
ON THE VORTEX WATER-WHEEL. 321 
these velocities, it is necessary that the circumference of the wheel should 
move with the velocity which a heavy body would attain in falling through 
a vertical space equal to half the vertical fall of the water, or in other words, 
with the velocity due to half the fall; and that the orifices through which 
the water is injected into the wheel-chamber should be conjointly of such 
area that when all the water required is flowing through them, it also may 
have a velocity due to half the fall. Thus one-half only of the fall is em- 
ployed in producing velocity in the water ; and, therefore, the other half still 
remains acting on the water within the wheel-chamber at the circumference 
of the wheel in the condition of fluid pressure. Now, with the velocity 
already assigned to the wheel, it is found that this fluid pressure is exactly 
that which is requisite to overcome the centrifugal force of the water in the 
wheel, and to bring the water to a state of rest at its exit, the mechanical 
work due to both halves of the fall being transferred to the wheel during the 
combined action of the moving water and the moving wheel. In the fore- 
going statements, the effects of fluid friction, and of some other modifying 
influences, are, for simplicity, left out of consideration ; but in the practical 
application of the principles, the skill and judgement of the designer must be 
exercised in taking all such elements as far as possible into account. To 
aid in this, some practical rules, to which the author as yet closely adheres, 
were made out by him previously to the date of his patent. These are to be 
found in the specification of the patent, published in the Mechanics’ 
Magazine for Jan. 18 and Jan. 25, 1851 (London). 
- In respect to the numerous modifications of construction and arrangement 
which are admissible in the Vortex, while the leading principles of action are 
retained, it may be sufficient here merely to advert,—first, to the use (as 
explained in the specification of the patent) of straight instead of curved 
radiating passages in the wheel; secondly, to the employment, for simplicity, 
of invariable entrance orifices, or of fixed instead of moveable guide-blades ; 
and lastly, to the placing of the wheel at any height, less than about thirty feet, 
above the water in the tail race, combined with the employment of suction 
pipes descending from the central discharge orifices, and terminating in the 
water of the tail race, so as to render available the part of the fall below the 
wheel. 
In relation to the action of turbines in general, the chief and most commonly 
recognised conditions, of which the accomplishment is to be aimed at, are 
that the water should flow through the whole machine with the least possible 
resistance, and that it should enter the moving wheel without shock, and be 
discharged from it with only a very inconsiderable velocity. The vortex is 
in a remarkable degree adapted for the fulfilment of these conditions. The 
water moving centripetally (instead of centrifugally, which is more usual in 
turbines) enters at the period of its greatest velocity (that is, just after passing 
the injection orifices) into the most rapidly moving part of the wheel, the 
circumference ; and, at the period when it ought to be as far as possible 
deprived of velocity, it passes away by the central part of the wheel, the part 
which has the least motion. Thus in each case, that of the entrance and 
that of the discharge, there is an accordance between the velocities of the 
moving mechanism and the proper velocities of the water. 
The principle of injection from without inwards, adopted in the vortex, 
affords another important advantage in comparison with turbines having the 
contrary motion of the water; as it allows ample room, in the space outside 
of the wheel, for large and well-formed injection channels, in which the 
water can be made very gradually and regularly to converge to the most 
contracted parts, where it is to have its greatest velocity. It is as a con- 
1852. x 
