Buckle's Rules for the Proportions of Centrifugal Fans. TO DETERMINE THE HORSE-POWER NECESSARY TO DRIVE THE FAN WHEN DISCHARGING AIR, THE VELOCITY OF THE TIPS OF THE VANES NOT TO EXCEED OF THE THEORETICAL VELOCITY, HAVING GIVEN THE DENSITY OF AIR REQUIRED, ALSO THE CUBic feet. RULE. First, find the horse-power, as directed in former examples when the fan is not discharging air. Then multiply ✈ part of the weight of air to be discharged by the fan per minute in pounds by o of the theoretical velocity, and divide by 33,000. The quotient will give the horse-power necessary to discharge this quantity of air, which add to the horse-power necessary to drive the fan when not discharging air, for the answer required. Example.-Let the pressure of the air required be 4 ounces per square inch, the column of mercury equal to the pressure = 5, and the weight of air to be discharged 220 pounds per minute, and V the velocity of fan in feet per minute. When the velocity of the tips of the vanes is equal to the theoretical velocity, then we proceed as in the last examples, only we take instead of (as in former examples) of the weight of air discharged, which is added to the horse power requisite to drive the fan when no efflux takes place. We should here again remark that when the fan is moving at this velocity, it is capable of discharging 480 pounds of air per minute without any falling off in density. In a recent set of experiments the inlet openings in the sides of the fan chest were contracted from 17, the original diameter, to 12 and 6 inches diameter, when the following results were obtained. First, the power expended with the opening contracted to 12 inches diameter, was as 2 to 1 compared with the opening of 17 inches diameter; the velocity of the fan being nearly the same, as also the quantity and density of air delivered. Second, the power expended with the opening contracted to 6 inches diameter, was as 2 to 1 compared with the opening of 17 inches diameter; the velocity of the fan being nearly the same, and also the area of the efflux pipe, but the density of the air was decreased one-fourth. These experiments show that the inlet openings must be made of sufficient size, that the air may have a free and uninterrupted action in its passage to the blades of the fan, for if we impede this action we do so at the expense of power. In a subsequent set of experiments made by Mr. Buckle, the fan employed was the same as the one detailed in the former experiments, the inlet openings being varied in diameter by adjustable rings of wood, the vane surface being modified accordingly. With an inlet 30 inches diameter, and vanes 8 inches long, width as before 10 inches, and same number of revolutions, the pressure of the air was equal to six ounces per square inch, the amount of power absorbed being 11.92 horses. Inlet, 24 inches diameter; length of vane 11 inches width 10 inches: 1,000 revolutions-gave a pressure of 5.8 ounces, the power required being 6·1 horses. Inlet, 201 inches; length of vane, 134 inches; width, 104 inches; 10816 revolutionsgave a pressure of 7.7 ounces, with 8.4 horse-power. Inlet, 15 inches; outlet 4 inches deep, and 7 inches wide; length of vane, 16 inches; width, 6 inches; 786 revolutions-gave a pressure of 4 ounces, with 2.9 horse-power. The same, with the outlet contracted to 4 inches deep, with 885 revolutions, gave a pressure of 4 ounces, but required 8-25 horse-power. Thus we see that with a vane 14 inches long, the tips of which revolve at the rate of 236.8 feet per second, air is con 271 densed to 9.4 ounces per square inch above the pressure of the atmosphere, with a power of 96 horses; but a vane 8 inches long, the diameter at the tips being the same, and having, therefore, the same velocity, condenses air to 6 ounces per square inch only, and takes 12 horse-power. The density of the latter is little more than of the former, while the power absorbed is nearly 1.25 to 1. Although the velocity of the tips of the vanes is the same in each case, the velocities of the heels of the respective blades are very different: for, whilst the tips of the blades in each case move at the rate of 236.8 feet per second, the heels of the 14 inch blades move at the rate of 908 feet per second; and the heels of the 8 inch move at the rate of 151-75 feet per second; or, the velocity of the heel of the 14 inch moves in the ratio of 1 to 1.67, compared with the heel of the 8 inch blade. The longer blade approaching nearer the centre, strikes the air with less velocity, and allows it to enter on the blade with greater freedom, and with considerably less force than the shorter one. The inference is, that the short blade must take more power at the same time that it accumulates a less quantity of air. In the 14 inch blade, the tip has a velocity 26 times greater than the heel; or, 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 vanes, it becomes compressed in proportion to its centrifugal force. The greater the length of 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. The following table gives the best proportions of ordinary fans. varying from 3 to 6 feet diameter: The dimensions here given are not prescribed as irrevocable, but as approximations to the best results in practice. In some cases, two fans fixed on one spindle would be found preferable to one wide one, as, by such an arrangement, twice the area of inlet opening is obtained, compared with a single wide fan; and they may be so constructed, where occasionally only half the quantity of air is required, that one of them may be disengaged by a clutch, whereby a saving of power would be effected. In a single fan of great width, the inlet opening must either be made too small in proportion to the width of the vane, or if it is made large enough for the width of the vane, the length of the vane becomes so short as to be quite incapable of producing air of the required pressure without overflowing at the inlet orifice. It has been found that by applying a circular sluice to the edge of the fan so as to contract the escaping orifice from 12 inches to 4 inches in depth, whereby the tip of the vane and the bottom of the outlet opening were nearly in a direct horizontal line, nearly the same quantity of air was expelled as with the original opening; and that the noise produced by the fan had nearly ceased. It therefore ap 272 Rankine on the Action and Proportions of Centrifugal Fans. pears, that the less this opening is made-provided we produce sufficient blast-the less noise will proceed from the fan; and by making the top of this opening level with the tips of the vane, the column of air has little or no reaction on the vanes. With respect to the degree of eccentricity which the fan should have with reference to the fan chest, of the diameter of the fan has been found in practice to answer well; that is, the space between the fan and the chest should increase, from of an inch at the top of the inlet to the transit pipe, to of the diameter of the fan at the bottom of a line perpendicular with the centre. The tunnel, or main pipe, from the fan chest may, for short distances varying from 50 to 100 feet in length, be made not less than 14 times the area of the outlet pipe in the fan chest ; and for distances varying from 100 to 200 feet in length, 14 times the area of the outlet pipe. The length of a tunnel may be continued to 300 or more feet, provided it be made of sufficient dimensions to allow the air to pass freely along it. Having recapitulated these investigations respecting the action of the fan, Mr. Buckle proceeds to offer some suggestions respecting its mechanical construction. And, first, it is essential that all parts maintain a just and proper balance. That the arms should be as light as is consistent with safety. Round arms are objectionable; and rectangular arms, with about the proportion of 24 times the width, for the depth at the centre, and with sufficient taper towards the tips, are to be preferred. Next, the bearings and journals of the fan spindle should be made of a length not less than four times the diameter of the necks of the spindle, and finally, the driving pulleys should be made as large as circumstances will admit of, so that the strap may have sufficient surface to prevent slipping.. A form of fan has been introduced in America, with the case diminishing in breadth from the inlet orifices to the edge, where the converging sides come to a point like a Gothic arch. On each side of the vanes and within the case a tapered mouth piece is placed, enlarging from the diameter of the inlet orifice to the diameter of the inner edge of the vanes, and these mouth pieces revolve with the vanes. Ventilating fans for mines have been successfully introduced by Nasmyth, Brunton, and others. It appears desirable that such fans should be of large diameter, and that they should be driven at a moderate speed. In many cases the fan is placed on the crank shaft of the engine. Even for high speeds this mode of driving the fan will answer, but the engine in such case should have its momentum balanced by the application of balance weights. Fans have been employed by Mr. Ruthven, of Edinburgh, and others, to blow air into one another, whereby it is made to issue from the last at a very considerable pressure. Gwynne has applied the principle of fans blowing the air into one another, as practised at some iron works, to his centrifugal pump, so as to enable it to pump from great depths. He sets a series of his pumps horizontally above one another, with an upright spindle passing through the whole, and the water discharged by the first pump enters the second, from whence it enters the third, and passes on to the fourth. BANKINE ON THE ACTION AND PROPORTIONS OF FANS. The most recent investigation on the subject of fans is that of Professor Rankine, who has examined the question with his usual ability. Professor Rankine shows that it is proper to make the inner edges of the fan of such a form that they will merely cleave the air without impinging upon it, and that the case should be very much larger than the fan, so as to enable a revolving stream of air to circulate there, in the manner proposed by Professor James Thomson, in the case of centrifugal pumps for water. In an experimental fan constructed by Professor Rankine, the mean radius of the case was to the radius of the fan as the velocity of the tips of the blades was to the velocity of the air in the discharge pipe. This fan was found to work efficiently and without noise. The proportion of the power wasted during the changes in the motion of the air, may be estimated by comparing the pressure which would be produced in the discharge pipe, if there were no waste of power, as computed theoretically, with the actual pressure as ascertained by experiment. The theoretical pressure depends on the figure of the blades, and the ratio of the diameter of the fan to that of the case, and is determined by the following equation :— FORMULA TO CALCULATE THE THEORETICAL PRESSURE AT THE OUTLET OF THE FAN-CASE. Let V velocity of tips of blades, in feet per second; v = velocity of air discharged at the outlet of the case, in feet per second; then theo2 V2 — v2 retical pressure in feet of air = ; finally, the theoretical 64.4 pressure in feet of air theoretical pressure in inches of water nearly. The difference between this and the actual pressure shows the loss by friction and agitation of the air. It is sufficient to state here, that the theoretical pressure at the outlet of a fan, formed and proportioned like that now described, is that due to the weight of a column of air of one and three quarter times the height from which a body must fall to acquire the velocity of the tips of the blades. In the experiment made, the number of turns per minute was 1,000. The circumference of the fan was 11 ft. Hence the velocity of the tips of the blades was 183 ft. per second. The height due to that velocity is 520 ft.; and one and three quarter times that height is 910 ft. It is usual to measure and state the pressures produced by blowing machines in inches of water. For the purposes of this calculation it is sufficiently accurate to take air as having one eight-hundredth part of the specific gravity of water. Then 910 ft. of air = 818=1·14 ft. of water 13.7 in. of water, which is the theoretical pressure at the commencement of the discharge pipe. The pressure was ascertained by experiment at a part of the discharge pipe between 40 and 50 ft. from the fan; the pipe was about 1 ft. square, and the loss of pressure in overcoming the friction in it must have been at least 2 in. of CHAPTER VI. ON MILL ENGINES. THE forms of engine employed to drive mills, and to accomplish the various mechanical operations for which a uniform rotatory motion is required, are very various, and it will be hardly possible within any moderate limits to describe all the kinds which have been brought into operation. It will be sufficient for all ordinary purposes, however, if we describe the principal kinds of rotative engine which are at present employed to drive mills and manufactories, and we shall offer such comment as we think useful as we proceed. Messrs. Boulton and Watt have supplied us with a statement of the speed of the piston in their engines of different powers, and it is as follows: make small engines of a somewhat greater nominal power than they formerly were reckoned at, which, since the nominal power is now a commercial unit, rather than a scientific one, is convenient in approximating the price per horse-power of the different sizes. The speed of the piston in feet per minute is about 128 times the cube-root of the stroke; and, as has already been mentioned, the nominal horse-power of an engine may be found by multiplying the square of the diameter of the cylinder in inches by the cube-root of the stroke in feet, and dividing by 47. On this principle the table of nominal horses power given at page 120 has been constructed, as also the more extended table given in the Appendix. The representations of the various parts of engines given in Plate VI. will make apparent the configuration of some of the main parts both of land and marine engines. An example of a ten horse power beam land engine, as constructed by Messrs Jukes, Coulson, and Co., of London, in the early part of this century, is given in Plate XII., which is a perspective view of the engine as employed to drive a sugar mill by which the juice is expressed from sugar canes. The piston makes a stroke of 3 feet, and works at the rate of 32 strokes per minute. The boiler c is 12 feet long and 5 feet diameter; its ends are round, and above the brickwork those ends form quarters of spheres. A is the furnace, and D the chimney. T is the feeding cistern at the top of the upright feeding pipe. The pulley and chain to suspend the float in that pipe with the balance weight to it and the other pulley, is fixed on the same axis with the chain w to suspend the damper in the flue. The steam-pipe, the nossels in front of the cylinder, the parallel motion, the great lever, the connectingrod and crank N, are sufficiently apparent in the drawing. The great lever is 10 feet long, and 18 inches deep in the middle. The flywheel a q is fixed upon the same axis as the crank N; that axis is 6 inches square, and 3 feet long between the bearings. The flywheel is 9 feet diameter outside, but the rim is represented much smaller than it should be. The fixed framing of the engine is on the plan of the independent engines introduced by Messrs. Boulton, Watt, and Co. The condensing cistern G G is made of cast iron, 15 feet long, 4 feet broad, and 43 feet high outside; it forms the basement for the whole engine, and is placed on foundation walls, upon which it stands sufficiently steady by its own weight. From each angle of the cistern, a vertical column w w rises up, to sustain the spring beam U u, which is a rectangular open frame of cast iron, in one piece. It is further supported beneath the fulcrum of the great lever, by two other columns v v, which stand up from the middle of the cistern. The cylinder bottom is made large enough to reach across the width of the cistern, and is bolted down upon the edges of it. The bearing for the neck of the axis of the crank N is also bolted down upon the edge of the cistern, and the pivot at the other end of the axis is supported by an iron standard erected upon the same foundation walls which support the cistern, leaving a sufficient space between the cistern and that standard to receive the fly-wheel, and the excentric by which the working gear is moved, and also the small pinion by which the sugar-mill is turned. This pinion, of which only a very small part can be seen in the drawing, is one foot diameter, with 15 teeth of 24 inches pitch and 6 inches broad The teeth are strengthNN 274 Description of a Ten Horses Power Beam Engine working a Sugar-Mill. ened by solid flanges at each side, which connect all the teeth together.* The great wheel o o, which is turned by the pinion, is 74 feet diameter, with 108 teeth of 24 inches pitch and 5 inches broad. It is fixed on the extreme end of its axis P, which rests in two bearings fastened on the edges of the cistern G. The necks of this axis are .6 inches diameter. The extreme end projects beyond the bearing over the edge of the cistern with a square of 6 inches, which is connected by a square box k with one end of a round axis 1, which is connected at the other end with the projecting end of the axis of the upper roller F F of the sugar-mill. The two lower rollers H H are placed side by side beneath the upper roller F, so that their centres form the angles of an isosceles triangle. The rollers are 22 inches diameter and 4 feet long, turned truly cylindrical on their outsides, and cut with small grooves parallel to their axes. The rollers are hollow within, and have centre sockets at their ends to fit upon their axes, and they are fastened by wedges. The axes are of wrought iron, 6 inches square, and 4 feet long between the bearings. The necks at one end of each of these axes are 6 inches diameter, and 6 long in the bearings; the pivots r, m, m, at the opposite ends, are 5 inches diameter and 6 inches long. The rollers are supported in a very massive frame of cast iron, consisting of two upright standards x x, erected upon a foundation plate B B, which is bedded upon masonry, and is formed with a border projecting upon all sides, to give it strength, and also to form a pan for the reception of the juice which is expressed from the sugarcanes in their passage between the rollers. The ends of the foundation plate в are adapted to receive the bases of the upright standards x x, which have feet spreading out from them sideways, and the foundation bolts which fasten the plate down upon the masonry pass through these feet. The form of the standards is sufficiently shown in the figure. The lower part of each standard consists of several upright pillars with openings between them. Above these are two cells to receive the brasses for the pivots m m of the two lower rollers HH, with strong regulating screws to set those brasses horizontally towards each other, in order to adjust their distance from the upper roller. Between these two cells a very strong upright standard rises up with a cell in the top to receive the brasses for the pivots r of the upper roller, and those brasses are kept down by a cap which is fastened over them by two strong bolts and nuts at top. The ends of the axes of the rollers project out beyond their bearings at the side of the frame towards the engine, and each one has a pinion fixed upon it; only the upper one of these pinions can be seen at u. The pinions of both the lower rollers H H are turned round by the teeth of the pinion u on the axis of the upper roller, but the horizontal distance between the centres of the lower rollers is rather greater than the oblique distance from the centre of the upper roller to the centres of either the two lower ones, and for the same reason there is a considerable opening between the surfaces of the two lower rollers; but both the lower rollers are very close to the upper roller, and only leave spaces of about of an inch between them, in order that the canes may be squeezed into that thickness in passing between the rollers. These pinions are nearly the same diameter as the rollers, and have each 22 teeth of 3·14 inches pitch, and 5 inches broad. The axis I is connected with the extreme end of the axis of the upper roller F by means of a circular box u, which is fixed on the end of the axis of the upper roller. The interior of the box is bored rather conical, to receive a circular plug, which is fixed upon the extreme end of the axis 1, so that the plug fits into the box in the same manner as the plug of a cock fits into its socket, and the plug is pressed into the box, by means of three or four screws, with so much force, that the friction of the plug in the box will suffice to turn the rollers round and perform their work properly; but if by accident the rollers become clogged up with canes, or with stones, or other solid matter, the plug will slip round within the box, so as to avoid breaking the teeth of the wheels, or stopping the engine, as might otherwise happen. The sugar-canes are presented to the rollers by a man, who spreads The teeth of the pinion are not so strong as they should be, but the motion being slow, the teeth are capable of enduring a much greater strain than if they acted with more rapidity. The strain upon these teeth is at the rate of 342 pounds for teeth of one inch pitch and one inch broad, which is more than double the strain of that which was put by Mr. Watt upon the teeth of his sun and planet-wheels. them out upon an inclined table K, which is made of iron plate; the ends of the canes pass down the inclined table, and are drawn in between the front lower roller H and the upper roller F, by which they are subjected to a very severe pressure, which squeezes out the juice or natural sap of the canes, and it trickles down from the rollers into the pan, which is formed in the middle of the foundation plate B. The ends of the canes which have passed downwards between the two rollers then meet with the back lower roller H, which by its motion turns those ends up again, so as to introduce them between the upper roller F and the back lower roller H, whereby the canes receive a second pressure, and the latter rollers being set nearer together than the former, the remainder of the juice is expressed; the canes then pass from the roller H down another inclined table L, and fall upon the ground. q is a spout in the side of the pan B, with a small shuttle to run off the collected juice into a trough, which conveys it away to the boiling-house. The inclined tables K and L are supported by upright pillars, as is seen in the drawing. The canes, after being pressed, are called cane trash, and are used as fuel for boiling the sugar, and for working the engine. As this fuel produces a less intense heat than coals, the fire-grate is of a large size, being 31 feet square 121 square feet. When the engine works at its proper speed of 32 strokes per minute, the rollers make 4:44 turns per minute, and their surfaces move at the rate of 256 feet per minute, which is too great. The cold water pump R, and the hot water pump s, are placed within the cistern G, as is shown in the figure, and 8, 8, is the feeding pipe which conveys the hot water for the supply of the boiler, from the hot water pump, to the feeding cistern T. There is also a waste pipe to carry away the surplus water, which is not represented. This engine had no governor, but a governor may be placed at the end of the engine, as shown at z, above the spring beams u, being fixed on the upper end of its upright axis Y, which has a beveled wheel upon the lower end of it within the cistern G, to be turned by another beveled wheel fixed upon a horizontal axis, which passes through the cistern to the outside, and has a spur wheel upon the end of it, which is turned from a similar wheel fixed upon the axis of the crank, with an intermediate wheel to convey the motion. When the governor is applied in this manner, the pannel at the end of the cistern G must be extended out in a circular form like a bow window, so as to leave a space for the beveled wheels within the cistern. Or else the axis of the governor may be placed farther away from the engine, and the beveled wheels may be at the end of the cistern on the outside. The valves of this engine are lifted by means of upright rods; and those lifting rods are raised up alternately by two tappets, which project out in opposite directions from a horizontal axis, and act beneath feet at the lower ends of the upright rods. This axis does not turn round continuously, but it is moved backwards and forwards by means of a lever 4 at the extreme end of it, which is connected with the compound rod 2, extending from the excentric circle, which is fixed upon the axis of the fly-wheel. Steam-engines are found to answer extremely well for turning sugar-mills, where water-mills cannot be had; and great numbers of steam sugar-mills are now exported to the East and West Indies, Cuba, Brazil, and other parts of the world. But those mills are now made of much greater size and strength than the one represented in Plate XII. The first application of the steam-engine to these mills was made by Mr. Rennie, about the year 1801, to be worked by an 8 horse-engine made by Boulton and Watt. It was sent to Demerara, and performed very well. It is advantageous to express the juice from the sugar-canes as soon as ever they are gathered, and before they have time to ferment. Cattle-mills are deficient in power to despatch the work for a large plantation, and extra cattle must be kept on purpose to turn the mills, because they are wanted at the most busy season of the year, when there are other employments for all the cattle that can be procured. The original form of sugar-mills had three rollers placed in a verti cal position, because that is most conveniently turned by cattle, without any wheelwork. The horizontal position of the rollers is a great improvement, and was first proposed by Mr. Smeaton to be turned by a water-mill in 1757. Maudslay's Portable Engine.-The next example of a beam mill |