.Chap. XVII.

THEORY OF THE MOTION’OF FLUIDS.

1147

incurvate the upper part BCD of the course into 15 D, that the water at the bottom maymove parallel to that at the top of the stream. To effect this, take the points B, D, about afoot distant from C, and raise the perpendiculars BE, D E ; the point of intersection E willbe the centre from which the arc B D is to be described, the radius being about 10-L inches.That the water may act more advantageously upon the float-boards of the wheel WAV, itmust assume a horizontal direction H K, with the same velocity that it would acquire whenit came to the point G ; but in falling from C to G, the water will dash upon the horizontalpart II G, and thus lose a great portion of its velocity ; it will be necessary, therefore, tomake it move along FII, an arc of a circle to which DF and KII are tangents, in thepoints F and II. For this purpose make GF and GH each equal to 3 feet, and raisethe perpendiculars F I, H I, which will intersect each other at the point I, distant about 4feet 9 T 4 ? inches from the points F and II, and the centre of the arc FH will bedetermined. The distance II K, through which the water runs, before it acts upon thewheel, should not be less than 2 or 3 feet, in order that the different portions of the fluidmay obtain a horizontal direction, and if IIK be much larger, the velocity of thestream would be diminished by its friction on the bottom of the course. That no watermay escape between the bottom of the course K H, and the extremities of the float-boards,K L should be about 3 inches, and the extremity O of the float-board, N O, should be beneaththe line H K K, sufficient room being left between O and M for the play of the wheel, orKLJI may be formed into the arc of a circle, K M, concentric with the wheel.

The line LM V, or the course of compulsion, should be prolonged, so as to support thewater as long as it can act upon the float-boards, and about 9 inches distant from () P, ahorizontal line passing through O, the lowest point of the fall; for if OL were much lessvhan 9 inches, the water, having spent the greater part of its force in impelling the float-l>oards, would accumulate below the wheel and retard its action : for the same reason thecourse of discharge should be connected with LM V by the curve VN, to preserve the re-maining velocity of the water, which would otherwise be destroyed by falling perpen-dicularly from V to N. The course of discharge is represented by V Z, sloping from thepoint O ; it should be about 16 yards long, having an inch of declivity in every 2 yards.

The canal which conducts the water from the course of discharge to the river shouldslope about 4 inches in the first 200 yards, S inches in the second 200 yards, decreasinggradually till it terminates with the river. The diameters of undershot wheels must be inaccordance with the machinery on which they are to act; when a great velocity is required,the wheel must be of a less diameter than is usually recommended ; when this is not required,the diameter of the wheel should be as large as possible.

Fig. 1737.

SIDE ELEVATION OP AN UNDERSHOT WHEEL

The number of float-boards, according to Pitot, should be equal to 360°, divided by thearc of the circle plunged in the canal, and their depth equal to the versed sine of thatarc; but this number experience has proved to be too small, and some engineers have