We were discussing various basic concepts of
thermodynamics in our previous post such as

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Today we will see here very important topic i.e.
Mass balance and energy balance for a steady flow process with the help of this
post.

We will use few important terms such as control volume
and also steady flow device in this post, hence let us see here first brief
introduction of control volume and steady flow system and after that we will
see here the mass balance and energy balance for steady flow process.

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**Let
us see here control volume system**

As we have already discussed that control volume is
basically defined as one fixed area upon which the study will be focused and
mass or matter will enter and leave the system continuously. Control volume
system will interact with its surrounding in terms of heat energy and work
energy.

For more detail about control volume system, please
refer the post “

*Control volume system in thermodynamics*”.###
**Similarly,
let us see here brief introduction of steady flow process or steady flow system**

Steady flow process is basically a process where
fluid is flowing through a control volume and thermodynamic properties of fluid
remains constant with respect to time while thermodynamic properties of fluid
may vary with respect to space coordinates. We can say in simple way that mass
and energy of the system throughout the control volume will be remaining
constant with respect to time.

For more detail about steady flow system, please
refer the post “

*Steady flow process in thermodynamics*”.###
**Let
us see now mass balance for a steady flow system**

Let we have one steady flow system as shown in
following figure, we can see here that one stream of fluid is entering in to
the control volume and one stream of fluid is leaving the control volume and
there will not be any accumulation of energy within the control volume system.

*Steady flow process*

As we have assumed here that this is a basically steady
flow system and therefore thermodynamic properties of fluid entering and
leaving the control volume will be constant with respect to time.

Let section 1-1 is entrance section of control
volume and fluid is entering to the control volume system from here and
similarly section 2-2 is exit section of control volume and fluid is leaving
the control volume system from here as shown in figure.

Let Q is the heat energy provided by the surrounding
to the system and work energy W is provided by the system to surrounding.

###
**Mass
balance for steady flow process**

For steady flow process, net quantity of mass
contained within the system will never change with respect to time and
therefore according to the principle of conservation of mass, we will have
following statement for mass balance for a steady flow process.

Net quantity of mass entering to the control volume
= Net quantity of mass leaving the control volume

Or we can also say that mass flow rate entering to
the control volume will must be equal to the mass flow rate leaving the control
volume and hence we will have following equation of mass balance for a steady
flow process.

Mass flow rate entering to the control volume = Mass
flow rate leaving the control volume

*ρ*_{1}V_{1}A_{1}= ρ_{2}V_{2}A_{2}
Above equation of mass balance for a steady flow process
is also termed as equation of continuity.

Where, V

_{1}and A_{1}are the velocity and area of cross section of stream respectively at section 1-1 of control volume system. Similarly, V_{2}and A_{2}are the velocity and area of cross section of stream respectively at section 2-2 of control volume system.###
**Let
us see now the energy balance for a steady flow process**

For steady flow process, net quantity of energy
contained within the system will never change with respect to time and
therefore according to the principle of conservation of energy, we will have
following statement for energy balance for a steady flow process.

Net quantity of energy entering to the control volume
= Net quantity of energy leaving the control volume

Rate of net energy entering to the control volume = Rate
of net energy leaving the control volume

Where, H

_{1}and H_{2}are enthalpy and Z_{1}and Z_{2}are the distance of entrance and exit section of control volume from datum line as shown in figure.
Above equation is termed as energy balance equation
for a steady flow process or we can also say this energy balance equation as
steady flow energy equation.

We will see another topic i.e. "

We will see another topic i.e. "

*Equivalence of Kelvin Planck statement and Clausius statement*" in our next post in the category of thermal engineering.
Do you have any suggestions? Please write in comment
box.

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**Reference**

Engineering thermodynamics by P.K Nag

Image Courtesy: Google

###

What is Carnot cycle and its efficiency?

First law of thermodynamics for a closed system undergoing a change of state

What is internal energy in thermodynamics?

What is heat pump in thermodynamics?

What is enthalpy in thermodynamics?

Displacement work or PdV work in thermodynamics

Difference between microscopic and macroscopic approach in thermodynamics

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**Also Read**

What is Carnot cycle and its efficiency?First law of thermodynamics for a closed system undergoing a change of state

What is internal energy in thermodynamics?

What is heat pump in thermodynamics?

What is enthalpy in thermodynamics?

Displacement work or PdV work in thermodynamics

Difference between microscopic and macroscopic approach in thermodynamics

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