: Flame quenching by solid surfaces has been studied by many workers, especially for the practical purpose of obtaining design data of flame arresters. Nevertheless, even a simple relation between hole diameter (D ) and length of flame path (L ) required for quenching has been not well known yet. This report intends to make some contribution for the basic understanding of quenching phenomena in narrow gaps.
    Determinations are made, with variations of D and L, on quenching diameters under atmospheric conditions and also on limiting pressures of quenching under raised and reduced pressures. Two kinds of hole are tested respectively: glass tubes and brass plates with a single hole. Flammable mixtures tested are those with air of methane, hydrogen or propane.
    Quenching diameters are determined by burner method (Fig.1). For a constant L, quenching diameter for a mixture is denied here as a mean value of a maximum hole diameter, which quenches flames in successive twenty tests, and a minimum hole diameter, through which at least one flame out of twenty tests passes. Some results are shown in Fig.3.
    Limiting pressures of quenching are determined in a closed system shown in Fig.2 : a hole under test is connected between an explosion chamber, in which explosions are originated, and a detection chamber which is embedded a thermocouple for the detection of flame transmission through the hole. It is known that the higher the initial pressure of the mixture is, the more easily a flame passes through the gap. The maximum initial pressure, below which no flame transmission occurs, is then a measure of quenching ability of the hole tested. This pressure is defined as "limiting pressure of quenching" by the hole, and means three successive quenchings in this report. The increments of initial pressure are 10 mmHg for methane-air and 50 mmHg for mixtures of hydrogen or propane, respectively. Some results are shown in Fig.4 and Fig.5. For holes drilled in brass plates (where L ≤ 10 mm), observed relations between hole dimensions and limiting pressures are reasonable for all mixtures tested, but, for glass tubes (25 ≤ L ≤ 100 mm), effect of hole length on limiting pressure is not apparent with hydrogen-air mixtures.
    From such curves as in Figs.4 and 5, one can obtain informations on limiting dimensions of holes required for quenching of flames : when a linear line, which corresponds to limiting pressure of 760 mmHg, is drawn in parallel with a horizontal axis, intersections with experimental curves give combinations of L and D of holes just required for quenching of flames, originated at an atmospheric initial pressure. For other pressures than atmospheric, relations between L and D are obtained through the same procedure.
    For a range of short length of flame path (L ≤ 10 mm), the limiting dimensions of holes for quenching of stoichiometric flames are interrelated by linear approximation. Results for limiting pressure of 760 mmHg are shown in Fig.8. Taking account of the equality of slopes of linear lines in Fig.8, and introducing the quenching diameter of each gas mixture, one may derive a following equation which stands approximately for all flammable gases tested :
    DD = 0.03 L + 0.44 D _q, where D _q is quenching diameter of the mixture. Similar approximations are applicable for pressures other than atmospheric, and those relations are expected to be useful for the design of flame arresters used in closed systems.