6.1. Derivation of the Linear Momentum Equation. Consider a fluid mass contained in a closed (control) surface S at an instant of time t. After a small time interval dt, t dt the fluid mass is moved and has the surface S\' at t dt in Fig. (6.1) . ? Fig. 6.1. The intersection of S and S\' divides the both partial surface S1 and S2. V1 is the fluid volume moved during the small time interval dt from S1 towards S\' and V3 that from S2 towards S\'.