Losses in Flues--The loss of draft in straight flues due to friction and inertia can be calculated approximately from formula (26), which was given for loss in stacks. It is to be borne in mind that C in this formula is the actual perimeter of the flue and is least, relative to the cross sectional area, when the section is a circle, is greater for a square section, and greatest for a rectangular section. The r.e.t.a.r.ding effect of a square flue is 12 per cent greater than that of a circular flue of the same area and that of a rectangular with sides as 1 and 1, 15 per cent greater. The greater resistance of the more or less uneven brick or concrete flue is provided for in the value of the constants given for formula (26). Both steel and brick flues should be short and should have as near a circular or square cross section as possible.
Abrupt turns are to be avoided, but as long easy sweeps require valuable s.p.a.ce, it is often desirable to increase the height of the stack rather than to take up added s.p.a.ce in the boiler room. Short right-angle turns reduce the draft by an amount which can be roughly approximated as equal to 0.05 inch for each turn. The turns which the gases make in leaving the damper box of a boiler, in entering a horizontal flue and in turning up into a stack should always be considered. The cross sectional areas of the pa.s.sages leading from the boilers to the stack should be of ample size to provide against undue frictional loss. It is poor economy to restrict the size of the flue and thus make additional stack height necessary to overcome the added friction. The general practice is to make flue areas the same or slightly larger than that of the stack; these should be, preferably, at least 20 per cent greater, and a safe rule to follow in figuring flue areas is to allow 35 square feet per 1000 horse power. It is unnecessary to maintain the same size of flue the entire distance behind a row of boilers, and the areas at any point may be made proportional to the volume of gases that will pa.s.s that point. That is, the areas may be reduced as connections to various boilers are pa.s.sed.
[Ill.u.s.tration: 6000 Horse-power Installation of Babc.o.c.k & Wilc.o.x Boilers at the United States Navy Yard, Washington, D. C.]
With circular steel flues of approximately the same size as the stacks, or reduced proportionally to the volume of gases they will handle, a convenient rule is to allow 0.1 inch draft loss per 100 feet of flue length and 0.05 inch for each right-angle turn. These figures are also good for square or rectangular steel flues with areas sufficiently large to provide against excessive frictional loss. For losses in brick or concrete flues, these figures should be doubled.
Underground flues are less desirable than overhead or rear flues for the reason that in most instances the gases will have to make more turns where underground flues are used and because the cross sectional area of such flues will oftentimes be decreased on account of an acc.u.mulation of dirt or water which it may be impossible to remove.
In tall buildings, such as office buildings, it is frequently necessary in order to carry spent gases above the roofs, to install a stack the height of which is out of all proportion to the requirements of the boilers. In such cases it is permissible to decrease the diameter of a stack, but care must be taken that this decrease is not sufficient to cause a frictional loss in the stack as great as the added draft intensity due to the increase in height, which local conditions make necessary.
In such cases also the fact that the stack diameter is permissibly decreased is no reason why flue sizes connecting to the stack should be decreased. These should still be figured in proportion to the area of the stack that would be furnished under ordinary conditions or with an allowance of 35 square feet per 1000 horse power, even though the cross sectional area appears out of proportion to the stack area.
Loss in Boiler--In calculating the available draft of a chimney 120 pounds per hour has been used as the weight of the gases per boiler horse power. This covers an overload of the boiler to an extent of 50 per cent and provides for the use of poor coal. The loss in draft through a boiler proper will depend upon its type and baffling and will increase with the per cent of rating at which it is run. No figures can be given which will cover all conditions, but for approximate use in figuring the available draft necessary it may be a.s.sumed that the loss through a boiler will be 0.25 inch where the boiler is run at rating, 0.40 inch where it is run at 150 per cent of its rated capacity, and 0.70 inch where it is run at 200 per cent of its rated capacity.
Loss in Furnace--The draft loss in the furnace or through the fuel bed varies between wide limits. The air necessary for combustion must pa.s.s through the interstices of the coal on the grate. Where these are large, as is the case with broken coal, but little pressure is required to force the air through the bed; but if they are small, as with bituminous slack or small sizes of anthracite, a much greater pressure is needed.
If the draft is insufficient the coal will acc.u.mulate on the grates and a dead smoky fire will result with the accompanying poor combustion; if the draft is too great, the coal may be rapidly consumed on certain portions of the grate, leaving the fire thin in spots and a portion of the grates uncovered with the resulting losses due to an excessive amount of air.
[Graph: Force of Draft between Furnace and Ash Pit--Inches of Water against Pounds of Coal burned per Square Foot of Grate Surface per Hour
Fig. 34. Draft Required at Different Combustion Rates for Various Kinds of Coal]
Draft Required for Different Fuels--For every kind of fuel and rate of combustion there is a certain draft with which the best general results are obtained. A comparatively light draft is best with the free burning bituminous coals and the amount to use increases as the percentage of volatile matter diminishes and the fixed carbon increases, being highest for the small sizes of anthracites. Numerous other factors such as the thickness of fires, the percentage of ash and the air s.p.a.ces in the grates bear directly on this question of the draft best suited to a given combustion rate. The effect of these factors can only be found by experiment. It is almost impossible to show by one set of curves the furnace draft required at various rates of combustion for all of the different conditions of fuel, etc., that may be met. The curves in Fig.
34, however, give the furnace draft necessary to burn various kinds of coal at the combustion rates indicated by the abscissae, for a general set of conditions. These curves have been plotted from the records of numerous tests and allow a safe margin for economically burning coals of the kinds noted.
Rate of Combustion--The amount of coal which can be burned per hour per square foot of grate surface is governed by the character of the coal and the draft available. When the boiler and grate are properly proportioned, the efficiency will be practically the same, within reasonable limits, for different rates of combustion. The area of the grate, and the ratio of this area to the boiler heating surface will depend upon the nature of the fuel to be burned, and the stack should be so designed as to give a draft sufficient to burn the maximum amount of fuel per square foot of grate surface corresponding to the maximum evaporative requirements of the boiler.
Solution of a Problem--The stack diameter can be determined from the curve, Fig. 33. The height can be determined by adding the draft losses in the furnace, through the boiler and flues, and computing from formula (30) the height necessary to give this draft.
Example: Proportion a stack for boilers rated at 2000 horse power, equipped with stokers, and burning bituminous coal that will evaporate 8 pounds of water from and at 212 degrees Fahrenheit per pound of fuel; the ratio of boiler heating surface to grate surface being 50:1; the flues being 100 feet long and containing two right-angle turns; the stack to be able to handle overloads of 50 per cent; and the rated horse power of the boilers based on 10 square feet of heating surface per horse power.
The atmospheric temperature may be a.s.sumed as 60 degrees Fahrenheit and the flue temperatures at the maximum overload as 550 degrees Fahrenheit.
The grate surface equals 400 square feet.
2000 34 The total coal burned at rating = ---------- = 8624 pounds.
8
The coal per square foot of grate surface per hour at rating =
8624 ---- = 22 pounds.
400
For 50 per cent overload the combustion rate will be approximately 60 per cent greater than this or 1.60 22 = 35 pounds per square foot of grate surface per hour. The furnace draft required for the combustion rate, from the curve, Fig. 34, is 0.6 inch. The loss in the boiler will be 0.4 inch, in the flue 0.1 inch, and in the turns 2 0.05 = 0.1 inch.
The available draft required at the base of the stack is, therefore,
_Inches_ Boiler 0.4 Furnace 0.6 Flues 0.1 Turns 0.1 --- Total 1.2
Since the available draft is 80 per cent of the theoretical draft, this draft due to the height required is 1.2 .8 = 1.5 inch.
The chimney constant for temperatures of 60 degrees Fahrenheit and 550 degrees Fahrenheit is .0071 and from formula (30),
1.5 H = ----- = 211 feet.
.0071
Its diameter from curve in Fig. 33 is 96 inches if unlined, and 102 inches inside if lined with masonry. The cross sectional area of the flue should be approximately 70 square feet at the point where the total amount of gas is to be handled, tapering to the boiler farthest from the stack to a size which will depend upon the size of the boiler units used.
Correction in Stack Sizes for Alt.i.tudes--It has ordinarily been a.s.sumed that a stack height for alt.i.tude will be increased inversely as the ratio of the barometric pressure at the alt.i.tude to that at sea level, and that the stack diameter will increase inversely as the two-fifths power of this ratio. Such a relation has been based on the a.s.sumption of constant draft measured in inches of water at the base of the stack for a given rate of operation of the boilers, regardless of alt.i.tude.
If the a.s.sumption be made that boilers, flues and furnace remain the same, and further that the increased velocity of a given weight of air pa.s.sing through the furnace at a higher alt.i.tude would have no effect on the combustion, the theory has been advanced[53] that a different law applies.
Under the above a.s.sumptions, whenever a stack is working at its maximum capacity at any alt.i.tude, the entire draft is utilized in overcoming the various resistances, each of which is proportional to the square of the velocity of the gases. Since boiler areas are fixed, all velocities may be related to a common velocity, say, that within the stack, and all resistances may, therefore, be expressed as proportional to the square of the chimney velocity. The total resistance to flow, in terms of velocity head, may be expressed in terms of weight of a column of external air, the numerical value of such head being independent of the barometric pressure. Likewise the draft of a stack, expressed in height of column of external air, will be numerically independent of the barometric pressure. It is evident, therefore, that if a given boiler plant, with its stack operated with a fixed fuel, be transplanted from sea level to an alt.i.tude, a.s.suming the temperatures remain constant, the total draft head measured in height of column of external air will be numerically constant. The velocity of chimney gases will, therefore, remain the same at alt.i.tude as at sea level and the weight of gases flowing per second with a fixed velocity will be proportional to the atmospheric density or inversely proportional to the normal barometric pressure.
To develop a given horse power requires a constant weight of chimney gas and air for combustion. Hence, as the alt.i.tude is increased, the density is decreased and, for the a.s.sumptions given above, the velocity through the furnace, the boiler pa.s.ses, breeching and flues must be correspondingly greater at alt.i.tude than at sea level. The mean velocity, therefore, for a given boiler horse power and constant weight of gases will be inversely proportional to the barometric pressure and the velocity head measured in column of external air will be inversely proportional to the square of the barometric pressure.
For stacks operating at alt.i.tude it is necessary not only to increase the height but also the diameter, as there is an added resistance within the stack due to the added friction from the additional height. This frictional loss can be compensated by a suitable increase in the diameter and when so compensated, it is evident that on the a.s.sumptions as given, the chimney height would have to be increased at a ratio inversely proportional to the square of the normal barometric pressure.
In designing a boiler for high alt.i.tudes, as already stated, the a.s.sumption is usually made that a given grade of fuel will require the same draft measured in inches of water at the boiler damper as at sea level, and this leads to making the stack height inversely as the barometric pressures, instead of inversely as the square of the barometric pressures. The correct height, no doubt, falls somewhere between the two values as larger flues are usually used at the higher alt.i.tudes, whereas to obtain the ratio of the squares, the flues must be the same size in each case, and again the effect of an increased velocity of a given weight of air through the fire at a high alt.i.tude, on the combustion, must be neglected. In making capacity tests with coal fuel, no difference has been noted in the rates of combustion for a given draft suction measured by a water column at high and low alt.i.tudes, and this would make it appear that the correct height to use is more nearly that obtained by the inverse ratio of the barometric readings than by the inverse ratio of the squares of the barometric readings. If the a.s.sumption is made that the value falls midway between the two formulae, the error in using a stack figured in the ordinary way by making the height inversely proportional to the barometric readings would differ about 10 per cent in capacity at an alt.i.tude of 10,000 feet, which difference is well within the probable variation of the size determined by different methods. It would, therefore, appear that ample accuracy is obtained in all cases by simply making the height inversely proportional to the barometric readings and increasing the diameter so that the stacks used at high alt.i.tudes have the same frictional resistance as those used at low alt.i.tudes, although, if desired, the stack may be made somewhat higher at high alt.i.tudes than this rule calls for in order to be on the safe side.
The increase of stack diameter necessary to maintain the same friction loss is inversely as the two-fifths power of the barometric pressure.
Table 54 gives the ratio of barometric readings of various alt.i.tudes to sea level, values for the square of this ratio and values of the two-fifths power of this ratio.
TABLE 54
STACK CAPACITIES, CORRECTION FACTORS FOR ALt.i.tUDES
_______________________________________________________________________ | | | | | | | Alt.i.tude | | R | | R^{2/5} | | Height in Feet | Normal | Ratio Barometer | | Ratio Increase | | Above | Barometer | Reading | R | in Stack | | Sea Level | | Sea Level to | | Diameter | | | | Alt.i.tude | | | |________________|___________|_________________|_______|________________| | | | | | | | 0 | 30.00 | 1.000 | 1.000 | 1.000 | | 1000 | 28.88 | 1.039 | 1.079 | 1.015 | | 2000 | 27.80 | 1.079 | 1.064 | 1.030 | | 3000 | 26.76 | 1.121 | 1.257 | 1.047 | | 4000 | 25.76 | 1.165 | 1.356 | 1.063 | | 5000 | 24.79 | 1.210 | 1.464 | 1.079 | | 6000 | 23.87 | 1.257 | 1.580 | 1.096 | | 7000 | 22.97 | 1.306 | 1.706 | 1.113 | | 8000 | 22.11 | 1.357 | 1.841 | 1.130 | | 9000 | 21.28 | 1.410 | 1.988 | 1.147 | | 10000 | 20.49 | 1.464 | 2.144 | 1.165 | |________________|___________|_________________|_______|________________|
These figures show that the alt.i.tude affects the height to a much greater extent than the diameter and that practically no increase in diameter is necessary for alt.i.tudes up to 3000 feet.
For high alt.i.tudes the increase in stack height necessary is, in some cases, such as to make the proportion of height to diameter impracticable. The method to be recommended in overcoming, at least partially, the great increase in height necessary at high alt.i.tudes is an increase in the grate surface of the boilers which the stack serves, in this way reducing the combustion rate necessary to develop a given power and hence the draft required for such combustion rate.
TABLE 55
STACK SIZES BY KENT"S FORMULA
a.s.sUMING 5 POUNDS OF COAL PER HORSE POWER
____________________________________________________________________ | | | | | | | | Height of Stack in Feet |Side of| | | |______________________________________________|Equiva-| | Dia- | Area | | | | | | | | | | | lent | | meter|Square| 50| 60| 70| 80 | 90 | 100| 110| 125| 150| 175|Square | |Inches| Feet |___|___|___|____|____|____|____|____|____|____| Stack | | | | |Inches | | | | Commercial Horse Power | | |______|______|______________________________________________|_______| | | | | | | | | | | | | | | | 33 | 5.94|106|115|125| 133| 141| 149| | | | | 30 | | 36 | 7.07|129|141|152| 163| 173| 182| | | | | 32 | | 39 | 8.30|155|169|183| 196| 208| 219| 229| 245| | | 35 | | 42 | 9.62|183|200|216| 231| 245| 258| 271| 289| 316| | 38 | | 48 | 12.57|246|269|290| 311| 330| 348| 365| 389| 426| 460| 43 | | 54 | 15.90|318|348|376| 402| 427| 449| 472| 503| 551| 595| 48 | | 60 | 19.64|400|437|473| 505| 536| 565| 593| 632| 692| 748| 54 | | 66 | 23.76|490|537|580| 620| 658| 694| 728| 776| 849| 918| 59 | | 72 | 28.27|591|646|698| 747| 792| 835| 876| 934|1023|1105| 64 | | 78 | 33.18|700|766|828| 885| 939| 990|1038|1107|1212|1310| 70 | | 84 | 38.48|818|896|968|1035|1098|1157|1214|1294|1418|1531| 75 | |______|______|___|___|___|____|____|____|____|____|____|____|_______| | | | | | | | | Height of Stack in Feet |Side of| | | |______________________________________________|Equiva-| | Dia- | Area | | | | | | | | | lent | | meter|Square| 100| 110 | 125 | 150 | 175 | 200 | 225 | 250 |Square | |Inches| Feet |____|_____|_____|_____|_____|_____|_____|_____| Stack | | | | |Inches | | | | Commercial Horse Power | | |______|______|______________________________________________|_______| | | | | | | | | | | | | | 90 | 44.18|1338| 1403| 1496| 1639| 1770| 1893| 2008| 2116| 80 | | 96 | 50.27|1532| 1606| 1713| 1876| 2027| 2167| 2298| 2423| 86 | | 102 | 56.75|1739| 1824| 1944| 2130| 2300| 2459| 2609| 2750| 91 | | 108 | 63.62|1959| 2054| 2190| 2392| 2592| 2770| 2939| 3098| 98 | | 114 | 70.88|2192| 2299| 2451| 2685| 2900| 3100| 3288| 3466| 101 | | 120 | 78.54|2438| 2557| 2726| 2986| 3226| 3448| 3657| 3855| 107 | | 126 | 86.59|2697| 2829| 3016| 3303| 3568| 3814| 4046| 4265| 112 | | 132 | 95.03|2970| 3114| 3321| 3637| 3929| 4200| 4455| 4696| 117 | | 144 |113.10|3554| 3726| 3973| 4352| 4701| 5026| 5331| 5618| 128 | | 156 |132.73|4190| 4393| 4684| 5131| 5542| 5925| 6285| 6624| 138 | | 168 |153.94|4878| 5115| 5454| 5974| 6454| 6899| 7318| 7713| 150 | |______|______|____|_____|_____|_____|_____|_____|_____|_____|_______|
Kent"s Stack Tables--Table 55 gives, in convenient form for approximate work, the sizes of stacks and the horse power of boilers which they will serve. This table is a modification of Mr. William Kent"s stack table and is calculated from his formula. Provided no unusual conditions are encountered, it is reliable for the ordinary rates of combustion with bituminous coals. It is figured on a consumption of 5 pounds of coal burned per hour per boiler horse power developed, this figure giving a fairly liberal allowance for the use of poor coal and for a reasonable overload. When the coal used is a low grade bituminous of the Middle or Western States, it is strongly recommended that these sizes be increased materially, such an increase being from 25 to 60 per cent, depending upon the nature of the coal and the capacity desired. For the coal burned per hour for any size stack given in the table, the values should be multiplied by 5.
A convenient rule for large stacks, 200 feet high and over, is to provide 30 square feet of cross sectional area per 1000 rated horse power.
Stacks for Oil Fuel--The requirements of stacks connected to boilers under which oil fuel is burned are entirely different from those where coal is used. While more attention has been paid to the matter of stack sizes for oil fuel in recent years, there has not as yet been gathered the large amount of experimental data available for use in designing coal stacks.
In the case of oil-fired boilers the loss of draft through the fuel bed is partially eliminated. While there may be practically no loss through any checkerwork admitting air to the furnace when a boiler is new, the areas for the air pa.s.sage in this checkerwork will in a short time be decreased, due to the silt which is present in practically all fuel oil.
The loss in draft through the boiler proper at a given rating will be less than in the case of coal-fired boilers, this being due to a decrease in the volume of the gases. Further, the action of the oil burner itself is to a certain extent that of a forced draft. To offset this decrease in draft requirement, the temperature of the gases entering the stack will be somewhat lower where oil is used than where coal is used, and the draft that a stack of a given height would give, therefore, decreases. The factors as given above, affecting as they do the intensity of the draft, affect directly the height of the stack to be used.