and further that the increased velocity of a given weight of air
passing through the furnace at a higher altitude would have no effect on
the combustion, the theory has been advanced[53] that a different law
applies.

Under the above assumptions, whenever a stack is working at its maximum
capacity at any altitude, 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 altitude, assuming 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 altitude 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 altitude is increased, the density
is decreased and, for the assumptions given above, the velocity through
the furnace, the boiler passes, breeching and flues must be
correspondingly greater at altitude 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 altitude 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