Chapter 7. Applications to Flow Processes-student

Chapter 7. Applications to Flow Processes-student - Chapter...

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Chapter 7 Applications of Thermodynamics to Flow Processes The discipline: “Fluid mechanics” and “Thermodynamics” Example-1: If the states and thermodynamic properties at entrance and exit are known, first law and second low can be used for calculating the exchange between the system and surrounding, but the details in the pipe is unknown Example-2: If some states and thermodynamic properties at entrance and exit are not known, can we calculate them at the exit by knowing some thermodynamic and fluidynamics properties in the pipe? Some differences between open and closed systems Flow process results from pressure gradients within the fluid. Moreover, temperature, velocity, and even concentration gradients may exist within the flowing fluid. Possible solutions An equation of state applied locally and instantaneously at any point in a fluid system.
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Useful Equations
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Duct flow of compressible fluids Consider an adiabatic, steady-state, one dimensional flow of a compressible fluid in the absence of shaft work and no change in potential energy S W Q z g u H + = + + 2 2 0 2 2 = + u H
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Duct flow of compressible fluids P P P S T T V S V = If we consider the specific volume of the fluid is a function of S and P : V = V(S,P) P P P S T T V S V = Also
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Pipe flow: If the flow is steady-state adiabatic flow of compressible fluids, constant cross-section A For subsonic flow, the maximum fluid velocity obtained in a pipe of constant cross section is the speed of sound, and this value is reached at the exit of the pipe. The lengthening of the pipe does not change the result. 0 1 1 1 2 2 2 2 - + - + - A u TdS C u udu P M M M β ( 29 0 1 1 2 2 2 - + + - A u TdS C u VdP P M dx dS C u T dx du u P - + = 2 2 2 1 M M dx dS C u V T dx dP P - + - = 2 2 1 1 M From (7.9) and (7.10) Rearrange Rearrange
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Dense (high P) and slow (low u) Low pressure and fast (big u) Steady flow: The total flow rate Steady-state adiabatic flow of compressible fluids, constant cross-section A m (mass/s) is the same for inlet and outlet
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This note was uploaded on 05/01/2011 for the course CHBE 2110 taught by Professor Gallivan during the Spring '08 term at Georgia Tech.

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Chapter 7. Applications to Flow Processes-student - Chapter...

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