Final answer:
The stream function satisfies the conservation of mass in the field of fluid dynamics because it accurately describes the flow of an incompressible fluid without violating mass conservation, which is demonstrated by the continuity equation that the stream function inherently satisfies.
Step-by-step explanation:
Yes, the stream function satisfies the conservation of mass in fluid dynamics within an incompressible fluid. The stream function is a mathematical construct used to describe the motion of a fluid without having to directly solve the entire velocity field. It automatically satisfies the continuity equation, which is the mathematical expression of the conservation of mass for fluids. Since the stream function relates to the velocity components in a way that inherently accounts for the incompressibility condition (divergence of velocity is zero), the mass within any stream tube (imaginary tube formed by streamlines) remains constant over time, showcasing the conservation of mass.
For example, consider a closed system where no mass is allowed to enter or leave. The total mass within this system must remain constant. When using a stream function to analyze the flow within this system, by definition, the flux of fluid through any closed boundary in the flow field will be zero, indicating that the mass within that boundary is not changing over time, hence conserving mass.