam from a boiler at a given pressure into another space at another pressure, and if you have a boiler at 100 pounds of steam absolute and let it flow into a space in which the pressure is lower, when the lower pressure is over 60 pounds while the flow takes place, yet when the lower pressure is below 60 pounds, it does not make any dif ference whether it is 60 pounds or 30 pounds, or a vacuum. It will flow from 100 pounds pressure into anything below 60 pounds with uniform velocity. That was the result shown in 1867, I think, by the experiments of Napier, and they excited a good deal of controversy at that time. People lost their tempers about it. I remember a number of papers in the Engineer, in which it was stated that it could not be true that such was the case, but it proved to be the case. Upon Professor Rankine investigating it, he proposed a reason for it. He showed why the theoretical computation proves that the greatest amount of steam flows against a lower pressure, which is about three-fifths of the upper pressure. When a committee of Scotch shipbuilders a number of years ago took up the subject of safety-valves, they verified the fact very deliberately, and in D. K. Clark's manual you will find that total given, and the three-fifths point was very accurately verified by those experiments. I have never gone over this exact ground. It is common to make the experiment to show the paradox, but I never have run over these particular pressures, so that, if that maximum is correct as given here, it certainly is new to the literature of the subject as I have read it for a number of years.

There was a point here that I should like to have a little expla nation about, and that is why it is that the coefficients of discharge are greater than computed. Why should the coefficient of discharge be greater actually than is computed by the theory? That was one of the most important suggestions ever made on the subject, and it leads into what Professor Peabody says he is going to do, namely, to investigate the flow of steam through an orifice which is not a straight tube. The explanation of this con