Difference between the Levels of High and Low Water Spring Tides, between Rotherhithe and Battersea in the year 1820. From Battersea Bridge to London Bridge, 5 miles; from London Bridge to Old Horse Ferry, 14 miles. From London Bridge to the Nore, 44 miles.* SECTION V.-Watermills. 1. The impulse of a current of water, and sometimes its weight and impulse jointly, are applied to give motion to mills for grinding corn and for various other purposes. Sometimes the impulse is applied obliquely to floatboards in a manner which may be comprehended at once by reference to a smokejack. In that, the smoke ascends, strikes the vanes obliquely, and communicates a rotatory motion. Imagine the whole mechanism to be inverted, and water to fall upon the vanes, rotation would evidently be produced; and that with greater or less energy in proportion to the quantity of water and the height from which it falls. Water-wheels of this kind give motion to mills in Germany, and some other parts of the continent of Europe. I have, also, seen mills of the same construction in Balta, the northernmost Shetland Isle. But wherever they are to be found, they indicate a very imperfect acquaintance with practical mechanics; as they occasion a considerable loss of power. 2. Water frequently gives motion to mills, by means of what is technically denominated an undershot wheel. This has a number of planes disposed round its circumference, nearly in the direction of its radii, these floatboards (as they are called) dipping into the stream, are carried round by it; as shown in the accompanying diagram. The axle of the wheel, of The preceding results will always be valuable, as they supply striking evidence of the effect of a broken dam, such as many of our old bridges present. I regret that the contrast occasioned by the large arches of the new bridge cannot yet be presented for though the old bridge is removed, the entire obstructions occasioned by the starlings were not taken away when this volume went to the press. course, by the intervention of proper wheels and pinions, turns the machinery intended to be moved. Where the stream is large and unconfined, the pressure on each floatboard is that corresponding to the head due to the relative velocities (or difference between the velocities of stream and floatboard): this pressure is, therefore, a maximum when the wheel is at rest; but the work performed is then nothing. On the other hand, the pressure is nothing when the velocity of the wheels equals that of the stream. Consequently, there is a certain intermediate velocity, which causes the work performed to be a maxi mum. The weight equal to the pressure is Q (H— √ h)2, Q being the quantity of water passing in a second, н the height due to v the velocity of the water, and h that due to u the velocity of the floatboard. Considering this as a mass attached to the wheel, its moving force is obtained by multiplying it into u and as ✔ H ✔h varies as v- u, this moving force varies as (v U)2 u which is a max. when u = v. In this case, then, the rim of the wheel moves with of the velocity of the stream; and the effect which it produces is so that the undershot wheel, according to the usual theory, performs work of the moving force. Friction, and the resistance of fluids, modify these results; but Smeaton and others have found that the maximum work is always obtained when u is between v and v. 3. Where the floats are not totally immersed, the water is heaped upon them; and in this case the pressure is that due to 2 H. 4. When the floatboards move in a circular sweep close fitted to them, or, in general, when the stream cannot escape without acquiring the same velocity as the wheel, the circumstances on which the investigation turns become analogous to what happens in the collision of non-elastic bodies. The stream has the velocity v before the stroke which is reduced to u, and the quantity of motion corresponding to the difference, or to v u, is transferred to the wheel; this turns with the velocity u; and therefore the effect of the wheel is as VU U9 ; which is a maximum when v = 2U; ()u, or, V V being then of the moving power. Hence appears the utility of constraining the water to move in a narrow channel. 5. The undershot wheel is used where a large quantity of water can be obtained with a moderate fall. But where the fall is considerable the overshot is almost always employed. Its circumference is formed into angular buckets, into which the h = v, the velocity of the circumf. of the wheel to produce a maximum effect, will = 2.67 ✔ H. Here, too, a fall of will give the water its due velocity of impact upon the wheel and 3 2 122-176 8 lbs = the mechanical effect, s being the section, in feet, of the stream that supplies the buckets. Mr. Smeaton's experiments led him to conclude that overshot wheels do most work when their circumferences move at the rate of 3 feet in a second, and that when they move considerably slower than this, they become unsteady and irregular in their motion. This determination is, however, to be understood with some latitude. He mentions a wheel 24 feet in diameter, that seemed to produce nearly its full effect, though the circumference moved at the rate of 6 feet in a second; and another of the diameter of 33 feet, of which the circumference had only a velocity of 2 feet in a second, without any considerable loss of power. The first wheel turned round in 12. 6, the latter in 51. 9. 6. Where the fall is too small for an overshot wheel, it is most advisable to employ a breast-wheel (such as exhibited in the margin), which partakes of its properties; its floatboards meeting at an angle, so as to be assimilated to buckets, and the water being considerably confined within them by means of an arched channel fitting moderately close, but not so as to produce unnecessary friction. But when the circumstances do not admit of a breast-wheel, then recourse must be had to the undershot. For such a wheel it is best, that the floatboards be so placed as to be perpendicular to the surface of the water at the time they rise out of it; that only one half of each should ever be below the surface, and that from 3 to 5 should be immersed at once. The Abbe Mann proposed that there should not be more than six or eight floatboards on the whole circumference. 7. Mills moved by the reaction of water are usually denominated Barker's Mills; sometimes, however, Parent's; at others, Segner's. But the invention is doubtless Dr. Barker's. In the marginal diagram, where c D is a vertical axis, moving on a pivot at D, and carrying the upper millstone m, after passing through an opening in the fixed millstone c. Upon this axis is fixed a vertical tube TT communicating with a horizontal tube A B, at the extremities of which A, B, are two apertures in opposite directions. When water from the mill-course M N is intro M N duced into the tube T T, it flows out of the apertures, A, B, and by the reaction or counter-pressure of the issuing water the arm A B, and consequently the whole machine, is put in motion. The bridge-tree a b is elevated or depressed by turning the nut c at the end of the lever c b.. In order to understand how this motion is produced, let us suppose both the apertures shut, and the tube T T filled with water up to T. The apertures A B, which are shut up, will be pressed outwards by a force equal to the weight of a column of water whose height is T T, and whose area is the area of the apertures. Every part of the tube A B sustains a similar pressure; but as these pressures are balanced by equal and opposite pressures, the arm A B is at rest. By opening the aperture at A, however, the pressure at that place is removed, and consequently the arm is carried round by a pressure equal to that of a column T T, acting upon an area equal to that of the aperture A. The same thing happens on the arm TB; and these two pressures drive the arm A B round in the same direction. This machine may evidently be applied to drive any kind of machinery, by fixing a wheel upon the vertical axis c D. 8. Mr. Rumsey, an American, and Mr. Segner, improved this machine, by conveying the water from the reservoir, not by a pipe, in greater part of which the spindle turns, but by at pipe which descends from a reservoir, as F, until it reaches lower than the arms A B, and then turns up by a curvilinear neck and collar, entering between the arms at the lower part, as shown in the figure. This greatly diminishes the friction. 9. Professor Playfair has correctly remarked that the moving force becomes greater, after the machine has begun to nove; for the water in the horizontal arms acquires a centriugal force, by which its pressure against the sides is increased. When the machine works to the greatest advantage, the centre of the perforations should move with the velocity hg, where r is the radius of the horizontal arm, measured from the axis of motion to the centre of the perforation, and r' the radius of the perpendicular tube, g being put for the force of gravity, or 32 feet. As 2 r is the circumference described by the centre of each perforation, is the time of a revolution in seconds. 2 πρ √hg The quantity✔g is also the velocity of the effluent water; therefore, when the machine is working to the greatest advantage, the velocity with which water issues is equal to that with which it is carried horizontally in an opposite direction; so that, on coming out, it falls perpendicularly down. 10. The following dimensions have been successfully adopted: viz. radius of arms from the centre of pivot to the centre of the discharging holes, 46 inches; inside diameter of the arms, 3 inches: diameter of the supplying pipe, 2 inches; height of the working head of water, 21 feet above the points of discharge. When the machine was not loaded, and had but one orifice open, it made 115 turns in a minute. This agrees to a velocity of 46 feet in a second, for the orifice, greater than the full velocity due to the head of water by between 9 and 10 feet the difference is due to the effect of the centrifugal force. The theory of this machine is yet imperfect; but there can be no doubt of its utility in cases where the stream is small with a considerable fall. Mr. James Whiteland, a correspondent of the Franklin Journal, proposes to make the horizontal arms of the mill of a curved form, such that the water will run from the centre to the extremity of the arms in a straight line when the machine is working. For the method of constructing the curve, see Mechanic's Magazine, No. 499. It is very clear, however, that the additional efficiency of the machine will not be so great by any means as the inventor anticipates. 2 F 2 |