A general theory of unsteady cavitating flow past hydrofoils and other obstacles is given for the case of cavities of finite length L. If the circulation Γ, the cavity volume V and L are known as functions of time, the theory yields explicit formulae for the velocity over the wetted surface and for the cavitation number σ. The theory is based on the approximation that the cavity is bounded by stream-lines, and so is valid only for slow rates of change of L, V and Γ. The possibility of allowing for the presence of a vortex sheet behind the cavity is discussed. The theory is extended to the case of a cascade of hydrofoils behind which extend growing cavities.

Two examples of the theory are discussed, namely the unsteady flow past a symmetrical wedge, and the unsteady flow past a flat plate hydrofoil cavitating from the leading edge.