Based on the axiomatization definitions of subsethood measure and similarity measure, similarity measuer induced by subsethood measure is discussed, and some real induced formulas are given.

With the differential geometry and engagement theories, induced curvature formulas of point engagement were deduced, and the formula of the local contact areas was given.

A formula is deduced for the velocity induced by the vortices in two-dimensional shallow water flows and it is used to correct the Biot-Savart law.