On the Momentum Theorem for a Continuous System of Variable Mass

Abstract

Theorems of linear momentum are derived for a control system having an arbitrary motion in a continuous velocity field. The resulting equations are valid for a system of variable mass. By allowing the control system to be at rest, the usual equations of fluid mechanics are obtained as a special case; by allowing the control system to move with the fluid, the momentum equations for a system of constant mass are obtained as a special case. In this way, it is possible to discuss a common, but incorrect, conception of the momentum equation for a system of variable mass.