Mass flow rate. Useful approximations to get simple algebraic forms for the natural laws. Across the INLETS AND OUTLETS of the CV: APPROX 1. Uniform property approximation: The variation of system properties (such as density, specific kinetic/potential/internal/total energy)
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Across the INLETS AND OUTLETS of the CV:
CAN BE NEGLECTED
Mass of the closed system as CV :
End
For “rate processes” dividing both sides by t and letting t0
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V
For “large processes” integrating both sides
+
Conservation of mass for open systemsConsider a “small process”
=
For the closed system [small process “green to red”] :
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Note: uniform property
approximation at inlets/outlets
is used here

V
+
First Law of Thermodynamics for open systemswhere
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V
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Splitting work into flow and nonflow workFlow work: work done at the inlets/outlets due to fluid
flowing in/out against pressure forces. At outlets, work
is done by the system on the surroundings. At inlets,
work is done by the surroundings on the system.
=Work other than flow work such as shaft work,
electric work, boundary displacement work.
For the closed system (going from green to red)
End
Begin

V
+
First Law of Thermodynamics for open systems
Inserting expression for flow work
and regrouping terms
For large processes provided all inlet/outlet conditions are steady (not changing with time) integrate both sides
For rate processes dividing both sides by t and letting t0
First Law of ThermodynamicsRecall enthalpy
defn.:
h=u+pv