Discussion Overview
The discussion centers around the Navier-Stokes equation for compressible flow, specifically whether it is expressed in the context of a control volume or a material volume. Participants explore the implications of the equation's integral form and its relation to conservative and non-conservative equations.
Discussion Character
- Homework-related
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants propose that the Navier-Stokes equation is written for a control volume due to its integral form and the expression of fluxes out of a cube, relating to conservation of momentum.
- Others express uncertainty, noting that integral forms of non-conservative equations also exist, which complicates the classification.
- One participant suggests that the first term on the right-hand side of the equation would not be present in the material volume form, arguing that no fluid enters or leaves a material volume, leading to its disappearance.
- Another participant asserts that the integral form for material volume is the same as for control volume, except that the first term on the right-hand side is absent, while the differential forms for both are identical.
- References to external resources, such as the Reynolds transport theorem, are made to support claims about the relationship between integral and differential forms.
Areas of Agreement / Disagreement
Participants express differing views on the presence of terms in the material volume form versus the control volume form, indicating that multiple competing views remain without a clear consensus.
Contextual Notes
Participants reference the integral and differential forms of the equations, but there is no resolution on the implications of these forms regarding conservativeness or non-conservativeness. The discussion also highlights the complexity of the topic, with assumptions about fluid behavior in different volume contexts remaining unresolved.