It will be evident, from what has been said, that the movements of the air in a confined space are dependent upon (1) the difference between the internal and external temperatures; (2) the area and friction at the apertures through which air enters and leaves the room; and (3) the height of the column of ascending warm air. The higher the chimney (assuming it to contain warm air), the greater the draught and the more efficient the ventilation of the room communicating with it. Hence ventilation is more difficult in upper rooms of large houses and in single-storeyed houses than in the lower storeys of large houses.
Allowance for Friction.—Practically the friction varies greatly according to the size, form, and material of outlet for air. A rough or sooty or angular chimney greatly impedes the outgoing current of air.
It is usual to reduce the theoretical velocity by 20 to 50 per cent. Apart from the friction which is governed by roughness and length of channels, that due to bends in the channel may be calculated by the formula 1/(1-sin2 θ), θ being the angle at any bend in this channel.
(It may be convenient to note that—
- sin2 90° = 1,
- sin2 60° = ¾
- sin2 45° = ½,
- sin2 30° = ¼.)
Thus every right angle in a bent shaft reduces the velocity in it by one-half.
The loss by friction in two similar tubes of equal sectional area varies (1) directly with the square of the velocity of the air currents; and (2) directly with the length of the outlet channel. In two similar tubes of unequal size the loss by friction is (3) inversely as the diameter of the cross-section in each.
When two tubes are of different shapes, the loss by friction is inversely as the square roots of the sectional areas.
Owing to the variable value of the co-efficient of friction (called c in the first formula given), it is usually preferable to measure the actual rate of progress of air through a given flue by means of an anemometer (wind measure). Then the velocity of the current of air and the area of the cross section of the flue being given, the volume of air discharged in a given time is represented by the product of these two and the time which has elapsed.
Thus, q = a × v.