Basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas

Self-similar function of one-dimensional nonsteady flow is extended to a general form. With total energy kept constant, basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas is derived using dimension theory in combination with the basic motion equations of hydromechanics. When a non-dimensional natural parameter L, which is the ratio of velocity of fluid (u) and self-similar surface (r), serves as the independent variable, the theoretical model reveals that self-similar law of non-dimensional nonsteady flow of ideal gas has the simplest mathematical form. The model overcomes the difficulty of divergence at the origin of self-similar function of Taylor and thus has significant importance.