heated air in the duct, and a column of equal height and cross-sectional area of weight of the external air. = Let d density, or weight in pounds, of a cubic foot of the external air. Let di = density, or weight in pounds, of a cubic foot of the heated air within the duct. Let hvertical height, in feet, of the vent-duct. h(d d) the pressure, in pounds per square foot, with which the air is forced into and out of the vent-duct. This pressure can be expressed in height of a column of the air of density within the vent-duct, and evidently the height of such column of equal h(d-d1) presssure would be di (3) Or, if t absolute temperature of external air, and t1 = absolute temperature of the air in vent-duct in the form, then the pressure equals The theoretical velocity, in feet per second, with which the air would travels through the vent-duct under this pressure is The actual velocity will be considerably less than this, on account of loss due to friction. This friction will vary with the form and cross-sectional area of the vent-duct and its connections, and with the degree of smoothness of its interior surface. On this account, as well as to prevent leakage of air through crevices in the wall, tin lining of vent-flues is desirable. The loss by friction may be estimated at approximately 50%, and so we find for the actual velocity of the air as it flows through the vent-duct: If V velocity of air in vent-duct, in feet per minute, and the external air be at 32° Fahr., since the absolute temperature on Fahrenheit scale equals thermometric temperature plus 459.4, from which has been computed the following table: Quantity of Air, in Cubic Feet, Discharged per Minute through a Ventilating Duct, of which the Cross-sectional Area is One Square Foot (the External Temperature of Air being 32° Fahr.). Height of Vent-duct in feet. Excess of Temperature of Air in Vent-duct above that of Multiplying the figures in above table by 60 gives the cubic feet of air discharged per hour per square foot of cross-section of vent-duct. Knowing the cross-sectional area of vent-ducts we can find the total discharge; or for a desired air-removal, we can proportion the cross-sectional area of vent-ducts required. Artificial Cooling of Air for Ventilation. (Engineering News, July 7, 1892.)-A pound of coal used to make steam for a fairly efficient refrigerating-machine can produce an actual cooling effect equal to that produced by the melting of 16 to 46 lbs. of ice, the amount varying with the conditions of working. Or, 855 heat-units per lb. of coal converted into work in the refrigerating plant (at the rate of 3 lbs. coal per horsepower hour) will abstract 2275 to 6545 heat-units of heat from the refrigerated body. If we allow 2000 cu. ft. of fresh air per hour per person as sufficient for fair ventilation, with the air at an initial temperature of 80° F., its weight per cubic foot will be .0736 lb.; hence the hourly supply per person will weigh 2000 x .0736 lb. = 147.2 lbs. To cool this 10°, the specific heat of air being 0.238, will require the abstraction of 147.2 × 0.238 x 10 = 350 heatunits per person per hour. Taking the figures given for the refrigerating effect per pound of coal as above stated, and the required abstraction of 350 heat-units per person per hour to have a satisfactory cooling effect, the refrigeration obtained from a pound of coal will produce this cooling effect for 2275 ÷ 350 = 61⁄2 hours with the least efficient working, or 6545 ÷ 350 = 18.7 hours with the most efficient working. With ice at $5 per ton, Mr. Wolff computes the cost of cooling with ice at about $5 per hour per thousand persons, and concludes that this is too expensive for any general use. With mechanical refrigeration, however, if we assume 10 hours' cooling per person per pound of coal as a fair practical service in regular work, we have an expense of only 15 cts. per thousand persons per hour, coal being estimated at $3 per short ton. This is for fuel alone, and the various items of oil, attendance, interest, and depreciation on the plant, etc., must be considered in making up the actual total cost of mechanical refrigeration. Mine-ventilation-Friction of Air in Underground Passages.-In ventilating a mine or other underground passage the resistance to be overcome is, according to most writers on the subject, proportional to the extent of the frictional surface exposed; that is, to the product lo of the length of the gangway by its perimeter, to the density of the air in circulation, to the square of its average speed, v, and lastly to a coefficient k, whose numerical value varies according to the nature of the sides of the gangway and the irregularities of its course. α The formula for the loss of head, neglecting the variation in density as ksv2 unimportant, is p = in which p = loss of pressure in pounds per square foot, s = square feet of rubbing-surface exposed to the air, v the velocity of the air in feet per minute, a the area of the passage in square feet, and k the coefficient of friction. W. Fairley, in Colliery Engineer, Oct. and Nov. 1893, gives the following formulæ for all the quantities involved, using the same notation as the above, with these additions: h = horse-power of ventilation; length of air-channel; o perimeter of air-channel; g = quantity of air circulating in cubic feet per minute; u = units of work, in foot. pounds, applied to circulate the air: w = water-gauge in inches. Then, To find the quantity of air with a given horse-power and efficiency (e) of engine: q= h x 33,000 X e The value of k, the coefficient of friction, as stated, varies according to the nature of the sides of the gangway. Widely divergent values have been given by different authorities (see Colliery Engineer, Nov. 1893), the most generally accepted one until recently being probably that of J. J. Atkinson, 0000000217, which is the pressure per square foot in decimals of a pound for each square foot of rubbing-surface and a velocity of one foot per minute. Mr. Fairley, in his "Theory and Practice of Ventilating Coal-mines," gives a value less than half of Atkinson's, or .00000001; and recent experiments by D. Murgue show that even this value is high under most conditions. Murgue's results are given in his paper on Experimental Investigations in the Loss of Head of Air-currents in Underground Workings, Trans. A. I. M. E., 1893. vol. xxiii. 63. His coefficients are given in the following table, as determined in twelve experiments: (Straight, normal section.. Coefficient of Loss of .00092 .000,000,00486 Rock. gangways. Straight, normal section.. .00122 .000,000,00645 The French coefficients which are given by Murgue represent the height of water-gauge in millimetres for each square metre of rubbing-surface and a velocity of one metre per second. To convert them to the British measure of pounds per square foot for each square foot of rubbing-surface and a velocity of one foot per minute they have been multiplied by the factor of conversion, .000005283. For a velocity of 1000 feet per minute, since the loss of head varies as v2, move the decimal point in the coefficients six places to the right Equivalent Orifice.-The head absorbed by the working-chambers of a mine cannot be computed a priori, because the openings, cross-passages, irregular-shaped gob-piles, and daily changes in the size and shape of the chambers present much too complicated a network for accurate analysis. In order to overcome this difficulty Murgue proposed in 1872 the method of equivalent orifice. This method consists in substituting for the mine to be considered the equivalent thin-lipped orifice, requiring the same height of head for the discharge of an equal volume of air. The area of this orifice is obtained when the head and the discharge are known, by means of the following formulæ, as given by Fairley: Let Q quantity of air in thousands of cubic feet per minute; w inches of water-gauge; A = area in square feet of equivalent orifice. Motive Column or the Head of Air Due to Differences of Temperature, etc. (Fairley.) Let Mmotive column in feet; T temperature of upcast; f weight of one cubic foot of the flowing air; t temperature of downcast; D= depth of downcast. To find diameter of a round airway to pass the same amount of air as a square airway the length and power remaining the same: Let D= diameter of round airway, A = area of square airway; 0= peri5 A3 X 3.1416 .78543 X O meter of square airway. Then D3. If two fans are employed to ventilate a mine, each of which when worked separately produces a certain quantity, which may be indicated by A and B then the quantity of air that will pass when the two fans are worked together will be 43+ B3. (For mine-ventilating fans, see page 521.) 3 Relative Efficiency of Fans and Heated Chimneys for Ventilation.-W. P. Trowbridge, Traus. A. S. M. E. vii. 531, gives a theoretical solution of the relative amounts of heat expended to remove a given volume of impure air by a fan and by a chimney. Assuming the total efficiency of a fan to be only 1/25, which is made up of an efficiency of 1/10 for the engine, 5/10 for the fan itself, and 8/10 for efficiency as regards friction, the fan requires an expenditure of heat to drive it of only 1/38 of the amount that would be required to produce the same ventilation by a chimney 100 ft. high. For a chimney 500 ft. high the fan will be 7.6 times more efficient. In all cases of moderate ventilation of rooms or buildings where the air is heated before it enters the rooms, and spontaneous ventilation is produced by the passage of this heated air upwards through vertical flues, no special heat is required for ventilation; and if such ventilation be suffi cient, the process is faultless as far as cost is concerned. This is a condition of things which may be realized in most dwelling houses, and in many halls, schoolrooms, and public buildings, provided inlet and outlet flues of ample. cross-section be provided, and the heated air be properly distributed. If a more active ventilation be demanded, but such as requires the smallest amount of power, the cost of this power may outweigh the advantages of the fan. There are many cases in which steam-pipes in the base of a chimney, requiring no care or attention, may be preferable to mechanical ventilation, on the ground of cost, and trouble of attendance, repairs, etc. The following figures are given by Atkinson (Coll. Engr., 1889), showing the minimum depth at which a furnace would be equal to a ventilatingmachine, assuming that the sources of loss are the same in each case, i.e., that the loss of fuel in a furnace from the cooling in the upcast is equivalent to the power expended in overcoming the friction in the machine, and also assuming that the ventilating-machine utilizes 60% of the engine-power. The coal consumption of the engine per I.H.P. is taken at 8 lbs. per hour: Average temperature in upcast... 150° F. 200° F. Minimum depth for equal economy... 960 yards. 1040 yards. 1130 yards. Heating and Ventilating of Large Buildings. (A. R. Wolff, Jour. Frank. Inst., 1893.)-The transmission of heat from the interior to the exterior of a room or building, through the walls, ceilings, windows, etc., is calculated as follows: S t 100° F. amount of transmitting surface in square feet; K = a coefficient representing, for various materials composing buildings, the loss by transmission per square foot of surface in British thermal units per hour, for each degree of difference of temperature on the two sides of the material; Q = total heat transmission = SK (t - to). This quantity of heat is also the amount that must be conveyed to the room in order to make good the loss by transmission, but it does not cover the additional heat to be conveyed on account of the change of air for purposes of ventilation. The coefficients K given below are those prescribed by law by the German Government in the design of the heating plants of its public buildings, and generally used in Germany for all buildings. They have been converted into American units by Mr. Wolff, and he finds that they agree well with good American practice: VALUE OF K FOR EACH SQUARE FOOT OF BRICK WALI.. Thickness of 1 brick wall. 4" 8" 12" 16" 20" 24" 28" 32" 36" 40" K = 0.68 0.46 0.32 0.26 0.23 0.20 0.174 0.15 0.129 0.115 1 sq. ft., wooden-beam construction, planked over or ceiled, 1 sq. ft., fireproof construction, floored over, 1 sq. ft., single window.. 1 sq. ft., single skylight.. 1 sq. ft., double window. 1 sq. ft., double skylight.. 1 sq..ft., door...... ............ as flooring, K = 0.083 ......as ceiling, K= 0.104 ........as flooring, K = 0.124 .......as ceiling, K= 0.145 .............. ....................... ............. ................. ........ ............... K = 1.030 K = 1.118 K = 0.518 K = 0.621 K = 0.414 These coefficients are to be increased respectively as follows: 10% when the exposure is a northerly one, and winds are to be counted on as important factors; 10% when the building is heated during the daytime only, and the location of the building is not an exposed one; 30% when the building is heated during the daytime only, and the location of the building is exposed; 50% when the building is heated during the winter months intermittently, with long intervals (say days or weeks) of non-heating. The value of the radiating-surface is about as follows: Ordinary bronzed cast-iron radiating-surfaces, in American radiators (of Bundy or similar type), located in rooms, give out about 250 heat-units per hour for each square foot of surface, with ordinary steam-pressure, say 3 to 5 lbs. per sq. in., and about 0.6 this amount with ordinary hot-water heating. Non-painted radiating-surfaces, of the ordinary "indirect." type (Climax or pin surfaces), give out about 400 heat-units per hour for each square foot of heating-surface, with ordinary steam-pressure, say 3 to 5 lbs. per sq. in.; and about 0.6 this amount with ordinary hot-water heating. A person gives out about 400 heat-units per hour; an ordinary gas-burner, about 4800 heat-units per hour; an incandescent electric (16 candle-power) light, about 1600 heat-units per hour. The following example is given by Mr. Wolff to show the application of the formula and coefficients: Lecture-room 40 × 60 ft., 20 ft. high, 48,000 cubic feet, to be heated to 69° F.; exposures as follows: North wall, 60 x 20 ft., with four windows, each 14 X 8 feet, outside temperature 0 F. Room beyond west wall and |