In hydrostatics, such volumes are motionless and their enclosing surfaces are impervious to the movement of fluid. We find the total force acting on the fluid in the volume by visualizing the fluid as a rigid body filling the volume. We will find that the concept of defining a volume of fluid in a flow field, surrounded by an imaginary enclosing surface, is extremely useful in fluid mechanics. We call such a volume a control volume and its surrounding surface a control surface . In this book, we will use only control volumes and their surfaces that are fixed in the reference frame of the flow field.
Control volumes fixed in space are the natural choice in an Eulerian flow description.
Control volumes and surfaces can be very useful in applying the laws of conservation of mass, momentum and energy to fluid flows. In many applications, there is incomplete information regarding the entire flow field but sufficient information about the fluid flow at the control surface to enable us to find total forces and moments on structures and the quantities of heat and work involved, as well as other useful information. The expressions of the physical laws governing fluid flow in integral form utilize control volumes and surfaces.