The Mechanics of Water-Wheels - A Guide to the Physics at Work in Water-Wheels with a Horizontal Axis

By Anon Anon

This book contains classic material dating back to the 1900s and before. The content has been carefully selected for its interest and relevance to a modern audience.

• Language: English
• Publisher: Read Books Ltd.
• Release date: Sep 26, 2016
• ISBN: 9781473358065

Book preview

WATER-WHEELS WITH A HORIZONTAL AXIS.

Undershot wheel with plane buckets or floats moving in a confined race.—These wheels are ordinarily constructed of wood. Upon a polygonal arbor A (Fig. 2) a socket C, of cast iron, is fastened by means of wooden wedges b. Arms D are set in grooves cast in the socket, and are fastened to it by bolts; these arms serve to support a ring E E, the segments of which are fastened to each other and to the arms by iron bands. In the ring are set the projecting pieces F F . . . ., of wood, placed at equal distances apart, and intended to support the floats G G . . . ., which, are boards varying from 0m.02 to 0m.03 in thickness, situated in planes passing through the axis of the wheel and occupying its entire breadth. A single set of the foregoing parts would not be sufficient to give a good support to the floats. In wheels of little breadth in the direction of the axis two parallel sets will suffice; if the wheels are broad, three or more may be requisite.

FIG. 2.

The number of arms increases with the diameter of the wheel. In the more ordinary kinds, of 3 to 5 metres in diameter, each socket carries six arms. The floats may be about 0m.35 to 0m.40 apart, and have a little greater depth in the direction of the radius, say 0m.60 to 0m.70.

From this brief description of the wheel, let us now see how we can calculate the work which it receives from the head of water. The water flows in a very nearly horizontal current through a race B G H F (Fig. 3), of nearly the same breadth as the wheel, a portion G H of the bottom being hollowed out, in a direction perpendicular to the axis, to a cylindrical shape, and allowing but a slight play to the floats. The liquid molecules have, when passing C B, a velocity v, but shortly after they are confined in the intervals limited by two consecutive floats and the race. They entered these spaces with a mean relative velocity equal to the difference between the horizontal velocity v, and the velocity v′ of the middle of the immersed portion of the floats, the direction of which last velocity is also very nearly horizontal. There result from this relative velocity a shock and disturbance which gradually subside, while the floats are traversing over the circular portion of the canal; so that if this circular portion is sufficiently long, and if there be not too much play between the floats and the canal, the water that-leaves the wheel will have a velocity sensibly equal to v′. The action brought to bear by the wheel on the water is the cause of the change in this velocity from v to v′, which gives us the means, as we shall presently see, of calculating the total intensity of this action.

FIG. 3.

For this purpose let us apply to the liquid system included between the cross sections C B, E F, in which the threads are supposed parallel, the theorem of quantities of motion projected on a horizontal axis. Represent by

b the constant breadth of the wheel and canal;

h, h, of the extreme sections which are supposed to be rectangular;

F the total force exerted by the wheel on the water, or inversely, in a horizontal direction;

P the expenditure of the current, expressed in pounds, per second;

II the weight of a cubic metre of the water;

θ Θ the short interval of time during which C B E F passes to C′ B′ E′ F′.

The liquid system C B E F, here under consideration, is analogous to the one treated in Note A (see Appendix), in which a change in the surface level takes place; and the manner of determining the gain in the quantity of motion during a short time θ, and calculating