Mass and Volume Conservation Flashcards
What are the two approaches when studying fluids?
- Lagrangian
- Eulerian
What is the Lagrangian approach?
Small elements (‘particles’) of fluid within the flow are followed for all time (cf. dynamics)
When is the Lagrangian approach useful?
Useful approach when
* One particle sufficient to describe the entire flow field
* All particles move together, e.g. rigid body motion
* When particles are few (non-continuum).
When is the Lagrangian approach not useful?
- Need to follow many particles
- Non-conservative Forces
- Dissipative Systems
What is the Eulerian approach?
The Eulerian Description is one in which a control volume is defined, within which fluid flow properties of interest are expressed as fields - provides a bulk description
What does mass conservation place restrictions on?
On the velocity field
What is mass conservation?
Mass flux in = Mass flux out
When is volume conserved?
When fluid density is constant
When does the volume conservation hold?
When the fluid volume in the control volume does not change with time.
What is the general equation for conservation?
Storage = fluxes in - fluxes out + sources - sinks
What is the equation for unsteady continuity?
dV/dt = Qin-Qout
What changes for fluids with free surface?
For fluids with a free surface, the fluid volume inside a CV can change with time
What happens when there is a net flux into the CV?
The water level will increase linearly
What is mass conservation?
Sum of masses
What happens when the fluid volume in the CV is constant?
The time derivative is zero and an algebraic relation between the volume fluxes is obtained
