Grashof takes e = 1⁄6H, and then
b = 6Q/H √ (2gH).
Allowing for the contraction of the stream, the area of opening through the sluice may be 1.25 be to 1.3 be. The inside width of the wheel is made about 4 in. greater than b.
Several constructions have been given for the floats of Poncelet wheels. One of the simplest is that shown in figs. 181, 182.
Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD making angles of 15° with OA. Then BD may be the length of the close breasting fitted to the wheel. Draw the bottom of the head face BC at a slope of 1 in 10. Parallel to this, at distances 1⁄2e and e, draw EF and GH. Then EF is the mean layer and GH the surface layer entering the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K is the centre from which the bucket curve is struck and KF is the radius. The depth of the shrouds must be sufficient to prevent the water from rising over the top of the float. It is 1⁄2H to 2⁄3H. The number of buckets is not very important. They are usually 1 ft. apart on the circumference of the wheel.
The efficiency of a Poncelet wheel has been found in experiments to reach 0.68. It is better to take it at 0.6 in estimating the power of the wheel, so as to allow some margin.
| Fig. 182. |
In fig. 182 vi is the initial and vo the final velocity of the water, vr parallel to the vane the relative velocity of the water and wheel, and V the velocity of the wheel.
Turbines.
§ 182. The name turbine was originally given in France to any water motor which revolved in a horizontal plane, the axis being vertical. The rapid development of this class of motors dates from 1827, when a prize was offered by the Société d’Encouragement for a motor of this kind, which should be an improvement on certain wheels then in use. The prize was ultimately awarded to Benoît Fourneyron (1802-1867), whose turbine, but little modified, is still constructed.