Quantity of Air Discharged by a Flue.

—Any change of temperature of air produces a change equal to ¹⁄₄₉₁ part of its volume, for each degree variation. If a cubic foot of air is raised in temperature 1°F., its volume is ¹⁄₄₉₁ part larger than the original volume, and its buoyancy in the surrounding air is increased correspondingly. Air that has a temperature higher than that surrounding it will tend to rise because it is lighter. The air rising from a hot-air register or from a heated surface are illustrations of this condition.

Since the change of volume—or what is the same thing, its tendency to rise—increases ¹⁄₄₉₁ for each degree difference in temperature, the upward velocity of highly heated air will be very great. In warm air that fills a chimney flue or a room, the same tendency exists, the warmest air rises to the highest point and if the air can escape, as in the case of a chimney, a draft will result.

The draft of a chimney, in quiet air, is due to the difference in temperature between the air inside the flue above that outside the house. A chimney that does not “draw” and causes a stove to “smoke,” will often produce sufficient draft after the flue has been warmed. The upward movement of the warmer air in the flue produces a constantly increasing velocity, until it reaches the top of the chimney. This is an accelerated velocity that may be calculated by use of the formula given in physics, to express the velocity of accelerated motion. The well-known formula V = √(2gh) may be modified to express the conditions existing in a flue and permit of the calculation of the quantity of air discharged.

The upward flow of air in a chimney flue being due to the difference in temperature of the air in the flue over the outside air, the flow of air from the rooms will continue as long as the difference in temperature exists. Moreover, the air that is discharged from the rooms will be replenished from the outside, and for the air sent out of the flue a corresponding amount will be brought into the rooms through any openings that exist—door or windows or through cracks or crevices, depending on the completeness with which the house is closed. In no case is a house air-tight. The air pressure registered by the barometer is always the same inside as that outside the building. During cold weather, when the windows and doors are closed, the air is escaping through the chimney and also through every little crack and chink in the top of the rooms where the air is warmest. The colder air is entering at the same time through the joints about windows, door casings, through the crevices in the walls and particularly through the open joints made by the baseboards and the floor. This latter entrance of cold air is one of the commonest causes of cold floors. The shrinkage of the baseboards and floors from the quarter-round moulding which forms the joint leaves openings through which cold air is freely admitted from partitions and outside walls. The cold, heavier air remains near the floor because it can rise only when heated or forced upward by a draft. If the same air were permitted to enter at points near the ceiling and mingle with the warmest air in the room, a more uniform temperature would result, as well as better ventilation. The entering cold air, mixing with the warm air at the top of the room, would be reduced in its temperature and weight. The heavier air in falling would diffuse with the air beneath it and thus improve the general quality of the atmosphere.

It is important to remember that the discharge of air through a chimney flue will depend, in considerable amount, on the rate the new air is able to enter the house. In a new, tightly constructed house, the flue is often capable of discharging air much faster than it can enter, when it must find its way in through accidental openings. In such cases an open door or window immediately improves the draft of the stove.

The ventilation in the average dwelling is and must be accomplished by natural draft that is generated through difference in temperature of the air. The possibility of providing an acceptable system of continuous ventilation is confined to the draft of the chimney or to a flue provided especially for that purpose. Such being the case, the dimensions of flues constructed for ventilation should be the subject of investigation. The work that a chimney or ventilating flue has to do is continuous and will last throughout its lifetime; its proportions should therefore be considered with more than passing care.

It has been stated that the method of calculating volumes of air that will pass through a flue is based on the formula used to express the velocity of accelerated motion. The fundamental formula must be changed to suit the conditions produced when air is heated and made buoyant by expansion.

As has been stated, the change in temperature of air 1°F. causes an increase or decrease ¹⁄₄₉₁ part of its volume for each degree change. Any portion of air, warmer than that which surrounds it, tends to rise because of its lighter weight; the tendency to rise increases with the difference in temperature. The draft of a flue is caused by this condition of difference in temperature between the air inside the flue and the outside atmosphere.

In order that this general condition may be expressed in the simplest form let: T = the temperature inside the flue in degrees F.

t = the temperature outside the flue in degrees F.
H = the height of the flue in feet.

The quantity (T-t)/491 expresses the difference in temperature in degrees, divided by the change of volume for each degree. This gives the constant upward tendency of the air in passing through the flue. If this quantity is placed in the formula V = √(2gh), so as to exert its influence through the height of flue H, the condition may be expressed:

V = √(2g((T-t)/491)H)

The factor g, representing the acceleration of gravity, is constant and equal to 32 feet per second. The quantity 2g may be removed from under the radical and the formula becomes:

V = 8√(((T-t)/491)H)

The formula may now be used to express the volume of discharge of air from a flue. Suppose such a flue contains an area of 1 square foot in cross-section and that it is desired to estimate the air discharged from the flue per hour. The value of g is given in feet per second, and in order to make the formula express the volume of air discharged in cubic feet per hour, it must be multiplied by the number of seconds in an hour. Volume discharged in cubic feet per hour

= 60 × 60 × 8√(((T-t)/491)H) = 28,800√(((T-t)/491)H)

This formula applies to conditions such as will permit uniform movement of the air in a straight flue, uninfluenced by irregular, odd-shaped passages and rough surfaces. Moreover, it is supposed that the air may enter the house as rapidly as it escapes. The theoretical discharge will, in most instances, be less than the calculated amount, because the air cannot enter the house as fast as it may be discharged by the flue. It is a common custom to consider the theoretical flue only 50 per cent. efficient. As applied to the formula, the constant 28,800 when reduced 50 per cent. will become 14,400, and will be so used in the calculations as follows.

As an illustration of the application of the formula, suppose that the temperature in the house and in the flue is 70°F. and that the outside temperature is 20°F. The height of the chimney is 30 feet. The area of the flue is 1 square foot. Volume = 14,400 √(((T - t)/491)H)
= 14,400√(((70 - 20)/491) × 30)
= 25,140 cubic feet per hour.

Such a ventilating flue would be sufficient in size, under the conditions given, to furnish air at the rate of 25,140 cubic feet per hour or 30 cubic feet per minute to 13 persons, provided of course that the air could enter the building at the rate demanded. Where no provision is made for the air to enter the building it must find its way by the accidental openings. A common illustration of this effect may be noticed in the rate at which the fire of a stove will burn in a tightly closed room. The opening of a door or window causes an immediate increase of combustion, because of the extra air supply. It is evident that in well-constructed houses other means should be provided for admitting air than that of accidental opening.

The following table calculated by the above formula gives the quantity of air in cubic feet per hour discharged through a flue of 1 square foot cross-section. The table shows the calculated discharge from flues of heights varying from 15 to 40 feet, and with temperature differences from 10° to 100° between the outside air and that of the house.

Height of flue in feet	Temperature of air in the flue above that of external air
Height of flue in feet	10	15	20	25	30	50	100
15	7,980	9,720	11,280	12,550	13,800	17,820	25,140
20	9,180	11,180	13,080	14,520	15,900	20,520	29,040
25	10,260	12,600	14,520	16,260	17,820	22,980	32,460
30	11,280	13,800	15,900	17,825	19,500	25,140	35,580
35	12,180	14,880	17,160	19,200	21,060	27,180	38,400
40	13,020	15,900	18,360	20,520	22,500	29,040	40,980

In Fig. 163 is illustrated the form of chimney that is often used for the ventilation of dwellings. This is built with three flues. The flue to the left—marked A at the top—is intended to carry away the smoke and gases from the kitchen range. The flue to the right is that to which is connected the smoke pipe from the furnace. The flue in the middle marked B is for ventilation. Occupying as it does the space between the other two, it is kept warm by the heat of the other flues and the draft is thus increased. Openings to the flue are shown in the different floors at the points R and S. The openings are furnished with registers which may be regulated to suit the weather conditions.

The dimensions of such a flue may be calculated by the formula given or the area may be taken from the table to correspond with required conditions. In all cases flues should be made ample in size, as they must often do their maximum work under the poorest conditions for the production of good draft.

The amount of air discharged from the flue as given in the table is due to the gravitational effect alone. The suction produced by the wind adds in a very large degree to the amount of air discharged. The quantity of air that will flow from a 30-foot flue, by reason of the suction of the wind, blowing 7 miles per hour is equal to the same flue working by gravity with a temperature difference of 20°. With a wind velocity of 7 miles per hour and a temperature as given, the capacity of the flue is doubled. It is easy, therefore, to understand why the rate at which fires burn is so greatly increased by high winds. At the time of very high winds, a chimney flue will carry away three and even four times the volume discharged at the time of atmospheric calm.