THERMODYNAMICS  THEORY



Mass and Volume Flow Rate

Mass Flow Rate Through a Duct 

The mass flow rate ()
is defined as the amount of mass flowing through a crosssection per
unit time. The mass flow rate of a fluid flowing in
or out of a pipe or duct is proportional to the crosssectional area
(A) of the pipe or duct, the density of the fluid (ρ),
and the velocity of the flow (V). The flow rate through a differential
area dA is:
d = ρV_{n}dA
where
V_{n} = the velocity component normal
to the area dA 



Normal Velocity Component 

Integrating the above equation to get the
total mass flow rate.
The volume flow rate ()
is the volume of the fluid flowing through a crosssectional area per
unit
time.
The mass and volume flow rate are related by






Conservation of Mass Principle

System Used for
Conservation of Mass Equation


The conservation of mass principle states
the following:
Net mass transfer to or from a system during
a process is equal to the net change in the total mass of the system
during that process. 
In an equation format, the conservation of mass principle is:
(Total mass entering the system)

(Total mass leaving the system)
=
(Net change in mass within the system)




Filling and Emptying Bathtub is an
Example of Mass Conservation 

or,
m_{in } m_{out} = Δm_{system}
where
Δm_{system} = m_{system@final} 
m_{system@initial}
The rate form of the conservation of mass principle is:
(Rate at which mass entering the system)

(Rate at which mass leaving the system)
=
(time rate of change in mass within the system)
or,






Conservation of Mass for Closed System

Mass Remains Constant for a
Closed System


A closed system is defined as a system which mass can
not cross its boundaries, but energy transfer is allowed. Since no mass
flows in or out of the system, the mass of the closed system remains
constant during a process.



