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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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Presentation Transcript
useful approximations to get simple algebraic forms for the natural laws
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)

CAN BE NEGLECTED

  • Therefore, these properties can be given representative average values at inlets and outlets.
the 1 d flow approximation
The 1-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
slide5

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

conservation of mass for open systems

Mass of the closed system as CV :

End

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

Begin

-

V

For “large processes” integrating both sides

+

Conservation of mass for open systems

Consider a “small process”

=

first law of thermodynamics for open systems

For the closed system [small process “green to red”] :

End

Begin

Note: uniform property

approximation at inlets/outlets

is used here

-

V

+

First Law of Thermodynamics for open systems

where

splitting work into flow and non flow work

End

Begin

-

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.

flow work

Note:

End

Begin

-

V

+

Flow work
slide10

For the closed system (going from green to red)

End

Begin

-

V

+

First Law of Thermodynamics for open systems

first law of thermodynamics

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 t0

First Law of Thermodynamics

Recall enthalpy

defn.:

h=u+pv

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