pirical expression to agree almost exactly with experiment, the

G

values of having been calculated by equation (10) from the

F

and the value of a is found to be such that this expression is almost exactly equal to

a being dependent on the temperature and internal pressure, and m having the same value as before.

These expressions, obtained on the hypothesis that for wellrounded mouthpieces the resistance is insensibly small, require next to be tested by experiment. The Author discusses fully the difficulties and sources of error to which experiments on the flow of air are liable.

Tables of experiments by Zeuner, Weisbach, and the Author are then given, and the values of a and m are calculated from them. If the hypothesis that k=n is true, these values should agree with the independent values given above. This is found to be the case. W. C. U.

Results of Experimental Researches on the Discharge of Air under Great Pressures. By Dr. Gustav Zeuner.

(Civilingenieur, xx., part 1, 1874, cols. 1-14.)

These researches on the flow of air through simple mouthpieces were made with a large apparatus belonging to the Federal Polytechnic School at Zurich. The Author gives a short history of the question for solution, to explain the necessity for the experiments. If air flows from one vessel in which the pressure is constant into another in which the pressure is also constant, the air expands during its flow from the mouthpiece in consequence of the difference of pressure which must be gradual between the two limits. According to the assumptions made, as to the law connecting the change of pressure and volume of the moving air, different formulæ of discharge are obtained. Let p2 be the pressure in the reservoir, from which the air is discharged (in kilogrammes per square mètre, lbs. per square foot), and p, that in the receiving vessel. Then, assuming the temperature of the air to remain constant, the formula of Navier (1827) is obtained, which gives for the velocity of discharge

and for the volume discharged V, measured at the inner pressure, per second and per square mètre (square foot) of mouthpiece area,

where R has a constant value, and for air and for metric measures, is equal to 96-012 feet (29-272 mètres); g is the acceleration of gravity, and T, the absolute temperature of the air in the reservoir on the centigrade scale.

If, on the contrary, it be assumed that the air flowing through the mouthpiece expands in an adiabatic curve-that is, without receiving or losing heat-then the formula of Weisbach (1855) is obtained, giving for the velocity of discharge

in which k is a constant, which for air is 141. The volume discharged is

The preceding formulæ had been given in 1839 by St. Venant and Wantzel. If the resistances be taken into account, the right-hand member of equation (II.) must be multiplied by a factor of correction, the co-efficient of discharge. Or, the investigation may proceed on the supposition that the resistances merely change the expansion curve. From theoretical considerations the Author was thus led to the following formulæ :

in which n is a constant to be determined by experiment, is smaller than k, and may be termed the exponent of discharge.

A consideration of these formulæ leads to the question requiring solution. If the inner pressure p, and the inner temperature T2 be invariable, and for different experiments different external pressures p1 be taken, then all three formulæ indicate that an external pressure exists, for which the discharge per second and per unit of mouthpiece area is a maximum. The values of the ratio which make V a maximum are then calculated, and are Pi shown to lie for all the formula between 0.5 and 0.6. Now, if the discharge is a maximum when the external pressure is

P2

about half the internal pressure, it follows that the discharge diminishes if the external pressure is further diminished, and the formulæ show that it becomes zero simultaneously with the external pressure. Accordingly, into a vacuum there is no discharge. It follows from this absurd result, either that all the formulæ are false, or that in using them some inadmissible assumption has been made. It is now believed that the latter is the case, and St. Venant and Wantzel, in 1839, pointed out that the pressure p, is not the pressure in the receiving vessel, but in the plane of the orifice, and that these two pressures are only identical when Pr: Pa is greater than about 04. They supposed that when the ratio is smaller, the discharge remains constant, and also P1 P2, if by p1 is understood the pressure in the plane of the mouthpiece. The ratio 0.4 was obtained from their experiments, to test the accuracy of the preceding hypothesis.

The work of St. Venant and Wantzel remained a long time unnoticed, owing chiefly to Poncelet having raised the objection that the scale of their experiments was too small. Max Hermann first returned to the question (1860) after Weisbach (1855) had rediscovered equation (II.). In 1871, Kankine investigated the question, reopened by Napier's experiments on a large scale on the flow of steam, and the Author then published his formula (III.). Considerations drawn from the mechanical theory of heat led to the conclusion that St. Venant and Wantzel's method of investigation was faulty, and other experiments did not furnish the data requisite for a solution of the question, because the pressures at which they were made were not sufficiently great.

The Author had for several years been convinced of the accuracy of the hypothesis of St. Venant and Wantzel, and felt the desirability of subjecting it to larger and more careful tests. His apparatus consisted of a cylindrical vessel of boiler plate, 13-78 feet (4.2 mètres) in length, and 164 foot (0.5 mètre) in diameter. Its capacity, gauged with great care, was 28-637 cubic feet (0.81088 cubic metre). The vessel was proved to ten atmospheres, and was furnished with a pump, by which air could be compressed into it. It carried a seating with a wide neck, having a tight cock with a wide passage through it, on the open end of which the mouthpiece could be fitted. A well-divided open mercury manometer was connected with the interior of the reservoir, and was capable of indicating pressures up to four atmospheres. The apparatus was similar to that of Weisbach, and the Author at first supposed that a simple extension of Weisbach's experiments to higher pressures would suffice to solve the question at issue. A series of experiments soon showed that a circumstance had to be taken into account, which had been overlooked, and which greatly affected the results. In Weisbach's method, after the air has been compressed, and the equilibrium of temperature re-established, the pressure in the reservoir is noted. The air is next allowed to flow for one or two minutes into the receiver, when the cock is quickly closed, and the height of the manometer observed.

After the mercury gauge has again become stationary, its height is again noted. During the discharge there is a fall of temperature in the reservoir. After closing the cock, heat enters through the sides of the reservoir, and the pressure rises, until, the temperature inside and outside having become equal, it again becomes constant. The three pressure observations suffice to test the accuracy of the formulæ of discharge, if the temperature and barometric pressure of the external air and the capacity of the reservoir are known. But they are not sufficient, unless, as Weisbach assumed, the air in the boiler expands without receiving or losing heat. During the relatively long period of discharge the pressure change in the reservoir followed a different law, in consequence of the heat imparted to it during expansion by the sides of the reservoir. The Author therefore adopted a new method of experiment. He permitted the air to flow, at intervals, in the following way. After the air in the reservoir was compressed to about four atmospheres, and the manometer showed the equilibrium of temperature to be established, the cock was opened, and the air allowed to flow for about ten seconds. At the end of the time the cock was closed, and the manometer level noted. After about ten or fifteen minutes the manometer was again noted. The experiments were thus continued till the pressure in the reservoir was reduced nearly to that of the external air. From the short duration of each experiment, the influence of the heat given to the air by the reservoir sides was so much diminished that it could be allowed for by a simple formula of approximation.

For any single experiment, let the initial pressure in millimètres of mercury column = h; the final pressure, after closing the mouthpiece and after the equilibrium of temperature is re-established, h1, and the time of discharge t. Then for a first approximation

=

log

h1

=

should be constant, so long as the inner pressure is more than about twice the external pressure, if the above hypothesis be true. On the other hand, the value of this expression must diminish with the inner pressure as soon as it becomes less than about double the external pressure.

The Author experimented with three kinds of mouthpieces: 1. Short, internally rounded concidal mouthpieces, of 0.161, 0.228, 0.276 inch (4.1, 5.78, and 7.0 mm.) diameter. 2. Short cylindrical mouthpieces, with the internal edges not rounded, of 0.228, 0.276 inch (5·79 and 7.0 mm.) diameter. 3. Orifices in thin plates of 0.161, 0.228, 0.276, 0.394 inch (4·09, 5·79, 7·0, and 10.0 mm.) diameter.

The first two kinds of mouthpieces gave results consistent with the hypothesis of Wantzel and St. Venant. The third kind, orifices in thin plates, showed a small departure from that hypothesis,

which the Author explains by the circumstance that the contraction of the jet alters with the pressure, increasing slowly as the pressure increases.

The defect in the method of experiment employed by St. Venant and Wantzel is then discussed, and one series of experiments is given as a sample of the results obtained.

W. C. U.

The Drainage System of Dantzic.

By HERR VON WINTER, Mayor of Dantzic.

(Baugewerks Zeitung, Sept. 27, 1874.)

At the last congress of the German Association for Public Health in Dantzic, Herr von Winter, the Mayor, gave a brief account of the drainage system which had been carried out between August 1869 and December 1871. The main sewers are of brickwork in cement, 4 feet 1 inch (4 Fuss) high, 2 feet 9 inches (2 Fuss 8 Zoll) broad, and 13,382 feet (13,000 Fuss) long, and lie 9 feet 3 inches to 20 feet 7 inches (9 to 20 Fuss) underground. There are seven iron doors for flushing, forty-five side-entrance shafts for cleansing, eighteen ventilating shafts, and ten outlets for rainwater. The street drain-pipes, of earthenware, 9.05 inches (9.18 Zoll) diameter, have a total length of 40,474 yards (118,000 Fuss), and carry off the water from the surface of the roads and roofs through four hundred and twenty gratings. Arrangements are made for preventing the sewer gas from entering the houses, and the ventilation of the sewers is provided for by three hundred and ten manholes, and one hundred and eighteen ventilating shafts projecting slightly above the roadway, the openings of which are closed by the pressure of gas from within, unless they are opened purposely and filled with charcoal. From the main sewers the sewage is conveyed by two wrought-iron pipes 18.53 and 27.8 inches (18 and 27 Zoll) in diameter, 15 feet under watermark, through the Mottlau to the pumping station on the island, there being a fall of 1 in 1,500 in the old town, and of 1 in 2,400 in the "Niederstadt." The flushing is performed in twenty days by six men. Before entering the pumping station, the sewage passes through two rotating sieves that separate the solid matter. Two Woolff's steam-engines of 60 HP. each, either of which is able to do the work, drive the sewage through 10,400 feet (10,100 Fuss) of cast-iron pipes 20 inches (22 Zoll) in diameter to the "Riesenfelder," a tract of dunes outside the town. There have been brought under cultivation 252 acres (400 Morgen), and, as grass did not seem to prosper, turnips, maize, tobacco, vegetables, grain and oats have been sown. During 1873, about 48 acres (75 Morgen) produced 423 bushels (280 Scheffel at 85 Pfund), and were sold on the spot at 42d. per bushel. The vegetables returned a gross sum of £16 108. (110 Thaler) per