to admit of being regulated in velocity for variable work, must, almost necessarily, be used with a gate not fully raised, it would appear proper to give them a velocity such, that they will give a good effect under these circumstances.
With this view, the following is extracted from the experiments in table II.
| Number of the experiment. | Height of the regulating gate, in inches. | Ratio of the velocity of the interior circumference of the wheel, to the velocity due the fall acting upon the wheel, corresponding to the maximum coefficient of effect. |
|---|---|---|
| 30 | 11.49 | 0.62645 |
| 62 | 8.55 | 0.56541 |
| 73 | 5.65 | 0.56205 |
| 84 | 2.875 | 0.48390 |
By this table it would appear, that, as turbines are generally used, a velocity of the interior circumference of the wheel, of about fifty-six per cent, of that due to the fall acting upon the wheel, would be most suitable. By reference to the diagram at plate VI., it will be seen that, at this velocity when the gate is fully raised, the coefficient of effect will be within less than one per cent, of the maximum.
Other considerations, however, must usually be taken into account, in determining the velocity; the most frequent is the variation of the fall under which the wheel is intended to operate. If, for instance, it was required to establish a turbine of a given power, on a fall liable to be diminished to one half, by backwater, and, that the turbine should be of a capacity to give the requisite power at all times; in this case, the dimensions of the turbine must be determined for the smallest fall; but if it has assigned to it a velocity, to give the maximum effect at the smallest fall, it will evidently move too slow for the greatest fall; and this is the more objectionable, as, usually, when the fall is greatest, the quantity of water is the least, and it is of the most importance to obtain a good effect. It would then be usually, the best arrangement, to give the wheel a velocity corresponding to the maximum coefficient of effect, when the fall is the greatest. To assign this velocity, we must first find the proportional height of gate, when the fall is greatest; this may be determined approximately by aid of the experiments on the Tremont Turbine.
We have seen that
Now, if h is increased to 2h, the velocity, and, consequently, the quantity of water discharged, will be increased in the proportion of to ; that is to say, the quantity for the fall 2h, will be .
