Mine Ventilation - Application of Kutter's Formula to Gases (with Discussion)

Much new data on the flow of gases have been discovered by recent experiments by the United States Bureau of Mines and others. Although additional investigation is still desirable, the information now collected seems sufficient to attempt a tentative coördination of the friction factors. This study is confined entirely to fluid friction when the density throughout the duct is so nearly constant that it may be so considered. In the subsequent discussion the following notation is used: v = mean velocity of fluid in duct, feet per second. v' = mean velocity of fluid in duct, meters per second. R = hydraulic radius of duct, feet. R' = hydraulic radius of duct, meters. S = the hydraulic slope. P = pressure absorbed by friction, pounds per square foot. p = pressure absorbed by friction, pounds per square inch. p' = pressure absorbed by friction, kilograms per square centimeter. A = sectional area of duct, square feet. O = perimeter of duct, feet. L = total length of duct, feet. L' = total length of duct, meters. d = diameter of a cylindrical duct, inches. w = density of the fluid, pounda per cubic foot. g = specific gravity of the fluid compared with water = w % 62.4. C, k and B, coefficients for formulas using English measures. C' = metric coefficient, v' = C'R'S. n = coefficient of roughness for English or metric units. The basic formula for the flow of all fluids at constant density appears in the three following forms, which may be denominated: (a) The slope formula, v = CRS (b) The ventilation formula, " n = (c) The pipe formula, C is Kutter's coefficient, which is extensively applied to the flow of water in ducts and channels of all kinds; E is Atkinson's coefficient, used principally with air in ventilation problems; B is a coefficient conveniently adapted to studying the flow of water, gases and vapors in pipes. 312