In M. Bossut's first experiments the apertures for the efflux of the water were all pierced perpendicularly in plates about a line thick.

M. Bossut has given in his Hydrodynamique (tome 11. p. 17.) the following table relative to the discharge through orifices pierced in thin plates: the measure is the Paris foot royal, which is to the English foot as 1535 to 1110, or 1666 to 1000; the fourth column, which expresses the relation between the results of the experiments or those of the theory, is from M. Prony.

If the numbers in the last column are multiplied together, and the 15th root of the last product taken, we shall have 61932 for the true mean of the effective discharges, compared with the theoretic discharge 1; and the arithmetical mean between the numbers in the last column standing against the heights 7 and 8, is 61938: the mean ratio between the actual and theoretic discharges, then, is not widely distaut from that of 62 to 1: whence it fol lows, from the remarks just given, that 62 is the number by which we must multiply the real area of the orifice to obtain the area of the smallest section of the contracted vein.

Another set of experiments made by M. Bossut, with different apertures, are the following, in which the water was kept constantly at the altitude of 11 feet, 8 inches, 10 lines, from the centre of each aperture.

5. With a square horizontal aperture, the side 1 inch................

11817

6. By a square horizontal aperture, the sides 2 inches..

47361

Constant height 9 feet.

7. Lateral circular aperture, 6 lines diameter....

8. Lateral circular aperture, 1 inch diameter....

Constant height 4 feet.

9. Lateral circular aperture, 6 lines diameter....

2018

$135

Constant height 7 lines.

11. By a lateral and circular orifice, 1inch diameter...

1331

2722

0-621331 0-62073)

1353

10. Lateral circular aperture, 1 inch diameter...

5436

628

From the preceding experiments, we may make the following deductions:

1. The quantities of fluid discharged in equal times from different sized apertures, the altitude of the fluids being the same, are nearly to each other as the areas of the apertures. Thus in the second and third experiments the areas of the apertures are as one to four, and the water discharged 9281 cubic inches to 37203 is nearly in the same

ratio.

2. The quantities of water discharged, in equal times, by the same aperture, with different altitudes of the reservoir, are nearly as the square roots of the corresponding altitude of the water in the reservoir above the centre of the aperture.' Comparing together the eighth and tenth experiments, in which the respective altitudes of the reservoir were of 9 and 4 feet, of which the square roots are 3 and 2, we find the water

discharged by the first was 8135 cubic inches, the second 5-136 cubic inches nearly in the proportion of 3 to 2, as before observed.

3. That, in general, the quantities of water discharged in the same time, by different apertures and under unequal altitudes of the reservoirs, are to each other in a compound ratio of the areas of the apertures and the square roots of the altitudes.

4. That, on account of the friction, the smallest apertures discharge less water than those that are larger and of a similar figure, the water in the respective reservoirs being at the same height.

5. That of several apertures whose areas are equal, that which has the smallest circumference will discharge more water than the others, the water in the reservoirs being at the saine altitude,' and this because there is less friction. Hence circular apertures are most advantageous, as they have less rubbing surface under the same area.

Hence, then, to make the formula in the theory furnish such results as would agree with experiments, we must reduce the aperture a in those theorems in the ratio of 62 to 1; or multiply the quantities resulting from the theorems as they now stand by the decimal 62; or, lastly, if great accuracy be required, take, instead of the constant multiplier 62, the number standing against the height of fluid in the reservoir above the orifice, in the last column of the table in the preceding article: thus, if the altitude of the fluid be 10 feet, the multiplier will be -61583.

If the water, instead of flowing through an aperture pierced in a thin substance, passes through the end of a vertical tube of the same diameter as the aperture, there is a much greater discharge of water, because the contracted stream is greater in the first instance than in the second. In the following experiments, the constant height of the water in the reservoir above the upper aperture of the tube was 11 feet 8 inches 10 lines, the diameter of the tube 1 inch.

tube is, the greater is the discharge of the water, because the contraction of the stream is less; it is, however, always somewhat contracted, even when it appears to fill the tube.

By comparing the quantities of water discharged in the third and fourth experiments, we find the two discharges 12168, 9282, are to each other nearly in the proportion of 13 to 10; but we have seen that the water discharged through a thin aperture without any contraction in the stream, would be to the same aperture with a contracted stream, as 1 to 62, or as 16 to 10. From hence we may conclude, that, the altitude in the reservoir and the apertures being the same, the discharge through a thin aperture without any contraction in the stream, the discharge through an additional tube, and the discharge through a similar aperture with a contracted stream, are to each other nearly as the numbers 16, 13, 10: these propor tions are sufficiently exact for practice. Hence it is plain that an additional tube only destroys in part the contraction of the streami, which contraction is greatest when the water passes through a thin aperture from a large reservoir.

If the additional tube, instead of being vertical, or placed at the bottom of the reservoir, was horizontal, or placed in the side, it would furnish the same quantity of water, provided it was of the same length, and that the exterior aperture was at the same distance from the surface of the water in the reservoir.

The

If the additional tube, instead of being cylindrical, was conical, having its largest base nearest the reservoir, it would discharge a greater quantity of water. most advantageous form that can be given in order to obtain the greatest quantity of water in a given time by a given aperture, is that which the stream assumes in coming out of the aperture; i. e. the tube must be of the form of a truncated cone, whose largest base should be of the same diameter as the aperture; the area of the small base should be to that of the larger base as 10 to and the distance from one base to the other should be the semidiameter of the largest base, and the efflux of water will be as abundant as it would be through a thin aperture equal to the smallest base, and where the stream was not contracted. This form may be applied where it is necessary to obtain a certain quantity of water from a river, an aqueduct, &c. by a canal or lateral tube.

16;

On comparing the efflux of water through additional tubes of different diameters, and with different altitudes of the water in the reservoirs, the following results were obtained; the additional tubes were two inches long, and were vertical and placed at the bottom of the reservoir.

It results from these experiments, 1. "That the discharges by different additional tubes, with the same altitude of the reservoir, are nearly in proportion to the area of the apertures, or to the squares of the diameters. 2. That the discharges of water by additional tubes of the same diameter, with different altitudes of water in the reservoir, are nearly proportional to the square root of the altitude of the reservoir. 3. That in general the discharges of water in the same time, through different additional tubes, with different altitudes of water in the same reservoir, are each other nearly as the product of the square of the diameters of the tubes by the square root of

to

the altitude of the reservoirs." So that additional tubes, transmitting water, follow (among themselves) the same laws as through the thin orifice. The following table was formed from the foregoing

ments.

experi

The mean of the numbers in the last column of this table is somewhat less than 81 as a very good approximation to the truth: using it as a constant co-efficient in the formula for the value of Q given in an earlier prop. when we wish to know the discharge through a cylindric tube of the dimensions specified at the head of column the third. Thus we shall have Q=81 a t gh; the dimensions being all in feet, or all in inches.

We now pass to M. Bossut's experiments on the exhaustion of vessels (which have no extraneous supply) by little orifices.

The experiments upon the time of complete exhaustion of vessels which empty freely are not easy to make, at least in a conclusive manner: for, besides that in some cases the complete exhaustion would, according to the theory, require an unlimited time, it is found that, when the surface of the water arrives within a small distance, as two or three inches, of a horizontal orifice, it forms above that orifice a conical or rather conoidal funnel, which diminishes the effect, and makes the conclusion of the discharge uncertain. It is best, therefore, not to make experiments upon the time of total discharge, but upon the time in which the upper surface is depressed through a certain vertical distance a, the greater the better, provided the upper surface has not sunk so low as to perinit the formation of the funnel just spoken of.

It was shown (equa. II.) that when the primitive height of the water in a prismatic vessel wash, the constant section of the vessel A, the time t employed by the fluid to descend through the space a was expressed by this equation :

Hence we see that the difference between the results of the computation and those of the experiments are extremely small: much smaller indeed than might be expected, considering the many circumstances which may contribute to vary the times given by observation. So that we may regard the formulæ given in this article as sufficiently correct for practice; at least within the limit suggested by the formation of the conoidal funnel. What has been here said, applies principally to horizontal apertures; but it may be applied without fear of material error to small lateral orifices, when the fluid in the reservoir stands higher than the upper side of the orifice, and taking for the height the distance of the centre of gravity of the orifice from the upper surface of the fluid.

Experimental Inquries of Venturi. The experiments and researches of M. J. B. Venturi, professor of natural philosophy at Modena, are neither so extensive nor so important as those of M. Bossut; but es he has noticed two or three curious circumstances relative to the motion of fluids, which seem to have escaped the observation of preceding philosophers, we shall present the reader with a concise account of the result of his inquiries.

I. In any fluid, those parts which are in motion carry along with them the lateral parts which are at rest.

To show the truth of this proposition, M. Venturi introduced a horizontal current of water into a vessel filled with the same fluid at rest. This stream entering the vessel with a certain velocity, passes through a portion of the fluid, and is then received in an inclined channel, the bottom of which gradually rises, until it passes over the border or rim of the vessel itself. The effect is found to be, not only that the stream itself passes out of the vessel through the channel,

but carries along with it the fluid contained in the vessel; so that after a short time no more of the fluid remains than was originally below the aperture at which the stream enters. This fact is adopted as a principle or primitive phenomenon by the author, under the denomination of the lateral communication of motion in fluids, and to this he refers many important hydraulic facts. He does not undertake to give an explana tion of this principle, but shows that the mutual attraction of the particles of water is far from being a sufficient cause to account for it.

II. If that part of an additional cylindric tube which is nearest the side of the reservoir be contracted, according to the form of the contracted vein of fluid which issues through a hole of the same diameter in a thin plate, the expenditure will be the same as if the tube were not contracted at all; and the velocity of the stream within this tube will be greater than that of a jet through a thin plate in the ratio of 121 to 100

III. The pressure of the atmosphere increases the expense of water through a simple cylindrical tube, when compared with that which issues through a hole in a thin plate, whatever may be the direction of the tube.

IV. In descending cylindrical tubes, the upper ends of which possess the form of the contracted vein, the discharge is such as corresponds with the height of the fluid above the inferior extremity of the tube.

V. In an additional conical tube the pressure of the atmosphere increases the expenditure in the proportion of the exterior section of the tube to the section of the contracted vein, whatever may be the position of the tube, provided its internal figure be adapted throughout to the lateral communication of motion.

VI. In cylindrical pipes the expenditure is less than through conical pipes, which diverge from the place of the contracted vein, and have the same exterior diameter.

For in the space between the inverted contracted vein and the sides of the cylinder eddies, or circular whirls, are produced, as in a basin which receives water by a channel; and these retard the efflux of the stream, and produce a corresponding failure in the effect.

VII. By means of proper adjutages applied to a given cylindric tube placed horizontally, it is possible to increase the expenditure of water through that tube in the proportion of 24 to 10, the charge or height of the reservoir remaining the same.

For this purpose the inner extremity of the tube AD (fig. 4. pl. 87) must be fitted at AB with a conical piece of the form of the contracted vein; this increases the expenditure as 121 to 10. Every other form will afford less. If the diameter at A be too great the contraction must be made beyond B, and the section of the vein will be smaller than the section of the tube. Secondly, at

the other extremity of the pipe BC apply a truncated conical tube CD, of which let the length be nearly nine times the diameter C, and its external diameter D must be 1.5 C. This additional piece will increase the expenditure as 24 to 121. So that the quantity of effluent water will be increased by the two adjutages in the ratio of 21 to 10. All this is on the supposition that the pipe BC has no elbows or sinuosities.

VII. The expenditures out of a straight tube, a curved tube in a quadrantal are, and an elbowed tube having the angle 90°, (each being posited horizontally) are cæt. par. nearly as 70, 50, and 45.

IX. The internal roughness of a pipe diminishes the expenditure, though the frie tion 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 have a diameter greater than the orifice to which it is applied; but, notwithstanding, the expenditure will be greatly diminished if the pipe should have enlarged parts, or swellings: for, by reason of these sudden changes in the interior dimensions of the pipe, much of the motion will be consumed in eddies. This, as M. Venturi remarks, is a very interesting circumstance, to which, perhaps, sufficient attention has not been paid in the construction of hydraulic machines. It is 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.

The above comprises what to us appeared most important in M. Venturi's researches, relative immediately to the subject of hydrodynamics. Those, however, who are desirous of seeing a more detailed account of this ingenious author's experiments may consult Mr. Nicholson's translation of his work "On the Lateral Communication of Motion in Fluids," sold by Taylor, Holborn. Practical Conclusions of Mr. Eytelwein. Mr. Eytelwein published at Berlin, in 1801, a treatise entitled Handbuch der Mechanik und der Hydraulik; from the second part of which, relative to hydrodynamics, we shall extract a few particulars,

1. In the chapter on the motion of water flowing out of reservoirs, and on the contraction of the stream, this gentleman makes the area of a section at the distance of about half its diameter from the orifice about of that of the aperture: hence the diameter is reduced to . The quantity of water dis. charged is very nearly, but not quite, sufficient to fill this section with the velocity due to the height; for finding more accurately the quantity discharged, the orifice must be supposed diminished to 619, or nearly Hence the square root of the beight may be multiplied by 5 instead of 8,

(an approximate root of 644) for the mean velocity in a simple orifice.

II. If we apply the shortest pipe that will cause the stream to adhere every where to its sides, which will require its length to be twice its diameter; the discharge will be about of the fall quantity, and the velocity may be found by taking 64 for a multiplier.

II. The greatest diminution is produced by inserting a pipe so as to project within the reservoir, probably because of the greater interference of the motions of the particles approaching its orifice in all direc tions in this case the discharge is reduced nearly to a half.

IV. A conical tube approaching to the figure of the contraction of the stream procured a discharge of 92, and when its edges were rounded off, a discharge of 98, calculating on its least section.

V. Mr. Eytelwein is of opinion that the assertion of Venturi is too strong, and oh. serves that where the pipe is already very long, scarcely any effect is produced by the addition of such a tube. He proceeds to describe a number of experiments made with different pipes, where the standard of com parison is the time of filling a given vessel out of a large reservoir, which was not kept always full, as it was difficult to avoid agita tion in replenishing it; and this circumstance was perfectly indifferent to the results of the experiments. They confirm the assertion that a compound conical pipe may increase the discharge to twice and a half a much as through a simple orifice, or to more than half as much more as would fill the whole section with the velocity due to the height: but where a considerable length of pipe intervenes the additional orifice ap pears to have little or no effect.

as

VI. The first chapter concludes with a general table of the coefficients for finding the mean velocity of the water discharged by the pressure of a given head under different circumstances.

1. For the whole velocity due to the height, the coefficient by which its square root is to be multiplied is 80205.

2. For an orifice of the form of the contracted stream, 7.8.

3. For wide openings, of which the bottom is on a level with that of the reservoir; for sluices with walls in a line with the orifice; for bridges with pointed piers, 77.

4. For narrow openings, of which the bottom is on a level with that of the reservoir; for smaller openings in a sluice with side walls; for abrupt projections and square piers of bridges, 69.

5. For short pipes, from two to four times as long as their diameter, 6·6.

6. For openings in sluices without side walls, 5.

7. For orifices in a thin plate, 5·1.

VI. In the chapter on the discharge by rectangular orifices in the side of a reservoir,