# Are conservation of mass and conservation of energy *independent* constraints for physical systems?

I'm modeling fluid systems and want to use conservation of mass (aka 'continuity') and conservation of energy as constraints to help solve for certain system parameters. But it occurred to me that the two constraints may not be independent and may make parameter identification difficult.

Are the two constraints always independent? If not does independence depend on the structure of the system?

My thoughts, fluid systems are almost always nonlinear. And if I'm not mistaken nonlinearity often invokes dependence.

• For some systems they are superfluous. For example, in library elasticity you don't need to use conservation of energy or mass. – nicoguaro Jun 13 at 0:53
• I am not sure what you are trying to solve exactly -- under some constraints, fluid systems will decouple the energy equation from the rest of the system (low Mach numbers for example). In others, they are tightly coupled because large internal energy changes can lead to large density changes and vice-versa. What kinds of systems are you interested in? – tpg2114 Jun 13 at 1:47
• Another important point when it comes to actually writing code to solve a model -- generality in equations can greatly reduce accuracy under limiting conditions. I'm happy to help point you in the right direction if you can give some more info on what kinds of systems you are looking at. – tpg2114 Jun 13 at 1:49
• Docscience, the two constraints you mentioned should be independent of each other. If you could give more details, it would be easier to be certain of this. – David White Jun 13 at 2:47
• If we use the equation of state in the form $p=p(\rho)$ then the energy equation can be integrated independently. – Alex Trounev Jun 13 at 3:20