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The effects of flame speed and explosion pressure on the flame-quenching performance of an in-line crimped-ribbon flame arrester was investigated using propane, ethylene, and hydrogen/air mixtures. The results show that the in-line arrester successfully stopped flames moving at high speeds and generating low explosion pressures, independently of pipe length and ignition distances, but failed for flames moving at low speeds and generating high explosion pressures. This indicates that both flame speed and explosion pressure are key parameters to evaluate the efficiency of an in-line flame arrester. Thus, the effect of increased pressure should be considered when the maximum flameproof speed by a given crimped-ribbon arrester is obtained. Furthermore, the relationship between the flameproof speed and explosion pressure is presented, based on the physical model of heat conduction, which is proved by experiments and provides more accurate reference for design and selection of crimped-ribbon flame arrester.