18.4 : Linear Momentum in Control Volume

Newton's second law is applied to obtain the linear momentum in a control volume in a fluid system. According to this law, the rate of change of linear momentum is equal to the sum of external forces acting on the system. When a control volume matches the fluid system at a specific moment, the forces acting on both are identical. Reynolds transport theorem helps explain this by breaking down the system's linear momentum into two components: the rate of change of linear momentum within the control volume and the net flow of linear momentum across the control surface.

As mass moves in and out of the control volume, it carries linear momentum with it, making the transfer of momentum analogous to the flow of mass. For control volumes that are fixed, nondeforming, and stationary, Newton's second law provides an accurate representation of the system's dynamics. It accounts for internal changes in momentum as well as the momentum flowing across the boundaries of the control surface. This theoretical framework is essential in fluid dynamics for analyzing forces, motion, and interactions within well-defined regions of flow, making it applicable to a wide range of engineering problems.