Smeaton on Overshot Wheels

Mr. Smeaton, in his Experimental Inquiry, previous to examining into the power and application of water, when acting by its gravity on avershot-wheels, says,:

"In reasoning without experiment, one might be led to imagine, that however different the mode of application is, yet that whenever the same quantity of water descends through the same perpendicular space, that the natural effective power would be equal, supposing the machinery free from friction, equally calculated to receive the full effect of the power, and to make the most of it : for if we suppose the height of a column of water to be 30 inches, and resting upon a base or aperture one inch square, every cubic inch of water that departs therefrom will acquire the same velocity or momentum, from the uniform pressure of 30 inches above it, that one cubic inch let fall from the top will acquire in falling down to the level of the aperture : one would therefore suppose, that a cubit- inch of water, let fall through a space of 30 inches, and there impinging upon another body, would be capable of producing an equal effect by collision, as if the same cubic inch had descended through the same space with a slower motion, and produced its effects gradually. But however conclusive this reasoning may seem, it will appear, in the course of the following deductions, that the effect of the gravity of descending bodies is very different from the effect of stroke of such as are non-clastic, though generated by an equal mechanical power."

When Mr. Smeaton had finished his experiments on undershot mills, he reduced the number of floats on the wheel, which were originally 24, to 12; which caused a diminution in the effect, on account of a greater quantity of water escaping between the floats and the floor : but a circular sweep being
adapted thereto, of such a length, that one float entered the curve before the preceding one quitted it, the effect came so near that of the former, as not to give any hopes of advancing it by increasing the number of floats beyond 24 in this particular wheel.

In these experiments the head was six inches, and the height of the wheel 24 inches, so that the whole descent was 30 inches: the quantity of water expended in a minute was CG; pounds, which, multiplied by 30 inches, gives the power =2900. After making the proper calculations, the effect was
computed at 1914; the ratio therefore of the power and effect will be as 2900 : 1914, or as 10 : 6.6, or as 3 to 2 nearly.

But if we compute the power from the height of the wheel only, we shall have 96j pounds, multiplied by 24 inches =2320 for the power, and this will be to the effect as 2320 : 1914, or as 10 : 82, or as 5 to 4 nearly.

From another set of experiments the following conclusions were deduced :

1. The effective power of the water must be reckoned upon the whole descent, because it must be raised that height in order to produce the same effect a second time. The ratios between the powers so estimated, and the effects at the maximum, differ nearly from that of 10 to 7-6, to that of 10 to 02, that is nearly from 4.3 tu 4.2. In those experimente where the heads of water and quantities expended are least, the proportion is nearly as 4 to 3 ; but where the beads and quantities are greatest, it approaches nearer to that of 4 to 2 ; and by a medium of the whole, the ratio is that of 3 to 2 nearly. Hence it appears, that the effect of overshot- wheels is nearly double to that of the undershot, and, by consequence, that non- elastic bodies, when acting by their impulse or collision, communicate only a part of their original power, the remainder being spent in changing their figure in consequence of the stroke. The ultimate conclusion is, that the effects, as well as the powers, are as the quantities of water and perpendicular heights multiplied together respectively.

2. By increasing the head from 3 to 1 1 inches, that is, the whole descent from 27 inches to 35, or in the ratio of 7 to 9 nearly, the effect is advanced no more than in the ratio of 8.1 to 8.4, that is, as 7 to 7-26; and consequently the increase of effect is not one-seventh of the increase of perpendicular height. Hence it follows, that the higher the wheel is in proportion to the whole descent, the greater will be the effect ; because it depends less upon the impulse of the head, and more upon the gravity of the water in the backets : and if we consider how obliquely the water issuing from the head must strike the buckets, we shall not be at a loss to account for the little advantage that arises from the impulse thereof, and shall immediately see of how little consequence this impulse is to the effect of an overshot- wheel.

This, however, like other things, is subject to limitation, for it is desirable that the water should have somewhat greater velocity than the circumference of the wheel, in coming thereon ; otherwise the wheel will not only be retarded by the buckets striking the water, but a portion of the power will be lost by the water dashing over the buckets. Continued>>