Control Volumes and Systems

You can analyze a fluid a few different ways.  For example you can use control volumes and systems.  However, before I start talking about control volumes and systems, let’s recall what a fluid is.  A fluid is a type of matter that is either a liquid or a gas.  It has the ability to be free moving while being able to interact with its surroundings.  Now since a fluid is free moving you will need to use different techniques to analyze it than you would use for a solid.


First, let’s discuss system.  A system is a collection of matter that has a fixed identity.  This means that there will always be the same number of fluid particles or atoms..  These fluid particles in turn could move, flow, and interacts with the surroundings.

There are many example that you could consider a system.  However, it must have an identifiable quantity of matter.  In turn, a system can be very large, like the earths atmosphere, or very small to the point that you are analyzing a single fluid particle.  Also, as stated above a system can interact with its surrounding in a variety of ways.  To name a couple, a system could transmit heat or exert a force onto its surroundings. What ever it is doing you must be able to “tag” the molecules within in the system so that you can keep track of how the move through out the system.  This could be by physically tagging molecules, or just keeping track of them in your mind.

For example, a compressor is an example of a system.  As it operates a certain amount of air will enter the compressor.  Also, as air enters the compressor the air will be compressed. This will result in the temperature of the air will changing. In addition pressure will also be exerted onto the walls of the compressor.  But what makes this a system is you will be able to track how much air is inside the compressor.

Control Volumes

A control volume, unlike a system, is volume in space that you define and that fluid will flow through.  As a result it is independent of mass.  In turn an area of interest will isolated from the surrounding environment.  It does this by replacing the surrounding environment with the equivalent forces.  In essence a control volume is equivalent to free body diagrams that are used in Statics and Dynamics.  It also allows the ability for the matter within the control volume to change with time, instead of having to keep track of it as you would with a system.

It can be very difficult to identify and keep track of a specific amount of fluid matter.  This is because even if you have a finite quantity of fluid, there is an uncountable number of fluid particle that are able to move about freely.  This defers from a solid, since the particles that make up a solid are easy to keep track of since they can’t move freely.  For example let’s take a look at a river.  You can not easily track a water particle moving along with a river. On the other hand you can easily track a branch floating on the surface of the river.

There are different type of control volumes.  You can have a stationary control volume.  A stationary control volume is fixed in space.  As a result it will only analyze fluid pass through that volume of space.  Another type of control volume is a moving control volume.  A moving control volume will move along with an object, such as a plane, to analyze the fluid that is interacting with the object of interest.  Finally,  you can also have a deforming control volume.  This means that the size of the control volume changes with time based off the object that is being analyzed.  For example if you were analyzing the air flowing out of a balloon, you would use a deforming control volume that will change with size of the balloon.


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