We study, in a unified manner the motion of a uniformly advancing piston in the planar (\(m=0\)), cylindrically symmetric (\(m=1\)) and spherically symmetric (\(m=2\)) isentropic flow governed by Euler’s equations. In the three dimensional space the piston is replaced by an expanding cylinder or a sphere which produces a motion in the medium outside. Under the hypothesis of self symmetry pair of ordinary differential equations is derived from Euler’s equations of fluid flow. Based on the analysis of critical solutions of this system of ordinary differential equations, unified treatment of motion of uniformly advancing piston is given with different geometries viz. planar, cylindrically symmetric and spherically symmetric flow configuration. In case of nonplanar flows, solutions in the neighbourhood of nontransitional critical points approach these critical points in finite time. Transitional solutions exist in nonplanar cases which doesn’t correspond to the motion of a piston. In the planar case, it is found that solutions take infinite time to reach critical line.

我们以统一的方式研究了均匀推进的活塞在平面 ( \(m=0\) )、圆柱对称 ( \(m=1\) ) 和球对称 ( \(m=2\)) 由欧拉方程控制的等熵流。在三维空间中，活塞被一个膨胀的圆柱体或一个球体代替，它在外部介质中产生运动。在自对称假设下，常微分方程组是由欧拉流体流动方程导出的。在分析该常微分方程组的临界解的基础上，给出了不同几何形状下匀速活塞运动的统一处理。平面、圆柱对称和球对称流动配置。在非平面流的情况下，非过渡临界点附近的解决方案在有限时间内接近这些临界点。在与活塞运动不对应的非平面情况下存在过渡解决方案。在平面情况下，