Analytical computation of five unresolved integrals in the linear theory of partially cavitating hydrofoils

Five non-tabulated integrals are analytically calculated. These integrals emerge from the linear theory of partially cavitating hydrofoils and propeller blades. They appear in a series of weight functions involved in the determination of the cavitation number and cavity shape. The present analytical results eliminate the need for unnecessary numerical integrations, which could be beneficial in reducing computational costs and improving the robustness of numerical models. • Five new analytical formulas are derived in closed form. • Elimination of numerical integration, leading to improved computational efficiency. • Application to the linear theory of partially cavitating hydrofoils.