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A shockless, conceptually-laminar formulation on extremely fast flame acceleration in semi-open obstructed pipes [Physical Review Letters 101 (2008) 164501; Combust. Flame 157 (2010) 1012], Refs. [8-9] is extended to pipes with both ends open/vented. The acceleration is devoted to a powerful jet-flow produced by delayed combustion in the pockets between the obstacles, and it leads to a prompt deflagration-to-detonation transition event. Starting with inviscid approximation, the analysis subsequently incorporates the viscous forces (hydraulic resistance). The theory is validated by the recent experiments [http://arxiv.org/abs/1208.6453], Ref. [11]. It is shown that hydraulic resistance is not required to drive the flame acceleration. In contrast, this is a supplementary effect, which actually moderates the acceleration rate. On the other hand, hydraulic resistance plays an important role: it is responsible for the initial delay, before the flame acceleration onset, observed in the experiments. It is demonstrated that flames accelerate strongly in open/vented obstructed pipes, and the acceleration mechanism is qualitatively the same as that in the semi-open ones. However, because of the flame-generated flow distributed upward and downward of the flame front, the acceleration rate in open pipes is noticeably less than that in the semi-open ones.