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# Mass flow rate - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Mass flow rate' - elita

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Presentation Transcript

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)

CAN BE NEGLECTED

• Therefore, these properties can be given representative average values at inlets and outlets.

The natural laws1-D flow approximation

• Approx 2. 1-D flow approximation: The flow velocity at the inlets and outlets has only a single component normal to the respective areas.

• Therefore, mass flow rate can be calculated by

### Deriving the laws of conservation of mass and energy for an open system starting from the laws expressed for a closed system

Mass of the closed open system starting from the laws expressed for a closed systemsystem as CV :

End

For “rate processes” dividing both sides by t and letting t0

Begin

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V

For “large processes” integrating both sides

+

Conservation of mass for open systems

Consider a “small process”

=

For the closed system open system starting from the laws expressed for a closed system[small process “green to red”] :

End

Begin

Note: uniform property

approximation at inlets/outlets

is used here

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V

+

First Law of Thermodynamics for open systems

where

End open system starting from the laws expressed for a closed system

Begin

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V

+

Splitting work into flow and non-flow work

Flow 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.

Note: open system starting from the laws expressed for a closed system

End

Begin

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V

+

Flow work

For the closed system open system starting from the laws expressed for a closed system(going from green to red)

End

Begin

-

V

+

First Law of Thermodynamics for open systems

Inserting expression for flow work open system starting from the laws expressed for a closed system

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 t0

First Law of Thermodynamics

Recall enthalpy

defn.:

h=u+pv