Air, like every other gas or combination of gases, possesses weight;
some persons who have been taught that the air exerts a pressure of 14.7
lb. per square inch, cannot, however, be got to realize the fact that a
cubit foot of air at the same pressure and at a temperature of 62 deg.
weighs the thirteenth part of a pound, or over one ounce; 13.141 cubic
feet of air weigh one pound. In round numbers 30,000 cubic feet of air
weigh one ton; this is a useful figure to remember, and it is easily
carried in the mind. A hall 61 feet long, 30 feet wide, and 17 feet high
will contain one ton of air.
[Illustration: FIG. 1]
The work to be done by a fan consists in putting a weight--that of the
air--in motion. The resistances incurred are due to the inertia of the
air and various frictional influences; the nature and amount of these
last vary with the construction of the fan. As the air enters at the
center of the fan and escapes at the circumference, it will be seen that
its motion is changed while in the fan through a right angle. It may
also be taken for granted that within certain limits the air has no
motion in a radial direction when it first comes in contact with a fan
blade. It is well understood that, unless power is to be wasted, motion
should be gradually imparted to any body to be moved. Consequently, the
shape of the blades ought to be such as will impart motion at first
slowly and afterward in a rapidly increasing ratio to the air. It is
also clear that the change of motion should be effected as gradually as
possible. Fig. 1 shows how a fan should not be constructed; Fig. 2 will
serve to give an idea of how it should be made.
[Illustration: FIG. 2]
In Fig. 1 it will be seen that the air, as indicated by the bent arrows,
is violently deflected on entering the fan. In Fig. 2 it will be seen
that it follows gentle curves, and so is put gradually in motion. The
curved form of the blades shown in Fig. 2 does not appear to add much to
the efficiency of a fan; but it adds something and keeps down noise. The
idea is that the fan blades when of this form push the air radially from
the center to the circumference. The fact is, however, that the air
flies outward under the influence of centrifugal force, and always tends
to move at a tangent to the fan blades, as in Fig. 3, where the circle
is the path of the tips of the fan blades, and the arrow is a tangent to
that path; and to impart this notion a radial blade, as at C, is perhaps
as good as any other, as far as efficiency is concerned. Concerning the
shape to be imparted to the blades, looked at back or front, opinions
widely differ; but it is certain that if a fan is to be silent the
blades must be narrower at the tips than at the center. Various forms
are adopted by different makers, the straight side and the curved sides,
as shown in Fig. 4, being most commonly used. The proportions as regards
length to breadth are also varied continually. In fact, no two makers of
fans use the same shapes.
[Illustration: FIG. 3]
As the work done by a fan consists in imparting motion at a stated
velocity to a given weight of air, it is very easy to calculate the
power which must be expended to do a certain amount of work. The
velocity at which the air leaves the fan cannot be greater than that of
the fan tips. In a good fan it may be about two-thirds of that speed.
The resistance to be overcome will be found by multiplying the area of
the fan blades by the pressure of the air and by the velocity of the
center of effort, which must be determined for every fan according to
the shape of its blades. The velocity imparted to the air by the fan
will be just the same as though the air fell in a mass from a given
height. This height can be found by the formula h = v² / 64; that is to
say, if the velocity be multiplied by itself and divided by 64 we have
the height. Thus, let the velocity be 88 per second, then 88 x 88 =
7,744, and 7,744 / 64 = 121. A stone or other body falling from a height
of 121 feet would have a velocity of 88 per second at the earth. The
pressure against the fan blades will be equal to that of a column of air
of the height due to the velocity, or, in this case, 121 feet. We
have seen that in round numbers 13 cubic feet of air weigh one pound,
consequently a column of air one square foot in section and 121 feet
high, will weigh as many pounds as 13 will go times into 121. Now, 121
/ 13 = 9.3, and this will be the resistance in pounds per _square foot_
overcome by the fan. Let the aggregate area of all the blades be 2
square feet, and the velocity of the center of effort 90 feet per
second, then the power expended will bve (90 x 60 x 2 x 9.3) / 33,000
= 3.04 horse power. The quantity of air delivered ought to be equal in
volume to that of a column with a sectional area equal that of one fan
blade moving at 88 feet per second, or a mile a minute. The blade having
an area of 1 square foot, the delivery ought to be 5,280 feet per
minute, weighing 5,280 / 13 = 406.1 lb. In practice we need hardly say
that such an efficiency is never attained.
[Illustration: FIG. 4]
The number of recorded experiments with fans is very small, and a great
deal of ignorance exists as to their true efficiency. Mr. Buckle is one
of the very few authorities on the subject. He gives the accompanying
table of proportions as the best for pressures of from 3 to 6 ounces per
square inch:
--------------------------------------------------------------
| Vanes. | Diameter of inlet
Diameter of fans. |------------------------| openings.
| Width. | Length. |
--------------------------------------------------------------
ft. in. | ft. in. | ft. in. | ft. in.
3 0 | 0 9 | 0 9 | 1 6
3 6 | 0 10½ | 0 10½ | 1 9
4 0 | 1 0 | 1 0 | 2 0
4 6 | 1 1½ | 1 1½ | 2 3
5 0 | 1 3 | 1 3 | 2 6
6 0 | 1 6 | 1 6 | 3 0
| | |
--------------------------------------------------------------
For higher pressures the blades should be longer and narrower, and
the inlet openings smaller. The case is to be made in the form of an
arithmetical spiral widening, the space between the case and the blades
radially from the origin to the opening for discharge, and the upper
edge of the opening should be level with the lower side of the sweep of
the fan blade, somewhat as shown in Fig. 5.
[Illustration: FIG. 5]
A considerable number of patents has been taken out for improvements
in the construction of fans, but they all, or nearly all, relate to
modifications in the form of the case and of the blades. So far,
however, as is known, it appears that, while these things do exert a
marked influence on the noise made by a fan, and modify in some degree
the efficiency of the machine, that this last depends very much more on
the proportions adopted than on the shapes--so long as easy curves
are used and sharp angles avoided. In the case of fans running at low
speeds, it matters very little whether the curves are present or not;
but at high speeds the case is different.--_The Engineer_.
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