<p>The Lagrangian integral time scale (LITS) is a crucial characteristic for investigating the changes in fluid dynamics induced by the chaotic nature, and the finite-time Lyapunov exponent (FTLE) serves as a key measure in the analysis of chaos. In this study, a new LITS model with an explicit theoretical basis and broad applicability is proposed based on the FTLE, along with a verification and evaluation criterion grounded in the Lagrangian velocity correlation coefficient. The model is used to cavitating the flow around a Clark-Y hydrofoil, and the LITS is investigated. It leads to the determination of model constants applicable to cavitating flow. The model is evaluated by the Lagrangian velocity correlation coefficient in comparison with other solution methods. All the results show that the LITS model can offer a new perspective and a new approach for studying the changes in fluid dynamics from a Lagrangian viewpoint.</p>