This video is going to go through a quick review of the idea using a control volume
Vs having a system.
When we are talking about fluid flow with a conceptual example of this.
Something everyone experiences and relies on their daily business is there blood flow.
So here we have a great picture of a particular artery, and we want to take a fluid for both
Eulerian and Lagrangian perspectives, and characterize how that fluid or that blood
is going to move through that artery.
Now a Eulerian approach would be to pretend you were sitting right here at this intersection,
and look at a particular point, and characterize how the fluid moves through that point.
Basically, therefore a function of position with time.
Now in contrast a Lagrangian approach would be to take a certain set of fluid particles
and track how each one individually flows from start to finish.
Similarly if we wanted to model the fluid flow and say the drug transport through the
blood stream.
We can take a collection of those particles and analysis the fluid flow from start to
wherever it desperate, and by doing so we would be looking at that particular system
of that drug.
The system would be tracked together regardless what happens to the shape or where it goes.
Maybe for instants we are really interested in a particular part of an artery, and what
happens to that as fluid flows past it.
So maybe we wanted to look at just certain area within that artery.
This approach we would say we are looking at a control volume.
This allows us to specifically focus on the effects on the fluid in that particular volume,
which is what we are typically most interested in anyways.
Now the problem arises in that most laws we use in fluids and thermodynamics for the system.
For example the mass must remain constant.
In system approaches it is a very much a Lagrangian system.
So using a control volume is very much a Eulerian approach.
So why is a control volume approach more the analysis for a fluid in motion?
In most cases.
It is a.
difficult to follow a deforming fluids.
You can imagine a system of particles flowing through an artery and having to track each
individual one as it branches and goes to multiple places, and what we are usually interested
in the effects of fluids with devices, such as a pump.
So we want to us a control volume approach in a Eulerian flow description and therefore
need to determine a relationship with governing laws to the systems.
Such a relationship is made using the Re transport Theorem.
This will be described in a later screencast.
So lets quickly review the concept of control volume and systems by going though a concept
test.
So here we have a depiction of a fire extinguisher and we are told that the control volume is
that inside of the extinguisher tank.
So the question is what is happening with the control volume mass.
If we track the mass in the tank to start and what happens to it with time and where
it goes.
That is a systems approach, but here we are just looking at a control volume.
So all though we know mass is conserved the mass within this control volume is decreasing
as it comes out of the extinguisher.
Now on the contrary if we would have said what has happened to the system of mass, and
we weren't told what the control volume was, and we were just looking at the gas initially
here as our system.
We know that the mass of that system is not going to change with time, and we would have
said constant.
So hopefully this gives you an idea of why we might want to look at control volumes and
yet still find a way to use the governing laws of your system when we do this analysis.