Conservation of mass

Definition

Conservation of mass is a fundamental principle stating that mass cannot be created or destroyed in an isolated system. This principle is crucial in fluid dynamics, as it helps to understand how mass flows through different regions and the relationships between various properties of fluids under different conditions.

5 Must Know Facts For Your Next Test

1. The conservation of mass applies to both compressible and incompressible fluid flows, though the equations used to describe them differ.
2. In an incompressible flow, the density remains constant, making it easier to apply the conservation of mass through the continuity equation.
3. For compressible flows, variations in density must be accounted for, making the conservation of mass more complex and requiring adjustments based on changes in pressure and temperature.
4. The principle is fundamental in deriving other important equations in fluid dynamics, such as the Navier-Stokes equations.
5. In real-world applications, conservation of mass helps in designing efficient systems like pipelines, airfoils, and engines by predicting how fluids will behave under different conditions.

Review Questions

• How does the concept of conservation of mass relate to the differences between Eulerian and Lagrangian descriptions of fluid motion?
  • In Eulerian descriptions, conservation of mass focuses on specific locations in space as fluid flows past them, emphasizing how mass enters and exits a control volume over time. In contrast, Lagrangian descriptions track individual fluid particles as they move through space and time, highlighting how each particle's mass is conserved along its path. Both approaches rely on the principle that the total mass within a defined system remains constant, reinforcing the idea that mass can neither be created nor destroyed.
• Discuss how streamlines, pathlines, and streaklines illustrate the application of conservation of mass in fluid dynamics.
  • Streamlines represent instantaneous flow patterns at a given moment and are closely tied to conservation of mass since they show the direction fluid elements are moving. Pathlines depict the trajectory of individual particles over time, reflecting how their motion adheres to mass conservation principles. Streaklines show the positions of particles released from a point source over time. Together, these visualizations help clarify how fluid mass is conserved within different flow scenarios while providing insights into velocity fields and changes in density.
• Evaluate the implications of conservation of mass for normal and oblique shock waves in compressible flows.
  • In normal and oblique shock waves, conservation of mass plays a critical role in understanding changes in fluid properties as supersonic flows transition to subsonic states. During these shock processes, while mass is conserved overall, there is an abrupt change in density, pressure, and velocity across the shock front. Evaluating these changes requires applying conservation principles along with other relationships like momentum and energy conservation. The interplay between these principles allows for predictions about how fluids behave during shocks and informs designs for supersonic vehicles.

Related terms

Continuity equation: A mathematical expression that describes the conservation of mass in a fluid flow, indicating that the mass flow rate must remain constant from one cross-section of a flow to another.

Fluid flow: The movement of liquid or gas from one location to another, which can be affected by various factors such as pressure, temperature, and velocity.

Density:

The mass per unit volume of a substance, which plays a vital role in determining how fluids behave and interact under different conditions.