PROPOSITION VII. By means of proper Ajutages applied to a given cylindric Tube, it is possible to increase the Expenditure of Water through that Tube in the proportion of Twenty-four to Ten, the Charge or Height of the Reservoir remaining the same. I shall here give an account of the different precautions necessary to be taken when the expenditure of water through a cylindrical tube of a given length is required to be the greatest possible. 1. The inner extremity of the tube A D (Fig. 13), must be fitted at A B with a conical piece of the form of the contracted vein; this increases the expenditure as 12.1 to 10. Every other form will afford less. If the diameter at A be too great, the contraction will be made beyond B, and the section of the vein will be smaller than the section of the tube. 2. At the other extremity of the pipe B Capply a truncated conical tube CD, of which let the length be nearly nine times the diameter C, and its external diameter D must be 1.8 C. This additional piece will increase the expenditure as 24 to 12.1, (Experiment 16). By this means the quantity of water will be increased by the two ajutages A B, CD, in the proportion of twenty-four to ten.† * Bossut, Art. 509. The idea that this ratio will apply to long pipes is erroneous; for it must obviously decrease as the force necessary to produce motion increases; and, therefore, in long pipes will have very little effect. It may also be inferred that the effect of a truncated tube applied at the outer extremity will depend considerably on the velocity of the efflux. The Roman law, mentioned in the next At Rome, the inhabitants purchase the right of conveying water from the public reservoirs into their houses. The law prohibits them from making the pipe of conveyance larger than the aperture granted them at the reservoir, as far as the distance of fifty feet.* The legislature was, therefore, aware, that an additional pipe of greater diameter than the orifice would increase the expenditure; but it was not perceived that the law might be equally evaded by applying the conical frustum CD beyond the fifty feet. From the second rule we learn, that it is not proper to make the flues of chimneys too large in the apartments; but that it will be sufficient if they be enlarged at their upper terminations, according to the form CD, Fig. 13. This divergency of the upper part will carry off the smoke very well, even when it is not practicable to afford chimneys of sufficient length to the upper apartments. The same observation is applicable to chemical furnaces for strong fire. 3. The pipe B C ought to be straight, without elbows or curvatures. To the experiments which Bossut has made on this head, I shall add the following: EXPER. 23.-The two tubes ABC, DEF, Fig. 14. Plate II, are 15 inches long; their diameter is 14.5 lines. The conical portions A, D, have the form of the contraction of the vein of fluid, and are applied to the orifice P, Fig. 1, which is 18 lines in diameter, with 32.5 inches depth, or charge of superincumbent fluid. The elbows, or flexures, BC, EF, are made paragraph has most likely limited the distance to that where the increase of expenditure would be inconsiderable for the size of pipe commonly used at the time.-ED. * Fontin. de Aquæduct. Art. 205, 106 et 112. † Art. 631, et seq. in the plane of the horizon. These two pipes are made of copper soldered with silver, and the workmanship carefully executed. The curvature B C was drawn out or bended, into the form of a quarter of a circle, by filling the tube with melted lead in order that it might preserve its diameter during the act, of bending. The elbow D E F is constructed in a right angle. The expenditure through these two tubes was compared with that afforded through a right-lined cylindrical tube of similar dimensions, and in like circumstances. The four cubical feet of water flowed out of the cylindrical tube in 45′′; out of the curved tube A BC in 50"; and out of the angular tube DEF in 70". It is of importance that the tube B C, Fig. 13, Plate I, should be of an equal diameter throughout. It is not enough that care be taken that there should be no contraction; it is also necessary that it should not be enlarged at any part. For such enlargements have nearly the same bad effect in the expenditure as contractions: The pipe A O, Fig. 12, affords a much less quantity of fluid with the dilatations DE, HI, than if it were of a diameter equal to that at B throughout its whole length. The following experiment agrees with the theory. EXPER. 24.-The circular orifice A, Fig. 12, has the form of the contraction of the vein, and the remaining part of the tube is interrupted by various enlargements of its diameter. This tube is applied to the aperture P, Fig. 1. The dimensions of its parts measured in lines are as follow:-Diameter at A = 11.2. Diameter at B, C, F, G, &c., = 9. 9. Length of BC= FG, &c., = 20. Length of C D E F = GH, &c., = 13. Diameter of the enlarged parts 24. The length of each of the enlarged parts was variable. The first time of trial it was 38 lines, the second 76, and the result of the experiment was the same in both cases. I afterwards applied to the same orifice a tube, having the same form, and the same diameter, as A B C, but cylindrical throughout, without any enlargements, and its length was thirty-six inches, the same as that of the tube with five enlarged parts; and, in this case, the expenditure of four cubical feet was made in 148". When the fluid passes from C to the middle of the enlarged part D E, part of the motion is diverted from the direction C F towards the lateral parts of the enlargement. This part of the motion is consumed in eddies, or against the sides. Consequently, there remains so much the less motion in the following branch FG. This is also the cause which destroys or weakens the pulse in the arteries beyond an aneurism. From this consideration we are justified in concluding, that if the internal roughness of a pipe diminishes the expenditure, the friction of the water against these asperities does not form any considerable part of the cause. A right-lined tube may have its internal surface highly polished throughout its whole length; it may every where possess a diameter greater than the orifice to which it is applied; but, nevertheless, the expenditure will be greatly retarded, if the pipe should have enlarged parts or swellings. This is a very interesting circumstance to which, perhaps, sufficient attention has not been paid in the construction of hydraulic machines. It is not enough that elbows and contractions are avoided; for it may happen, by an intermediate enlargement, that the whole advantage may be lost, which may have been procured by the ingenious dispositions of the other parts of the machine. PROPOSITION VIII. In the Machine for blowing by means of a Fall of Water, the Air is afforded to the Furnace by the accelerating Force of Gravity, and the lateral Communication of Motion, combined together. I The academy of Toulouse, in the year 1791, invited philosophers to determine the cause and the nature of the stream of air which is produced by the fall of water in certain forges. propose, in this place to develope the complete action of this kind of blowing apparatus, and to ascertain the best form of construction. Kircher is the first I know of, who has explained the production of wind by a fall of water.* Barthes, the father, has given a theory which appears to me to be defective in many respects.† Dietrich was of opinion, that this wind is produced by the decomposition of water. Fabri had a similar notion in the last century.§ Most philosophers are well acquainted with this kind of engine.|| I shall begin with an idea, the foundation of which did not escape the penetration of Leonardo da Vinci. Suppose a number of equal balls to move in contact with each other along the horizontal line A B, Fig. 15, Plate II. Imagine them to pass * Mundus Subterr. lib. xiv. cap. 5, edit. 1662. § Physic. Tract. i. lib. ii. prop. 243. Art. des Forges, part. ii.. Mariotte des Eaux, part i. disc. iii. Transact. No. 473, &c. |