730 ore REPORT—1890. 
8. On the General Theory of Ventilation, with some Applications. 
By W. N. Suaw, M.A. 
For successful ventilation two primary conditions must be satisfied: (1) there 
must be a sufficient supply of air; (2) the entering air must be suitably distributed 
in the ventilated space. These two conditions suggest corresponding divisions of 
the subject. That part dealing with the amount of air supplied is referred to by the — 
term ‘general circulation,’ while the other part, which is concerned with distribu- 
tion, may be said to deal with ‘local circulation.’ In this paper the general circula~ — 
tion alone is discussed. The motion of the air is supposed to be ‘steady.’ 
If numbers are used, the units supposed to be employed are the foot, pound, 
and second respectively. 
The process of ventilation is treated as the flow of air through a duct of more 
or less complicated shape. For an ordinary room with open fireplace the parts of 
the complete duct are (1) the inlet openings (often indefinite), (2) the room itself, 
and (8) the chimney. 
The motion of air upon which the ventilation depends is due to the existence 
of a ‘ head,’ which is numerically expressed by the work done in driving unit mass 
of air through the whole length of the duct. If the work is measured in foot- 
pounds and the mass in pounds, the head is expressed as a number of feet in 
height of air, and therefore corresponds to a pressure-difference that can be ex- 
pressed as difference of water-level or lbs.-weight per square foot. 
The head may be due to one or more of the following causes :— 
(1) Wind impinging directly upon an opening ; 
(2) Wind blowing across an opening ; 
(83) Ventilating fans and blowing machines ; 
(4) High temperature in a vertical shaft. 
The numerical value of the head in feet of air can be calculated from certain 
data for each of the four causes. 
The volume of air flowing in the unit of time across any imagined cross-section 
of. the duct can be expressed in cubic-feet per second, and is called the ‘ flow.’ 
The following general laws of ventilation are established :— 
Law I. Continuity of flow—The mass of air flowing per second across all 
transverse sections of the duct is the same. Hence the flow across any section is 
inversely proportional to the density of air at that section. If the variations of 
density are negligeable we may say that the flow is the same across every section. ~ 
It would be strictly so if the air were an incompressible fluid. 
Law II. Definition of resistance and of equivalent orifice.—For any duct the 
ratio of the head to the square of the flow is a constant which depends on the 
shape and dimensions of the duct, and is called the ‘ resistance of the duct.’ Two 
ducts may give the same flow for the same head, although they may be of widely 
different shapes; thus every duct, no matter how complicated, is equivalent to and 
can be represented by an orifice of suitable size in a thin plate. The thin-plate 
orifice equivalent to a duct is called (following M. Murgue) the ‘ equivalent orifice — 
of the duct.’ If r bethe resistance of a duct, and a the area of its equivalent 
orifice, R=1/27a? approximately. [Foot, Ib. sec. units. ] 
The resistance of a duct of known form can be calculated from its dimensions ; 
bends, gratings, &c., increase its resistance, and can be allowed for, as shown in 
Péclet’s Traité de la Chaleur. 
Law III. Ducts in series.—If a duct is formed by connecting ‘in series’ two 
or more separate ducts, its resistance is the sum of the resistances of the several 
components, provided that two ducts are only, understood to be connected when 
the opposed ends of each communicate with an ample air-space (otherwise closed) 
separating them. 
The head for the complete circulation may be regarded as the sum of the heads 
for each component duct. 
Law IV. Parallel ducts—When ducts are arranged parallel, or in ‘ multiple 
arc’ (as when a number of openings are made side by side in one wall), they are 
a 
