Direct Solution Of Problems Involving Natural Ventilation

THE subject of the flow of air through a mine under the influence of natural ventilation has proved an elusive one. To my knowledge only cut and try algebraic solutions have been used where multiple paths are involved. The object of this paper is to present a method for the graphical determination of the flow induced by the natural ventilation pressure (N.V.P.) alone or in combination with a fan. The N.V.P., measured in pounds per square foot, induced by two columns of air between two horizontal planes at different elevations, is equal to the difference in weight of the two columns, assuming each to have a cross-sectional area of 1 sq. ft. Pressure in pounds per square foot is converted into inches of water by dividing by 5.19. Methods of calculating the N.V.P. have been discussed in the literature. In this paper, for simplification of exposition, the change in pressure due to the weight of superimposed air will be assumed directly proportional to the length of the column. The actual methods of calculating the N.V.P. do not affect the solutions to be presented. It must be realized that the precision to be obtained from the small- scale, inked diagrams presented is not as great as would be obtained from large-scale, penciled curves that would be used in practice. The accuracy of the curves does not warrant reading "volumes" closer than the nearest thousand cubic feet per minute. CASE I. DUCTS IN SERIES The simplest type of problem is to determine the flow when two shafts are connected by a crosscut, as shown in Fig. 1. In this example, the resistance of the shafts is to be taken as 0.0001 in. of water for a flow of 1000 cu. ft. per minute for a length of 1000 ft. The resistance of a crosscut is to be taken as 0.0005 in. of water for a flow of 1000 cu. ft. per minute. The small pressures necessary to cause changes in velocity will not be considered, because the accuracy of other obtainable data does not warrant their consideration.