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Mass flow rate

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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Mass flow rate

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  1. Mass flow rate

  2. 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.

  3. 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

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

  5. 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” =

  6. 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

  7. 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.

  8. Note: End Begin - V + Flow work

  9. For the closed system (going from green to red) End Begin - V + First Law of Thermodynamics for open systems

  10. 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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