## Lecture 2: The One-Fluid Formulation

1. The governing equations for the isothermal flow of two immiscible fluids are derived using:
The conservation of momentum and energy
The conservation of momentum and mass
The conservation of mass and energy
The conservation of mass, momentum and energy
None of the above

2. In general, the conservation of mass equation states that
Density increases if the flow is compressed
Density decreases if the flow is compressed
Density increases if the flow is expanded
Density of a material particle remains constant
None of the above

3. Incompressibility requires that
Volume is conserved
The density of a material particle is constant
The convective derivative of the density is zero
All of the above
None of the above

4. For incompressible flows the pressure
Is a function of two thermodynamic variables
Is always positive
Is whatever it takes to make the flow incompressible
Is found once the velocity has been determined
None of the above

5. The conservation of momentum says that for a control volume fixed in space
Inflow of momentum must be equal to outflow of momentum
The rate of change of momentum is equal to the body forces
The rate of change of momentum is equal to the net influx of momentum plus body and surface forces
Only surface forces increase the momentum
None of the above

6. For two-dimensional flow the force on a finite length surface element is given by
Curvature times the length of the surface element
The pull on one end of the element minus the pull on the other end
The curvature times the normal vector
The normal vector times the area
None of the above

7. The surface tension for an interface separating immiscible fluid
Depends on the curvature of the interface
Depends on the curvature of the interface times the normal vector
Is always constant
Keeps the interface length constant
None of the above

8. The motion of the marker function identifying different fluids
Is governed by the mass conservation equation
Is governed by an advection equation
Is governed by a wave equation
Is governed by a diffusion equation
None of the above

9. The one fluid formulation, where a single set of equations is used for two fluids separated by a sharp interface, is
Only valid for incompressible flows
Only holds for inviscid flows
Requires extra equations for the singular forces at the interface
Equal to writing separate equations for each fluid with the appropriate boundary conditions
None of the above

10. Simulations of immiscible multifluid flows with a sharp interface:
Require the use of moving grids
Require the interface to be aligned with a grid line
Require the use of an unstructured grid.
Can be done using stationary structured grids
None of the above