Water-wheels, next to steam-engines, are the most common motive agents. For centuries water-wheels remained without much improvement or change down to the period of turbine wheels, when it was discovered that instead of being a very simple matter, the science of hydraulics and water-wheels involved some very intricate conditions, giving rise to many problems of scientific interest, that in the end have produced the class known as turbine wheels.

A modern turbine water-wheel, one of the best construction, operating under favourable conditions, gives a percentage of the power of the water which, after deducting the friction of the wheel, almost reaches the theoretical coefficient or equals the gravity of the water; it may therefore be assumed that there will in the future be but little improvement made in such water-wheels except in the way of simplifying and cheapening their construction. There is, in fact, no other class of machines which seem to have reached the same state of improvement as water-wheels, nor any other class of machinery that is constructed with as much uniformity of design and arrangement, in different countries, and by different makers.

Water-wheels, or water-power, as a mechanical subject, is apparently quite disconnected with shop manipulation, but will serve as an example for conveying general ideas of force and motion, and, on these grounds, will warrant a more extended notice than the seeming connection with the general subject calls for.

In the remarks upon steam-engines it was explained that power is derived from heat, and that the water and the engine were both to be regarded as agents through which power was applied, and further, that power is always a product of heat. There is, perhaps, no problem in the whole range of mechanics more interesting than to trace the application of this principle in machinery; one that is not only interesting but instructive, and may suggest to the mind of an apprentice a course of investigation that will apply to many other matters connected with power and mechanics.

Power derived from water by means of wheels is due to the gravity of the water in descending from a higher to a lower level; but the question arises, What has heat to do with this? If heat is the source of power, and power a product of heat, there must be a connection somewhere between heat and the descent of the water. Water, in descending from one level to another, can give out no more power than was consumed in raising it to the higher level, and this power employed to raise the water is found to be heat. Water is evaporated by heat of the sun, expanded until it is lighter than the atmosphere, rises through the air, and by condensation falls in the form of rain over the earth's surface; then drains into the ocean through streams and rivers, to again resume its round by another course of evaporation, giving out in its descent power that we turn to useful account by means of water-wheels. This principle of evaporation is continually going on; the fall of rain is likewise quite constant, so that streams are maintained within a sufficient regularity to be available for operating machinery.

The analogy between steam-power and water-power is therefore quite complete. Water is in both cases the medium through which power is obtained; evaporation is also the leading principle in both, the main difference being that in the case of steam-power the force employed is directly from the expansion of water by heat, and in water-power the force is an indirect result of expansion of water by heat.

Every one remembers the classification of water-wheels met with in the older school-books on natural philosophy, where we are informed that there are three kinds of wheels, as there were "three kinds of levers"—namely, overshot, undershot, and breast wheels—with a brief notice of Barker's mill, which ran apparently without any sufficient cause for doing so. Without finding fault with the plan of describing water-power commonly adopted in elementary books, farther than to say that some explanation of the principles by which power is derived from the water would have been more useful, I will venture upon a different classification of water-wheels, more in accord with modern practice, but without reference to the special mechanism of the different wheels, except when unavoidable. Water-wheels can be divided into four general types.

First. Gravity wheels, acting directly from the weight of the water which is loaded upon a wheel revolving in a vertical plane, the weight resting upon the descending side until the water has reached the lowest point, where it is discharged.

Second. Impact wheels, driven by the force of spouting water that expends its percussive force or momentum against the vanes tangental to the course of rotation, and at a right angle to the face of the vanes or floats.

Third. Reaction wheels, that are "enclosed," as it is termed, and filled with water, which is allowed to escape under pressure through tangental orifices, the propelling force being derived from the unbalanced pressure within the wheel, or from the reaction due to the weight and force of the water thrown off from the periphery.

Fourth. Pressure wheels, acting in every respect upon the principle of a rotary steam-engine, except in the differences that arise from operating with an elastic and a non-elastic fluid; the pressure of the water resting continually against the vanes and "abutment," without means of escape except by the rotation of the wheel.

To this classification may be added combination wheels, acting partly by the gravity and partly by the percussion force of the water, by impact combined with reaction, or by impact and maintained pressure.

Gravity, or "overshot" wheels, as they are called, for some reasons will seem to be the most effective, and capable of utilising the whole effect due to the gravity of the water; but in practice this is not the case, and it is only under peculiar conditions that wheels of this class are preferable to turbine wheels, and in no case will they give out a greater per cent. of power than turbine wheels of the best class. The reasons for this will be apparent by examining the conditions of their operation.

A gravity wheel must have a diameter equal to the fall of water, or, to use the technical name, the height of the head. The speed at the periphery of the wheel cannot well exceed sixteen feet per second without losing a part of the effect by the wheel anticipating or overrunning the water. This, from the large diameter of the wheels, produces a very slow axial speed, and a train of multiplying gearing becomes necessary in order to reach the speed required in most operations where power is applied. This train of gearing, besides being liable to wear and accident, and costing usually a large amount as an investment, consumes a considerable part of the power by frictional resistance, especially when such gearing consists of tooth wheels. Gravity wheels, from their large size and their necessarily exposed situation, are subject to be frozen up in cold climates; and as the parts are liable to be first wet and then dry, or warm and cold by exposure to the air and the water alternately, the tendency to corrosion if constructed of iron, or to decay if of wood, is much greater than in submerged wheels. Gravity wheels, to realise the highest measure of effect from the water, require a diameter so great that they must drag in the water at the bottom or delivering side, and are for this reason especially affected by back-water, to which all wheels are more or less liable from the reflux of tides or by freshets. These disadvantages are among the most notable pertaining to gravity wheels, and have, with other reasons—such as the inconvenience of construction, greater cost, and so on—driven such wheels out of use by the force of circumstances, rather than by actual tests or theoretical deductions.

Impact wheels, or those driven by the percussive force of water, including the class termed turbine water-wheels, are at this time generally employed for heads of all heights.

The general theory of their action may be explained in the following propositions:—

1. The spouting force of water is theoretically equal to its gravity.

2. The percussive force of spouting water can be fully utilised if its motion is altogether arrested by the vanes of a wheel.

3. The force of the water is greatest by its striking against planes at right angles to its course.

4. Any force resulting from water rebounding from the vanes parallel to their face, or at any angle not reverse to the motion of the wheel, is lost.

5. This rebounding action becomes less as the columns of water projected upon the wheel are increased in number and diminished in size.

6. To meet the conditions of rotation in the wheel, and to facilitate the escape of the water without dragging, after it has expended its force upon the vanes, the reversed curves of the turbine is the best-known arrangement.

It is, of course, very difficult to deal with so complex a subject as the present one with words alone, and the reader is recommended to examine drawings, or, what is better, water-wheels themselves, keeping the above propositions in view.

Modern turbine wheels have been the subject of the most careful investigation by able engineers, and there is no lack of mathematical data to be referred to and studied after the general principles are understood. The subject, as said, is one of great complicity if followed to detail, and perhaps less useful to a mechanical engineer who does not intend to confine his practice to water-wheels, than other subjects that may be studied with greater advantage. The subject of water-wheels may, indeed, be called an exhausted one that can promise but little return for labour spent upon it—with a view to improvements, at least. The efforts of the ablest hydraulic engineers have not added much to the percentage of useful effect realised by turbine wheels during many years past.

Reaction wheels are employed to a limited extent only, and will soon, no doubt, be extinct as a class of water-wheels. In speaking of reaction wheels, I will select what is called Barker's mill for an example, because of the familiarity with which it is known, although its construction is greatly at variance with modern reaction wheels.

There is a problem as to the principle of action in a Barker wheel, which although it may be very clear in a scientific sense, remains a puzzle to the minds of many who are well versed in mechanics, some contending that the power is directly from pressure, others that it is from the dynamic effect due to reaction. It is one of the problems so difficult to determine by ordinary standards, that it serves as a matter of endless debate between those who hold different views; and considering the advantage usually derived from such controversies, perhaps the best manner of disposing of the problem here is to state the two sides as clearly as possible, and leave the reader to determine for himself which he thinks right.

Presuming the vertical shaft and the horizontal arms of a Barker wheel to be filled with water under a head of sixteen feet, there would be a pressure of about seven pounds upon each superficial inch of surface within the cross arm, exerting an equal force in every direction. By opening an orifice at the sides of these arms equal to one inch of area, the pressure would at that point be relieved by the escape of the water, and the internal pressure be unbalanced to that extent. In other words, opposite this orifice, and on the other side of the arm, there would be a force of seven pounds, which being unbalanced, acts as a propelling power to drive the wheel.

This is one theory of the principle upon which the Barker wheel operates, which has been laid down in Vogdes' "Mensuration," and perhaps elsewhere. The other theory alluded to is that, direct action and reaction being equal, ponderable matter discharged tangentally from the periphery of a wheel must create a reactive force equal to the direct force with which the weight is thrown off. To state it more plainly, the spouting water that issues from the arm of a Barker wheel must react in the opposite course in proportion to its weight.

The two propositions may be consistent with each other or even identical, but there still remains an apparent difference.

The latter seems a plausible theory, and perhaps a correct one; but there are two facts in connection with the operation of reaction water-wheels which seem to controvert the latter and favour the first theory, namely, that reaction wheels in actual practice seldom utilise more than forty per cent. of useful effect from the water, and that their speed may exceed the initial velocity of the water. With this the subject is left as one for argument or investigation on the part of the reader.

Pressure wheels, like gravity wheels, should, from theoretical inference, be expected to give a high per cent. of power. The water resting with the whole of its weight against the vanes or abutments, and without chance of escape except by turning the wheel, seems to meet the conditions of realising the whole effect due to the gravity of the water, and such wheels would no doubt be economical if they had not to contend with certain mechanical difficulties that render them impracticable in most cases.

A pressure wheel, like a steam-engine, must include running contact between water-tight surfaces, and like a rotary steam-engine, this contact is between surfaces which move at different rates of speed in the same joint, so that the wear is unequal, and increases as the speed or the distance from the axis. When it is considered that the most careful workmanship has never produced rotary engines that would surmount these difficulties in working steam, it can hardly be expected they can be overcome in using water, which is not only liable to be filled with grit and sediment, but lacks the peculiar lubricating properties of steam. A rotary steam-engine is in effect the same as a pressure water-wheel, and the apprentice in studying one will fully understand the principles of the other.