surprised many persons not familiar with the theory of the flow of fluids. For those who have any doubt I advise a study of the description of the ajutage of Venturi, given in all treatises on hydraulics. This ajutage presents at first a narrowing, then a space gently expanding, like a Guibal chimney. But this theory requires that in this expanding part there should be an integral restitution of active force developed to recover the obstruction; consequently the yield of the ajutage is the same as if the narrowing did not exist.

FIG. 5.

B

As in our Fig. 5 above, the yield of A will be the same as that of B. We cannot hope, however, in practice, in the Guibal chimney any more than in the ajutage of Venturi, to see realised a perfect restitution of active force. It is certain, however, that this effect is produced to an important degree, as has been witnessed by numerous observers.

In place of a single chimney we may imagine a series of small chimneys starting from each point in the circumference. This arrangement has been proposed by M. Harzé in the Revue Universelle of Liège, 1870. The effect may be the same, perhaps better, but I do not believe that the idea has ever been carried out.

What assistance does the Guibal chimney give to the depression? The answer is immediately given by the theory

of Bernouilli, the application of which presents itself at each step in this study. If in effect V is the speed of the air at the bottom of the chimney and W the speed at the top, this theory will immediately give for the corresponding increase of pressure the difference

The speed V is that which the air possesses on leaving the vanes; it is thus the resultant of the tangential speed u and of the speed relative to the outlet V2 The parallelogram of these speeds furnishes the known relation between them

a being the angle at which the vanes strike the exterior circumference.

In substituting this value of V2 in the preceding expression we shall have for this latter

The ventilator alone without envelope or chimney has given already

Adding together, then, it becomes, all simplifications made,

an expression of the total depression developed by the Guibal ventilator.

We have now this interesting question, Under what inclination a should the vanes strike the exterior circumference

с

for the machine to develop the maximum of depression? The reply is simple. It is that this inclination is 90°, in fact this value of a makes the negative term

disappear, and there remains only for the theoretical depression

So the vanes of the Guibal ventilator, and in general every ventilator intended to restore the active force, should strike normally to the exterior circumference. We may besides foresee, without any analysis, from the moment in fact that the speed of expulsion is utilised, that a gratuitous waste of power takes place if the vanes are inclined.

However, this condition was not apparent at once to the inventor, for his first machines generally had inclined vanes. But it has been realised in machines recently constructed, as we saw in the large ventilator which was shown at the Champ de Mars in the Belgian section.

I will assume now that throughout the remainder of this study I need not trouble myself further as to the angle a. The line which results for the vanes of the ventilator is given by Fig. 6. The vanes begin at the circumference of the ouïe with an inclination to enable them to receive the air without shock. They continue upwards with a gentle curve, and end in a right line following the radius.

One condition still remains to be fulfilled in order that the ventilator may be, so to say, perfect—an ideal of which we have spoken above: it is necessary that the air expelled should escape without speed. From the theoretical point of view in which we place it, the solution is clearly shown. We have only to imagine that the chimney is prolonged with an

increasing capacity to a sufficiently great height, so that the speed of the air at its summit may be considered as nothing. Then W becomes equal to zero, and the total depression developed by the perfect ventilator takes the unquestionably simple form

which we may translate into ordinary language by saying that the theoretical depression is the double of the height created by the tangential speed.

This value forms the basis of the theory, but I repeat that it only applies to an ideal ventilator. In practice, a thousand

FIG. 6.

imperfections of detail will prevent the initial depression attaining such an elevated point. We are obliged to introduce a coefficient of reduction, and to write

K being a fraction more or less near unity in proportion as the constructor shall have made more or less effort to realise the indications of reasoning and calculation. This fraction

K, which expresses the proportion of the initial depression to the theoretical depression, is, properly speaking, the useful effect in depression in the ventilator. I will call it afterwards the manometrical yield, reserving, according to usage, the mechanical yield, or the yield, properly speaking, of the proportion of the work utilised to the work of the motor. Already we have seen that for uncovered ventilators the manometrical yield must be always less than half. In fact,

u2

2g

2

2g

is

the maximum depression in these machines, already less than half of With the covered ventilators

u2
9

the yield largely exceeds this limit, but will remain far short of unity.

I should observe incidentally that this value of the depression fully justified the principle admitted by the Commission of Gard, that all the ventilators having the same tangential speed are theoretically equal.

Having thus determined the value of the initial depression, there remains nothing more for us than to carry forward the two formulæ established in the preceding paragraph. We then obtain the two following expressions, which comprehend the whole theory of centrifugal ventilators :First, The value of the effective depression

The ventilator is defined by its tangential speed and its orifice of passage-data which depend only on the constructor;