Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 66

The momentum equation is based on Newton's second law applied to a mechanical system, which states that the sum of all forces acting on the system is equal to the time rate of change of linear momentum of the system. In fluid mechanics problems, the same principle can be applied to a CV, having some bounding surfaces, CS, permeable to fluid:

(3.43)

The derivation of Eq. (3.43) can be found in basic fluid mechanics textbooks, such as [15]. The expression states that the sum of the forces acting on the CV is equal to the rate of change of momentum inside the CV (first term at the second member) added to the net rate at which momentum is leaving the CV through the CS (last term in the equation). The forces acting on CV can be of different nature: surface forces, , acting on the control surface, and body forces , acts throughout the volume. The surface forces are those related to fluid pressure and frictional effects, while the only body forces usually taken into consideration is gravity.

The above momentum equation is very useful to study the interaction between the fluid and the surrounding solid surfaces. In fluid power systems, the momentum equation is typically used to determine the force applied by the fluid in a piping system. The following problem provides a representative example.