A common three-light chandelier will burn about 12 feet per hour, and hence requires 21,600 cubic feet of air to properly dilute the combustion products. It must also be remembered, that coal gas always contains some sulphur compounds which are burnt up to sulphuric acid, and that gas fittings are seldom perfect; hence a gas supply is pretty certain to more or less continuously add its quota of impurity even when not burning. The other means by which apartments are made impure are the presence of any kinds of organic decomposable matter, the oxidation of fresh paint, the drying of size on the walls, and dust either produced in the house. itself or driven in from outside. In hospitals, infirmaries and wherever there are sick people, the air is liable to be dangerously contaminated with emanations from the discharges from wounds, or expectoration from diseased lungs; in such cases the greater amount of air dilution and the larger in reason the cubic space the better.

(37) Velocity of Air which can be borne without Discomfort.

Having fixed the amount of air to be supplied, the next question is the manner in which this is to be effected, and this again depends upon the velocity with which the air can be supplied (if we adopt natural ventilation) through the ventilators. If it were possible to place a person without discomfort in a cube of 100 feet and drive the outside air through this cube at a high velocity, the amount of cubic space per head would not be of such great importance. It has however been shown by Parkes and others that air at a temperature of between 55° to 60° F. can stream through an opening at a rate of 2 miles per hour (3 feet per second) without causing any discomfort, but at a speed greater than this it becomes perceptible, that is, a "draught" is experienced; warm air of 90° may be brought in at a higher speed than cool, but even in this case there are limits. A cubic space of 500 cubic feet with an inlet opening of 12 square inches could be supplied with 3,000 cubic feet of air hourly, but the velocity would be 7 miles an hour or 10 feet per second. This would of course be so uncomfortable in cold weather, that the tenant of such a room would block up the ventilators. A change of four times in the hour is about the limit. which in practice can be borne, hence the minimum cubic space should be 750 cubic feet.

(38) Principles Governing Air Movement.

Previous to entering on details of the methods by which ventilation can be accomplished, it is necessary to explain fully the principles which govern air movement.

All simple ventilation depends for its motive power on a difference of temperature between two columns of air, the heated air ascends, the cold air descends. Investigating the reason of this more closely, the cause of an air current is, that under the influence of heat, the specific gravity of a body of air is made lighter than that of the air in its immediate neighbourhood, and just as in the case of liquids of two different specific gravities, the heavier forces the lighter upwards. If, for example, there be two columns of air in a U tube each 10 feet high so long as there is no change of temperature or aspirating force the two columns will exactly balance, and no movement will take place, but if the temperature of the one limb is raised say 20°, then the heated air will expand 10 x 20 x 002 and became 104 feet in height and movement must ensue. The velocity of this movement is calculated by Montgolfier's rule which is constructed on the following data. The velocity in feet per second of falling bodies is nearly equal to eight times the square root of the height through which they have fallen, and fluids pass through an orifice in a partition with a velocity equal to that which a body would attain in falling through a height equal to the difference in depth of the fluid on the two sides of the partition. The air pressure at the surface of the earth is ever varying, but it is taken to average 14 lbs. to the square inch, and this is the weight of a column of air of equal density 5 miles in height. Air therefore rushes into a vacuum at the same speed as that which a heavy body would acquire in falling a height of 5 miles, 1,339 feet per second, or if it rush instead of into a vacuum into a room in which the pressure is less than outside, the velocity with which it rushes in is due (if we disregard friction) to the falling of a body through a height which represents the difference of pressure outside and inside. This velocity can in ordinary cases be theoretically obtained by multiplying the height from the aperture at which air enters to that from which it escapes by the difference of temperature between the outside and inside, and multiplying this by the coefficient1 of

1 The exact coefficient is .002039°.

=

the expansion of air for 1° F. 002; thus a column 40 feet high, and a difference of temperature between the external air and the internal of 20° would give 16 for 40 × 20 × 002 1.6, and 1.6 feet is the height in feet which will produce the velocity of the inflowing current. To calculate the velocity from this the square root of 1-6 must be multiplied by 8 which will give the velocity in one second of time, 8 x 1.6 10.12 and this again multiplied by 60 gives the velocity per minute. Or if the cubic delivery be required the velocity per second must be multiplied by the area of the opening and this by 60.

In practice a large allowance must be made for friction; in the case of a Tobin's tube, the tube being short and wide, the allowance of one fourth of the velocity to be deducted would be sufficient, but where the length of the tube is great and its diameter small, one half or more of theoretical velocity will have to be deducted. If one fourth be deducted from the above example the velocity per minute is 455 feet; if one half, then the velocity is 304 feet per minute; if the shaft be a chimney having a cross sectional area of 1 foot by 5 feet, then the efflux in cubic feet per minute will be 304 × 5=172·0 cubic feet per minute.

Quite as important as friction in hindering the action of ventilation is the alteration of specific gravity of contaminated air. In most cases of air contamination the specific gravity of the air is increased and therefore more difficult to move, e.g., the specific gravity of air being 1.000, that of carbon dioxide is 1.529, of sulphuretted hydrogen 1-177, and generally the stinking organic vapours are heavier than air and tend on that account, if the air is still, to hang about the localities from which they emanate, or if there are air currents, the stenches are apt to flow down towards the basements of houses from the upper stories; those for instance who have laboratories on top floors know how readily sulphuretted hydrogen seems to flow down the staircase, and the same is true of ether vapour. It is scarcely necessary to say that in such cases calculations based upon the movements of pure air give erroneous results.

(39) Inlets and Outlets.

The great variation in temperature in this country renders it difficult to arrange the inlets and outlets so that they will deal with

the proper quantity of air in all seasons, it has therefore been found best in practice to take some definite standard per head. The size usually accepted is 24 square inches for inlet, and the same for outlet; these are safe figures. The outlets should admit of being closed or regulated in size so as to adapt themselves to the contingencies of very cold weather. The student should nevertheless know how to calculate the delivery of air by any opening if the size of the opening, the height of the heated column of air, and the difference of temperature be known. This may be done from the formula already given. For instance, in the above example, a chimney for that particular difference of temperature has passing through it 172 × 60 = 10,320 cubic feet per hour; it is required to reduce the size so that 3,000 cubic feet only pass up the chimney when there is a temperature difference of 40°. The size of the opening is at present 5 square feet, or 72 square inches, and it must be reduced 3,000 × 72 in the proportion of 3,000 to 10,320, 20.93, so 10,320 that the openings would have to be reduced to 20-93 square inches.

=

De Chaumont has given a generally applicable and useful formula based on Montgolfier's rules, and giving the discharge per hour in square inches. No correction is made for friction, and therefore in the case of long tubes, the sizes must be increased in the proportion of 3 : 4.

Another kind of formula is given by Mr. Morrison in a valuable paper on the ventilation of tunnels (Proc. of the Institution of Civil Engineers, 1876), which will be found useful in calculating the pressure necessary to force air through shafts. Mr. Morrison's remarks are worthy of quotation. He says:

"The friction of air varies as the square of the velocity multiplied by the pressure against the sides of the passage. This pressure being uniform, its total amount depends upon the total surface, that is, the length multiplied by the perimeter of the cross section. The force required to propel air through any passage is therefore equal to the square of the velocity into the total surface multiplied by the coefficient of friction. It is more convenient to state the force in lbs. per square inch or per square foot, or as so many inches of water pressure; the above result should therefore be divided by the area of the cross section.

"The best form of the formula for practical purposes of ventilation

seems to be: H

H

=

head of pressure in feet of air of same density as the flowing air.

L = length of the pipe or passage in feet.

Р

A

V

K

=

=

=

=

perimeter of cross section in feet.

area of pipe or passage in square feet.
velocity in thousands of feet per minute.
co-efficient of friction = 0·03.

"This formula is perfectly general, and may be used for any fluid; H will always be the head stated in feet of the flowing fluid.

The pressure of 1 foot of air, at 60° F. is 0-0765 lb. per square foot. The pressure of 1 inch of water is 5.2 lbs. per square foot. Therefore if it be desired to reduce any result in feet of air to its equivalent in inches of water, the process is simply to 0.0765 divide it by 68; e.g. the head required for a current of 5.2 10 miles per hour through a tunnel 7 miles long, the perimeter KV2PL 0.03 × 0.8802 × 83 × 36960

=

83 feet is: H

=

A

of air 2 inches of water.

=

For circular passages, taking D for the diameter, the formula becomes H = K V2 ×

4 L
D

"These formulæ are only applicable to passages whose diameter is small in proportion to their length. For short passages the length should be increased by about 50 diameters of the passage: thus the 4 (L+ 50 D

formula for circular passages becomes H = KV2 × D

PL+ 200 A

and that for irregular-shaped passages, H = K V2 × A "The value 0.03 is reduced from a formula explained by Mr. Hawksley, Past-President, in a discussion on the Ventilation of Coal Mines.1

"In a Paper on the Ventilation of Coal Mines, read before the Geological Society of Manchester in 1862, Mr. Atkinson adopts the same formula as the Author, but gives a constant nearly ten 1 Vide Minutes of Proceedings Inst. C.E., vol. vi., p. 192.