An investigation is made into the possible types of similarity solutions that can describe the symmetric flow of a fluid into an empty spherical cavity. The flow is homentropic, and the fluid obeys a perfect gas law $p\; =\; k \rho ^{\gamma}$. Values of γ in the range 7 ≥ γ > 1 are discussed. In this range, we find that similarity solutions in which the flow accelerates into the cavity exist for $\gamma \textgreater {\frac{3}{2}$. For these solutions, the radius R of the cavity decreases as the nth power of time measured from the instant at which the cavity disappears. This power n increases monotonically as γ decreases, and attains the value 1 for $\gamma = {\frac{3}{2}$ Similarity solutions in which the cavity collapses with constant velocity are given by the value n = 1, and such solutions are possible for all values of γ in the range considered.