The Balance Principle and the Reynolds Transport Theorem in Introductory Fluid Mechanics

This paper traces the evolution of the use of the Reynolds transport theorem to derive finite control volume equations for mass, momentum, and energy in introductory engineering fluid mechanics textbooks used in the United States. The paper demonstrates the superior merits of an alternative approach using the balance principle. The balance principle is easier to teach, to understand, and to apply in more complex situations. It better prepares students to understand the derivation of the partial differential equations of fluid mechanics and the finite volume equations of computational fluid dynamics. For these reasons, instructors should consider using the balance principle instead of (or at minimum in addition to) the Reynolds transport theorem in introductory fluid mechanics courses.