diameter in inches = 4.92 (H. P.)^{2/5} (29)
In both of these formulae H. P. = the rated horse power of the boiler.
From this formula the curve, Fig. 33, has been calculated and from it
the stack diameter for any boiler horse power can be selected.
For stoker practice where a large stack serves a number of boilers, the
area is usually made about one-third more than the above rules call for,
which allows for leakage of air through the setting of any idle boilers,
irregularities in operating conditions, etc.
Stacks with diameters determined as above will give an available draft
which bears a constant ratio of the theoretical draft, and allowing for
the cooling of the gases in their passage upward through the stack, this
ratio is 8. Using this factor in formula (25), and transposing, the
height of the chimney becomes,
d^{1}
H = ----- (30)
.8 K
Where H = height of stack in feet above the level of the grates,
d^{1} = available draft required,
K = constant as in formula.
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 retarding
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 1½,
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
space, it is often desirable to increase the height of the stack rather
than to take up added space 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 passages 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 pass that
point. That is, the areas may be reduced as connections to various
boilers are passed.
[Illustration: 6000 Horse-power Installation of Babcock & Wilcox 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 accumulation 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 assumed 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 pass
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 accumulate 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 spaces 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 assumed as 60 degrees Fahrenheit and
the flue temperatures at the maximum overload as 550 degrees Fahrenheit.
The grate surface equals 400 square feet.
2000 × 34½
The total coal burned at rating = ---------- = 8624 pounds.
8