FIG. 1.
FIG. 2.
Turbines.—While studying those effects produced by jets of water impinging upon plain or concave surfaces corresponding to buckets of turbines, it simplifies matters to separate these results due to impact from others due to reaction. And it will be well at the outset to draw a distinction between the nature of these two pressures, and to remind ourselves of the laws which lie at the root and govern the whole question under present consideration. Water obeys the laws of gravity, exactly like every other body; and the velocity with which any quantity may be falling is an expression of the full amount of work it contains. By a sufficiently accurate practical rule this velocity is eight times the square root of the head or vertical column measured in feet. Velocity per second = 8 sqrt (head in feet), therefore, for a head of 100 ft. as an example, V = 8 sqrt (100) = 80 ft. per second. The graphic method of showing velocities or pressures has many advantages, and is used in all the following diagrams. Beginning with purely theoretical considerations, we must first recollect that there is no such thing as absolute motion. All movements are relative to something else, and what we have to do with a stream of water in a turbine is to reduce its velocity relatively to the earth, quite a different thing to its velocity in relation to the turbine; for while the one may be zero, the other may be anything we please. ABCD in Fig. 1 represents a parallelogram of velocities, wherein AC gives the direction of a jet of water starting at A, and arriving at C at the end of one second or any other division of time. At a scale of 1/40 in. to 1 ft., AC represents 80 ft., the fall due to 100 ft. head, or at a scale of 1 in. to 1 ft., AC gives 2 ft., or the distance traveled by the same stream in 1/40 of a second. The velocity AC may be resolved into two others, namely, AB and AD, or BC, which are found to be 69.28 ft. and 40 ft. respectively, when the angle BAC—generally called x in treatises on turbines—is 30 deg. If, however, AC is taken at 2 ft., then A B will be found = 20.78 in., and BC = 12 in. for a time of 1/40 or 0.025 of a second. Supposing now a flat plate, BC = 12 in. wide move from DA to CB during 0.025 second, it will be readily seen that a drop of water starting from A will have arrived at C in 0.025 second, having been flowing along the surface BC from B to C without either friction or loss of velocity. If now, instead of a straight plate, BC, we substitute one having a concave surface, such as BK in Fig. 2, it will be found necessary to move it from A to L in 0.025 second, in order to allow a stream to arrive at C, that is K, without, in transit, friction or loss of velocity. This concave surface may represent one bucket of a turbine. Supposing now a resistance to be applied to that it can only move from A to B instead of to L. Then, as we have already resolved the velocity A C into AB and BC, so far as the former (AB) is concerned, no alteration occurs whether BK be straight or curved. But the other portion, BC, pressing vertically against the concave surface, BK, becomes gradually diminished in its velocity in relation to the earth, and produces and effect known as "reaction." A combined operation of impact and reaction occurs by further diminishing the distance which the bucket is allowed to travel, as, for examples, to EF. Here the jet is impelled against the lower edge of the bucket, B, and gives a pressure by its impact; then following the curve BK, with a diminishing velocity, it is finally discharged at K, retaining only sufficient movement to carry the water clear out of the machine. Thus far we have considered the movement of jets and buckets along AB as straight lines, but this can only occur, so far as buckets are concerned, when their radius in infinite. In practice these latter movements are always curves of more or less complicated form, which effect a considerable modification in the forms of buckets, etc., but not in the general principles, and it is the duty of the designer of any form of turbine to give this consideration its due importance. Having thus cleared away any ambiguity from the terms "impact," and "reaction," and shown how they can act independently or together, we shall be able to follow the course and behavior of streams in a turbine, and by treating their effects as arising from two separate causes, we shall be able to regard the problem without that inevitable confusion which arises when they are considered as acting conjointly. Turbines, though driven by vast volumes of water, are in reality impelled by countless isolated jets, or streams, all acting together, and a clear understanding of the behavior of any one of these facilitates and concludes a solution of the whole problem.
Experimental researches.—All experiments referred to in this paper were made by jets of water under an actual vertical head of 45 ft., but as the supply came through a considerable length of ½ in. bore lead piping, and many bends, a large and constant loss occurred through friction and bends, so that the actual working head was only known by measuring the velocity of discharge. This was easily done by allowing all the water to flow into a tank of known capacity. The stop cock had a clear circular passage through it, and two different jets were used. One oblong measured 0.5 in. by 0.15 in., giving an area of 0.075 square inch. The other jet was circular, and just so much larger than ¼ in. to be 0.05 of a square inch area, and the stream flowed with a velocity of 40 ft. per second, corresponding to a head of 25 ft. Either nozzle could be attached to the same universal joint, and directed at any desired inclination upon the horizontal surface of a special well-adjusted compound weighing machine, or into various bent tubes and other attachments, so that all pressures, whether vertical or horizontal, could be accurately ascertained and reduced to the unit, which was the quarter of an ounce. The vertical component p of any pressure P may be ascertained by the formula—
p = P sin alpha,
where alpha is the angle made by a jet against a surface; and in order to test the accuracy of the simple machinery employed for these researches, the oblong jet which gave 71 unit when impinging vertically upon a circular plate, was directed at 60 deg. and 45 deg. thereon, with results shown in Table I., and these, it will be observed, are sufficiently close to theory to warrant reliance being placed on data obtained from the simple weighing machinery used in the experiment.
Table I.—Impact on Level Plate.--------------+--------------------+----------+----------+----------
| Inclination of jet | | |
Distance. | to the horizonal. | 90 deg. | 60 deg. | 45 deg.
--------------+--------------------+----------+----------+----------
| | Pressure | Pressure | Pressure
| | | |
/ | Experiment \ | / | 61.00 | 49.00
1½ in. < | > | 71.00 < | |
\ | Theory / | \ | 61.48 | 50.10
| | | |
| | | |
/ | Experiment \ | / | 55.00 | 45.00
1 in. < | > | 63.00 < | |
\ | Theory / | \ | 54.00 | 45.00
| | | |
--------------+--------------------+----------+----------+----------
In each case the unit of pressure is ¼ oz.
In the first trial there was a distance of 1½ in. between the jet and point of its contact with the plate, while in the second trial this space was diminished to ½ in. It will be noticed that as this distance increases we have augmented pressures, and these are not due, as might be supposed, to increase of head, which is practically nothing, but they are due to the recoil of a portion of the stream, which occurs increasingly as it becomes more and more broken up. These alterations in pressure can only be eliminated when care is taken to measure that only due to impact, without at the same time adding the effect of an imperfect reaction. Any stream that can run off at all points from a smooth surface gives the minimum of pressure thereon, for then the least resistance is offered to the destruction of the vertical element of its velocity, but this freedom becomes lost when a stream is diverted into a confined channel. As pressure is an indication and measure of lost velocity, we may then reasonably look for greater pressure on the scale when a stream is confined after impact than when it discharges freely in every direction. Experimentally this is shown to be the case, for when the same oblong jet, discharged under the same conditions, impinged vertically upon a smooth plate, and gave a pressure of 71 units, gave 87 units when discharged into a confined right-angled channel. This result emphasizes the necessity for confining streams of water whenever it is desired to receive the greatest pressure by arresting their velocity. Such streams will always endeavor to escape in the directions of least resistance, and, therefore, in a turbine means should be provided to prevent any lateral deviation of the streams while passing through their buckets. So with screw propellers the great mass of surrounding water may be regarded as acting like a channel with elastic sides, which permits the area enlarging as the velocity of a current passing diminishes. The experiments thus far described have been made with jets of an oblong shape, and they give results differing in some degree from those obtained with circular jets. Yet as the general conclusions from both are found the same, it will avoid unnecessary prolixity by using the data from experiments made with a circular jet of 0.05 square inch area, discharging a stream at the rate of 40 ft. per second. This amounts to 52 lb. of water per minute with an available head of 25 ft., or 1,300 foot-pounds per minute. The tubes which received and directed the course of this jet were generally of lead, having a perfectly smooth internal surface, for it was found that with a rougher surface the flow of water is retarded, and changes occur in the data obtained. Any stream having its course changed presses against the body causing such change, this pressure increasing in proportion to the angle through which the change is made, and also according to the radius of a curve around which it flows. This fact has long been known to hydraulic engineers, and formulæ exist by which such pressures can be determined; nevertheless, it will be useful to study these relations from a somewhat different point of view than has been hitherto adopted, more particularly as they bear upon the construction of screw propellers and turbines; and by directing the stream, AB, Fig. 3, vertically into a tube 3/8 in. internal diameter and bent so as to turn the jet horizontally, and placing the whole arrangement upon a compound weighing machine, it is easy to ascertain the downward pressure, AB, due to impact, and the horizontal pressures, CB, due to reaction. In theoretical investigations it may be convenient to assume both these pressures exactly equal, and this has been done in the paper "On Screw Propellers" already referred to; but this brings in an error of no importance so far as general principles are involved, but one which destroys much of the value such researches might, otherwise possess for those who are engaged in the practical construction of screw propellers or turbines. The downward impact pressure, AB, is always somewhat greater than the horizontal reaction, BC, and any proportions between these two can only be accurately ascertained by trials. In these particular experiments the jet of water flowed 40 ft. per second through an orifice of 0.05 square inch area, and in every case its course was bent to a right angle. The pressures for impact and reaction were weighed coincidently, with results given by columns 1 and 2, Table II.