Abstract: Differential equations of ideal gas under gravity are madedimensionless by choosing statistical quantities \rho (R), p(R),u(R) as the unit with respect toscale factor R (t) and substituting time t with spatial scalefactor R (t). The equations that have separable variables areobtained based on \it\Pi theory, then a serial of differential equationshaving fractal structure characteristics are obtained. Statisticalquantities of ideal gas under gravity Y(R) have generalizedfractal characteristics. This result shows that the local differentialequations of fluid can be the fundamental equations of the dynamics ofstatistical fractal structures.