Page images
PDF
EPUB

Motion of water in rivers,

Hydraulic machines.

Sa2/D 10

reduced to th part, so that the preceding formula in that case must be
changed iuto = = a2√ D. When the water flows in iron pipes, the
deduction to be made is much greater. It is obvious that the quantity of fric-
tion must increase in all cases with the length of the tubes. Suppose the diame-
ter of the pipe to be r, then a (or the area of the pipe), æo.
=2. Hence we
Such is the theoretical

have Пr2 =

Q
8/D

; and of consequence r =

8D/D

expression for the diameter of the tube; but experiment gives us a very differ-
ent expression, from it we have a=
When the Magistrates of

5Q 40/D

Edinburgh first brought water into that city by leaden pipes, they applied to Dr. Desaguliers, and to Mr. Maclaurin, to inform them what quantity of water they could obtain by means of a pipe of a given diameter. After the pipes were laid, the quantity of water discharged was measured and found to be only th of Desagulier's estimate, and th of the estimate of Maclaurin.

The motion of water in rivers was first accurately investigated by Du Buat. It exhibits the greatness of the friction in a very striking point of view; for the motion of rivers soon become equable: Hence the whole force of gravity must be nearly employed in overcoming the force of friction. The mean velocity of most rivers may be reckoned about four feet per second, or not quite three miles in the hour. The water next the bottom moves slowest, and the rapidity gradually and equably increases from the bottom to the surface, which moves with the greatest rapidity. The same thing holds from the centre of the stream to the edges of the river. When a river winds, its velocity is diminished, and the diminution is the greater the more abruptly the direction is changed. The greatest velocity of a winding river is usually at its concave edge, which is contrary to what one would naturally expect.

Hydraulic machines are usually divided into three kinds; those that are put in motion by the impulse, by the weight, and by the reaction of water.

Unless the wheel go slower than the water, it will be able to do no work. If the velocity be too small, it will also do very little work. Hence there is some intermediate velocity which will give the greatest advantage. Theory gives us the greatest advantage when the velocity of the wheel is one third that of the stream. But the experiments of Mr. Smeaton, to whom we are indebted for the first accurate experimental investigation of the theory of the different kinds of water wheels, have shewn that the velocity of the wheel may be a little greater than 4d of that of the stream.

Theoretical reasoning gives us the work done by such a wheel equal to of the water expended. But practice gives us the double of this, or nearly d of the water expended.

ths

A

ths,

[ocr errors]

There are two kinds of water wheels; namely, the undershot, in which the Water shoeks water escapes below the wheel, and acts by pressure; and the overshot, which is moved by the weight of the water filling the buckets on one side, and of course turning the wheel round. An overshot wheel must go slowly, otherwise part of the water is thrown off and lost by the centrifugal force. This wheel is much more powerful than the undershot, the effect produced being equal to 2 thirds of the water expended. The greatest effect is produced when the circumference of the wheel moves with a velocity of three feet per second.

E

A

The Hydraulic machines set in motion by the reaction of water, have the advantage of requiring very little apparatus; but a considerable fall is necessary to enable them to act with efficacy. I do not know any example of such a hydraulic engine in Great Britain: though there are certainly many spots where they might be erected with advantage, Suppose a cylinder A B terminating in a box, and moveable about an axis, D E. Suppose a hole to be opened at c, if the whole be filled with water, the fluid issuing out at c, from the reaction of the column of water on the side opposite to c will cause the whole to move round. At F there is another hole on the opposite side of the box. There may be another box with similar holes crossing the box CF at right angles. It is obvious that if a stream of water constantly enter at E sufficient to keep the cylinder and boxes full, the whole will turn round, and may be made to put in motion any apparatus proportional to the force with which it

[graphic]

moves.

F

D

C

When a body moves through water, the resistance is rather greater than the square of the velocity; and it varies exceedingly according to the shape of the body in motion. Thus the resistance to a sphere is much greater than to a sphere cut in two, with a cylinder interposed between them. A long body with the hinder end pointed, is much less resisted than when that end is flat. The reason is, because the water displaced does not close in upon the body instantaneously, and of course the pressure from behind must be diminished as the flatness of that surface increases.*

The papers on Hydraulics in the Philosophical Transactions amount to 34. Papers in the But of these there are no fewer than 15 of so little value, that we may without Transactions, impropriety leave them out of consideration. The remaining 19 are of various degrees of importance. Some of the statements given in the preceding pages

A very curious and valuable set of experiments on this subject have been made by Col. Beaufoy, F. R. S. of the Tower Hamlet Militia. But unfortunately he has not thought proper to communicate his results to the public.

have been derived from them. We shall take a view of the contents of these papers in the same manner as we have done of those concerning the preceding branches of this subject.

1. We may mention two books on the subject of Hydraulics, of which an account is given in the Philosophical Transactions; the first is the Traité du Mouvement des Eaux et des autres Corps fluides, by Mariotte. This book contains some good experiments on the quantity of water discharged from a given orifice in the side of a vessel.* The other is entitled De Motu Aquæ mixto, and is written by Poleni, a Professor at Padua. It contains a very good historical account of the progress of discoveries relative to Hydraulics before the publication of this book. He deduces a theorem from a set of experiments which he made, and concludes from it that diminishing the breadth of rivers at the mouth, often lessens instead of increases their velocity. A proposition quite inconsistent with experience, and therefore inadmissible.†

2. There are four very elaborate papers by Dr. Jurin, in which he gives the theory of water issuing out at a hole from a vessel. The theory is not confirmed by experiments; but there is no doubt that it is very nearly just, and that it would not differ much from the result of experiments, if made with precision.‡

3. Dr. Desaguliers has given us a description of a pump for raising water, contrived by Mr. Hoskins, in which, instead of the common piston with leather, the vacuum is accomplished by means of mercury. In the common pumps the loss of water is about 4th at an average, and often more. In this new pump the whole water given by the capacity of the engine is discharged. But the great expence of mercury, and the probability that it would be speedily oxydized in such a situation, will ever prevent contrivances of this nature from coming into

common use.

4. The discharge of water through long pipes is much smaller than through short. This difference is partly occasioned by the friction. But Dr. Desaguliers turning his thoughts to the subject, found that there was another cause; namely, the air confined in the upper part of the pipes, which diminished their bore, and of course might lessen the quantity of water discharged almost to any amount. With the assistance of his friends, he contrived a very ingenious apparatus for letting out this air, whenever it accumulated, to which he gave the very fanciful appellation of Jack in a box.

5. Mr. Beighton, a celebrated civil engineer of the time, has given us an accurate description of the water-works at London Bridge, which consist of a

* Phil. Trans. 1686. Vol. XVI p. 119.

+ Phil. Trans. 1717. Vol. XXX. p. 723.

† Phil. Trans 1718. Vol. XXX. p. 748; and 1722. Vol. XXXII. p. 179; and 1739. Vol. XLI. p. 5 and 65.

Phil. Trans. 1722. Vol. XXXII. p. 5.

Phil. Trans. 1726. Vol. XXXIV. p. 77.

set of forcing pumps, driven by the tide, for raising water out of the river Thames, for the use of that part of the city which is in the neighbourhood. The quantity of water, which these pumps raise to the height of 120 feet, amounts to 1563 hogsheads in the hour; supposing a loss of 4th of the quantity calculated from the capacity of the cylinders.*

6. Mr. Robertson has given us the formula for calculating the fall of water under bridges, in consequence of the diminution of the breadth of the current by the piers; and has applied his formula to London and Westminster bridges, the only two existing at London at the time when he wrote. The breadth of the Thames, at London bridge, is 926 feet. The sum of the water ways, at the time of the greatest fall, is 236 feet. The fall at London bridge is four feet nine inches. The breadth of the Thames, at Westminster bridge, is 1220 feet; but at the time of the greatest fall there is water only through the 13 large arches, which amount to 820 feet; to which, adding the breadth of the 12 intermediate piers, equal to 174 feet, we obtain 994 feet for the breadth of the river at that time. The fall amounts only to an inch.†

7. The next paper which we have to mention is a very valuable one, by Mr. Smeaton, entitled, An Experimental Inquiry concerning the natural Powers of Water and Wind to turn Mills and other Machines depending on a circular Motion. This paper is so very long, that we cannot attempt giving a general view of its contents. It was from it that the first accurate views respecting overshot and undershot wheels were obtained. The principles laid down at the commencement of this article were derived from this paper.

8. The next paper we shall mention is a dissertation by M. Mallet, of Geneva, on the most advantageous construction of water wheels.§

9. Mr. Whitehurst has given a curious account of a contrivance for raising water, employed at Oulton, Cheshire, the seat of Philip Egerton, Esq. The water was contained in a reservoir, from the bottom of which there passed a pipe to the kitchen, sixteen feet below the reservoir. This pipe had two extremities; one of them furnished with a stop-cock, was for the use of the kitchen; the other, furuished with a valve, terminated near the bottom of a stout vessel containing air. From the bottom of this air vessel, there passed a tube to another reservoir, higher than the original reservoir, and destined for the brew-house. When water was drawn for the kitchen, the water in the pipe acquired, by running, a considerable velocity. Hence, when the stopcock was shut, it acted on the valve, forced it open, and rushing into the air vessel, compressed the air which it contained. This happening every time that water was drawn for the use of the kitchen, which was very frequenily, the

* Phil. Trans. 1781. Vol. XXXVII. p. 5. Phil. Trans. 1759. Vol. LI. p. 100.

+ Phil. Trans. 1758. Vol. L. p. 492.

₫ Phil. Trans, 1767. Vol. LVII. p. 372.

Aerostatics.

water made its way into the brew-house reservoir, and supplied it sufficiently.*

10. Major Renuel, so well known by his important geographical labours, has given us a very curious and entertaining account of the Ganges and Burrampooter; two mighty rivers, which, rising from opposite sides of the mountains of Thibet, run, the one west, and the other east, and afterwards meeting in Bengal, flow united into the sea, discharging a most enormous mass of water. The average breadth of the Ganges is about a mile; that of the Burrampooter, between three and five miles. When the Ganges swells, in the rainy season, the average rise is about 31 feet. The fall of the Ganges is about four inches per mile; and the river flows at the rate of about three miles in the hour; but in the rainy season the rate is increased to six miles in the hour. The average quantity of water discharged by the Ganges into the sea, is 80,000 cubic feet per second; but, during the rainy season, the quantity discharged amounts to 405,000 cubic feet. The Ganges varies its channel very much during its course through Bengal, wearing away the banks on one side, while land is formed on the other side. It empties itself into the sea by eight great channels. Major Rennel was the original discoverer that the Sanpoo, of Thibet, is the same with the Burrampooter. Before that time, the Sanpoo had been supposed to discharge itself into the sea by the Gulph of Ava. To him, then, we are indebted for our knowledge of the Burrampooter, as one of the largest rivers of Asia.t

11. The last paper we shall mention, consists of a valuable set of experiments, on the resistance of bodies moving in fluids; made by Mr. Vince. He shows, that the resistance is much greater than that given by theory; and hence deduces, very justly, that every theory of such resistances can only be deduced from experiment.‡

SECTION II.-Of Pneumatics.

Under the word Pneumatics, in our language, two different branches of Hydrodynamics are usually included; namely, the consideration of elastic fluids in a state of rest, and in a state of motion. Some persons, indeed, have lately distinguished the first branch by the name of Aerostatics; and the second, by that of Pneumatics. As they occupy only a very subordinate place in the Philosophical Transactions, it will not be necessary for our purpose to divide Pneumatics into two separate sections.

I. Galileo may be considered as the founder of this science; for he was the first person that supposed the air to have weight. This truth was established by

* Phil. Trans. 1775. Vol. LXV. p. 277.

‡ Phil. Trans. 1798. Vol. LXXXVIII. p. 1.

+ Phil. Trans. 1781. Vol. LXXI. p. 87.

« PreviousContinue »