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Open and Closed Systems

In Chapter 4 we studied closed systems in which no mass crossed the system boundaries.
In this chapter we will be considering

open systems

For closed systems we considered a control mass.
The mass remains constant throughout the process.

Thus

Closed
System

For open systems we consider a

.
The mass does not necessarily remain constant.

Thus, we must keep track of the mass flow rate in,

, and the mass flow rate out,

, of the control volume .

Open
System

Lesson 5A: page 1 of 6

In chapter 4, we used the conservation of mass principle to write mass balance equations on closed systems.
In this lesson we will apply the conservation of mass principle to open systems.
Recall that mass crosses the boundary of open systems.
In an integral mass balance, mass crossing a system boundary is expressed as an amount.
For example during a process 32 kg of water entered a system.
In this course, however, a differential mass balance is more common.
A differential mass balance is used when mass flows continuously across the system boundary.
For example, watered entered that system at a RATE of 12 kg/min during a process.
The symbol for a mass flow rate is an m with a dot over it and I will sometimes call this symbol m-dot
Systems can also have mass leaving the system during a process as well.
In that case, we can use the subscripts in and out on the symbol m-dot, so we don’t get the two streams confused.
Now, let’s write the two different kinds of mass balance equations: integral and differential.