Method to calculate ultrasonic wave velocity by using chemical composition of austenitic stainless steels

Partial differential equationEquations ( 1) and (2) were partially differentiated with respect to each parameter E, ν, and ρ to simulate a deviation in ultrasonic wave velocity coused by a deviation in each parameter.Partial differentiation of Eq. ( 1) with regard to E gives Eq. ( 9).Partial differentiation of Eq. ( 1) with regard to νgivesEq.(10).Partial differentiation of Eq. ( 1) with regard to ρ gives Eq. ( 11).Partial differentiation of Eq. ( 2) with regard to E gives Eq. ( 12).