would be useless to make the vanes of the fan of a greater width than the inlet opening can freely supply. On the proportion of the length and width of the vane and the diameter of the inlet opening rest the three most important points, viz., quantity and density of air, and expenditure of power. In the 14-inch blade the tip has a velocity 2.6 times greater than the heel; and, by the laws of centrifugal force, the air will have a density 2.6 times greater at the tip of the blade than that at the heel. The air cannot enter on the heel with a density higher than that of the atmosphere; but in its passage along the vane it becomes compressed in proportion to its centrifugal force. The greater the length of the vane, the greater will be the difference of the centrifugal force between the heel and the tip of the blade; consequently the greater the density of the air.

Reasoning from these experiments, Mr. Buckle recommends for easy reference the following proportions for the construction of the fan:

1. Let the width of the vanes be one fourth of the diameter; 2. Let the diameter of the inlet openings in the sides of the fan-chest be one half the diameter of the fan; 3. Let the length of the vanes be one fourth of the diameter of the fan.

In adopting this mode of construction, the area of the inlet openings in the sides of the fan-chest will be the same as the circumference of the heel of the blade, multiplied by its width; or the same area as the space described by the heel of the blade.

Best Proportions of Fans. (Buckle.)

PRESSURE FROM 3 OUNCES TO 6 OUNCES PER SQUARE INCH; OR 5.2 INCHES TO 10.4 INCHES OF WATER.

PRESSURE FROM 6 OUNCES TO 9 OUNCES PER SQUARE INCH, AND UPWARDS, OR 10.4 INCHES TO 15.6 INCHES OF WATER.

The dimensions of the above tables are not laid down as prescribed limits, but as approximations obtained from the best results in practice.

Experiments were also made with reference to the admission of air into the transit or outlet pipe. By a slide the width of the opening into this pipe was varied from 12 to 4 inches. The object of this was to proportion the opening to the quantity of air required, and thereby to lessen the power necessary to drive the fan. It was found that the less this opening is made, provided we produce sufficient blast, the less noise will proceed from the fan; and by making the tops of this opening level with the tips of the vane, the column of air has little or no reaction on the vanes.

The number of blades may be 4 or 6. The case is made of the form of an arithmetical spiral, widening the space between the case and the revolving blades, circumferentially, from the origin to the opening for discharge. The following rules deduced from experiments are given in Spretson's treatise on Casting and Founding:

The fan-case should be an arithmetical spiral to the extent of the depth of the blade at least.

The diameter of the tips of the blades should be about double the diameter of the hole in the centre; the width to be about two thirds of the radius of the tips of the blades. The velocity of the tips of the blades should be rather

more than the velocity due to the air at the pressure required, say one eighth more velocity.

In some cases, two fans mounted on one shaft would be more useful than one wide one, as in such an arrangement twice the area of inlet opening is obtained as compared with a single wide fan. Such an arrangement may be adopted where occasionally half the full quantity of air is required, as one of them may be put out of gear, thus saving power.

H==

Pressure due to Velocity of the Fan-blades.-"By increasing the number of revolutions of the fan the head or pressure is increased, the law being that the total head produced is equal (in centrifugal fans) to twice the height due to the velocity of the extremities of the blades, or v2 approximately in practice" (W. P. Trowbridge, Trans. A. S. M. E., vii. 536.) This law is analogous to that of the pressure of a jet striking a plane surface. T. Hawksley, Proc. Inst. M. E., 1882, vol. lxix.. says: pressure of a fluid striking a plane surface perpendicularly and then escaping at right angles to its original path is that due to twice the height h due the velocity."

The

(For discussion of this question, showing that it is an error to take the pressure as equal to a column of air of the height =v2+2g, see Wolff on Windmills, p. 17.)

Buckle says: From the experiments it further appears that the velocity of the tips of the fan is equal to nine tenths of the velocity a body would acquire in falling the height of a homogeneous column of air equivalent to the density." D. K. Clark (R. T. & D., p. 924), paraphrasing Buckle, appar ently, says: "It further appears that the pressure generated at the circum ference is one ninth greater than that which is due to the actual circumferential velocity of the fan." The two statements, however, are not in v2 harmony, for if v = 0.9 √2gH, H = 1.234 and not 13 2g

v2 0.81 × 2g

v2

2g

If we take the pressure as that equal to a head or column of air of twice the height due the velocity, as is correctly stated by Trowbridge, the paradoxical statements of Buckle and Clark-which would indicate that the actual pressure is greater than the theoretical-are explained, and the v2 formula becomes H= .617 and v1.278 √gH = 0.9 √2gH, in which H g is the head of a column producing the pressure, which is equal to twice the h = multiplied by the coefficient .617. The difference between 1 and this coefficient expresses the loss of pressure due to friction, to the fact that the inner portions of the blade have a smaller velocity than the outer edge, and probably to other causes. The coefficient 1.273 means that the tip of the blade must be given a velocity 1.273 times that theoretically required to produce the

theoretical head due the velocity of a falling body (or

head H.

v2

To convert the head H expressed in feet to pressure in lbs. per sq. in. multiply it by the weight of a cubic foot of air at the pressure and temperature of the air expelled from the fan (about .08 lb. usually) and divide by 144. Multiply this by 16 to obtain pressure in ounces per sq. in. or by 2.035 to obtain inches of mercury, or by 27.71 to obtain pressure in inches of water column. Taking .08 as the weight of a cubic foot of air,

in which v= velocity of tips of blades in feet per second.

66

66

66

Testing the above formula by the experiment of Buckle with the vane 14 inches long, quoted above, we have p = .00001066v2 = 9.56 oz. The experiment gave 9.4 oz.

Testing it by the experiment of H. I. Snell, given below, in which the circumferential speed was about 150 ft. per second, we obtain 3.85 ounces, while the experiment gave from 2.38 to 3.50 ounces, according to the amount of opening for discharge. The numerical coefficients of the above formulæ are all based on Buckle's statement that the velocity of the tips of the fan is equal to nine tenths of the velocity a body would acquire in falling the

height of a homogeneous column of air equivalent to the pressure. Should other experiments show a different law, the coefficients can be corrected accordingly. It is probable that they will vary to some extent with different, proportions of fans and different speeds.

Taking the formula v = 80 VP1, we have for different pressures in ounces per square inch the following velocities of the tips of the blades in feet per second:

P1 ounces per square inch.... 2 3 4 5 6 7 8 10 12 14 บ = feet per second... 113 139 160 179 196 212 226 253 277 299

A rule in App. Cyc. Mech, article "Blowers," gives the following velocities of circumference for different densities of blast in ounces: 3, 170; 4, 180; 5, 195; 6, 205; 7, 215.

The same article gives the following tables, the first of which shows that the density of blast is not constant for a given velocity, but depends on the ratio of area of nozzle to area of blades:

Velocity of circumference, feet per second. 150 150 150 170 200 200 220 Area of nozzle area of blades. 2 1 1/2 1/4 2 1/6 % Density of blast, oz. per square inch........ 1 2 3 4 4 6 6 QUANTITY OF AIR OF A GIVEN DENSITY DELIVERED BY A FAN. Total area of nozzles in square feet X velocity in feet per minute corresponding to density (see table) = air delivered in cubic feet per minute.

Density,

ounces

per sq. in.

per min.

ounces

Velocity, feet

per sq. in, per minute.

5

11,000

9

15,000

Experiments with Blowers. (Henry I. Snell, Trans. A. S. M. E. ix. 51.-The following tables give velocities of air discharging through an aperture of any size under the given pressures into the atmosphere. The volume discharged can be obtained by multiplying the area of discharge opening by the velocity, and this product by the coefficient of contraction: 85 for a thin plate and .93 when the orifice is a conical tube with a convergence of about 3.5 degrees, as determined by the experiments of Weisbach. The tables are calculated for a barometrical pressure of 14.69 lbs. (= 235 oz.), and for a temperature of 50° Fahr., from the formula V = V2gh. Allowances have been made for the effect of the compression of the air, but none for the heating effect due to the compression.

At a temperature of 50 degrees, a cubic foot of air weighs .078 lbs., and calling g32.1602, the above formula may be reduced to

V1 = 60 /31.5812 × (235+P) × P,

where V1 = velocity in feet per minute.

P pressure above atmosphere, or the pressure shown by gauge, in oz per square inch.

Experiments on a Fan with Varying Discharge-opening.

Revolutions nearly constant.

.09

1550.70

.10

1635.00

The fan wheel was 23 inches in diameter, 65% inches wide at its periphery, and had an inlet of 121⁄2 inches in diameter on either side, which was partially obstructed by the pulleys, which were 5 9/16 inches in diameter. It had eight blades, each of an area of 45.49 square inches,

The discharge of air was through a conical tin tube with sides tapered at an angle of 311⁄2 degrees. The actual area of opening was 7% greater than given in the tables, to compensate for the vena contracta.

In the last experiment, 89.5 sq. in. represents the actual area of the mouth of the blower less a deduction for a narrow strip of wood placed across it for the purpose of holding the pressure-gauge. In calculating the volume of air discharged in the last experiment the value of vena contracta is taken at.

Experiments were undertaken for the purpose of showing the results obtained by running the same fan at different speeds with the discharge-opening the same throughout the series.

The discharge-pipe was a conical tube 81⁄2 inches inside diameter at the end, having an area of 56.74, which is 7% larger than 53 sq. inches; therefore 53 square inches, equal to .368 square feet, is called the area of discharge, as that is the practical area by which the volume of air is computed.

Experiments on a Fan with Constant Discharge-opening and Varying Speed.-The first four columns are given by Mr. Snell, the others are calculated by the author.

Mr. Snell has not found any practical difference between the efficiencies of blowers with curved blades and those with straight radial ones.

From these experiments, says Mr. Snell, it appears that we may expect to receive back 65% to 75% of the power expended, and no more.

The great amount of power often used to run a fan is not due to the fan itself, but to the method of selecting, erecting, and piping it.

(For opinions on the relative merits of fans and positive rotary blowers. see discussion of Mr. Snell's paper, Trans. A. S. M. E., ix. 66, etc.)

Comparative Efficiency of Fans and Positive Blowers.(H. M. Howe, Trans. A. I. M. E., x. 482.)-Experiments with fans and positive (Baker) blowers working at moderately low pressures, under 20 ounces, show that they work more efficiently at a given pressure when delivering large volumes (i.e., when working nearly up to their maximum capacity) than when delivering comparatively small volumes. Therefore, when great vari ations in the quantity and pressure of blast required are liable to arise, the highest efficiency would be obtained by having a number of blowers, always driving them up to their full capacity, and regulating the amount of blast by altering the number of blowers at work, instead of having one or two very large blowers and regulating the amount of blast by the speed of the blowers.

There appears to be little difference between the efficiency of fans and of Baker blowers when each works under favorable conditions as regards quantity of work, and when each is in good order.

For a given speed of fan, any diminution in the size of the blast-orifice de creases the consumption of power and at the same time raises the pressure of the blast; but it increases the consumption of power per unit of orifice for a given pressure of blast. When the orifice has been reduced to the normal size for any given fan, further diminishing it causes but slight elevation of the blast pressure; and, when the orifice becomes com. paratively small, further diminishing it causes no sensible elevation of the blast pressure, which remains practically constant, even when the orifice is entirely closed.

Many of the failures of fans have been due to too low speed, to too small pulleys, to improper fastening of belts, or to the belts being too nearly ver tical; in brief, to bad mechanical arrangement, rather than to inherent de fects in the principles of the machine.