the following formula for computing the velocity of flow of air: P1 = absolute pressure in vessel from which flow takes place; P1 = absolute pressure in surrounding space. To find the volume discharged the velocity must be multiplied by the area and that result by a coefficient which Prof. Unwin gives as follows: Conoidal mouthpieces of the form of the contracted vein, with effective pressures of .23 to I.I atmosphere.... Circular sharp-edged orifices.... Short cylindrical mouthpieces... The same, rounded at the inner end. In the flow of air or gases through pipes the same considerations hold that have been stated for water. There is the same condition respecting the head which produces pressure and that which produces velocity, and in addition we have those changes due to the compressible nature of the fluid moved. Taking into account all these conditions, Prof. Unwin gives as a formula for the flow of air in a circular pipe 1 = length in feet; = coefficient of friction = : 0.005(1 + 3/10d); po greatest absolute pressure; 0.01212 for a diameter varying from 1.64 ft. to 0.164 ft. For a temperature of 60° F. and for a pipe one foot in diameter and 100 feet long, = 0.006. For barometer reading of 30 inches, pressure being expressed in inches of water, po = 407, we have from which the third column of the following table is calculated. The preceding table gives the velocity of air in feet per second as calculated from the accurate formula of Prof. Unwin, and also from the approximate formula v = V Vagh, using a coefficient of 0.7. The table is calculated for a barometric pressure of 30 inches and for a temperature of 60° F. For any other temperature the results must be multiplied by factors which are calculated as explained below. For the discharge at any other temperature divide the above results by the square root of 520 multiplied by 460 plus the temperature. For temperature of 32 degrees multiply by .972, 40 degrees .981, 50 degrees .987, 70 degrees 1.01, 80 degrees 1.018, 90 degrees 1.03, 100 degrees 1.04, 110 degrees 1.05, 120 degrees 1.06, 130 degrees 1.07. D 33. The Effect of Heat in producing Motion of Air.The effect of heat is to expand air in proportion to its absolute temperature for each degree of increase. If a column of air be heated it will expand and occupy more space. In other words, a given bulk will have less weight as its temperature is increased; which has the effect of producing lack of equilibrium, and the warmer air will be replaced by colder air, causing a velocity which is in proportion to the change in temperature. The case is analogous to the action of two fluids in the branches of a U-tube, Fig. 14, DABC,—the heavier fluid in DA and the lighter fluid in BC. The action of gravity causes the heavier fluid to flow downward and displace the lighter fluid, causing an upward motion. in BC. If a volume of the lighter fluid with height greater than BC balances the weight of the heavier fluid DA, the flow which is produced will take place with a head equal to the difference in height of AD, and an equal weight of the lighter fluid. The flow will take place in the same manner whether the heavier fluid be confined in a tube arranged as in the dotted lines, Fig. 14, or whether it be drawn from a large vessel, or from the surrounding air. Let the head which produced the draught be equal to ', the height of the flue BC as ; let t be the temperature of the outside air or heavier fluid and t' that of the lighter fluid; and let a be the coefficient of expansion, which for one degree of temperature of air will be FIG. 14. Since the expansion is directly proportional to the increase in temperature, we shall have in general: h By substituting for a its value, we shall have the following for the head producing the flow in case air is the moving fluid: 460 + is the absolute temperature of the air. The velocity is equal to the square root of twice the force of gravity, 32.16, into the head which produces the flow, as follows: The velocities given above, multiplied by 60 and by the area of crosssection, will give the discharge in cubic feet per minute. Mr. Alfred R. Wolff takes the actual discharge as 0.5 of that given by the formula, so that the actual discharge in cubic feet per minute would be, with 50 per cent allowance for friction, in which F equals the area of cross-section of the flue in square feet. The table on next page gives the discharge per square foot of area of flue for various temperatures and heights computed from the formula. The above formulæ are for the discharge of air from a flue. The volume, and consequently the velocity, for the entering air will be proportional to its absolute temperature; and hence to obtain the quantity of air entering when 7' is the temperature at entering and 7 that at dis460 + T' charging multiply the preceding formula by 460 + 7 34. The Inlet for Air.--The air for ventilation is usually warmed and a portion or all of the heat required for warming is introduced at the same time. TABLE SHOWING THE QUANTITY OF AIR, IN CUBIC FEET, Excess of Temperature of Air in Flue above that of External Air. It is found from experience that if the velocity of the entering air is very great it produces a disagreeable current, which is generally known as a draught, and is more or less, dangerous to health. The following table from Loomis' Meteorology gives the relation between the velocity and force of air: RELATION BETWEEN VELOCITY AND FORCE OF AIR. |