C8_Isothermal_Macroscopic_Balances

C8_Isothermal_Macroscopic_Balances - Macroscopic Balances...

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Unformatted text preview: Macroscopic Balances for Isothermal Systems Macroscopic systems Microscopic balances over a fluid element Inlet (plane 1) Outlet (plane2) Macroscopic balance over the entire system Common flow problems- Time of draining/filling- Average velocity and mass flow rate at the inlet(s) and outlet(s)- Fluid pressure at the inlet(s) and outlet(s)- Viscous and pressure forces exerted by a fluid on fixed boundaries- Works by pressure and viscous forces done on moving boundaries- Viscous loss (part of kinetic energy lost due to viscous friction) Macroscopic Balances for Isothermal Systems Macroscopic systems A method for solving the flow problems Writing and solving- The equation of macroscopic mass balance- The equation of macroscopic momentum balance- The equation of macroscopic mechanical energy balance Common assumptions (used through all derivations and problems below)- Uniform pressure and fluid properties (e.g., density and viscosity) over the inlet(s) and outlet(s) cross sections- Velocities at the inlet(s) and outlet(s) cross sections are taken as average velocities (i.e., velocity averaged over time AND cross section)- Insignificant viscous stresses at the inlet(s) and outlet(s)- Fluid flow could be represented by streamlines. In other words, there always exists an representative streamline connecting an inlet and an outlet Inlet (plane 1) Outlet (plane 2) Macroscopic Balances for Isothermal Systems Macroscopic mass balance z=0 z=L Macroscopic mass balance equation ( ) ( ) in out tot in out w w d m u S u S dt = An example Total mass at time t in the sphere 2 1 1 3 tot h m Rh R = Mass flow rate at plane 2 (quasi-steady state) ( ) ( ) ( ) ( ) ( ) 4 2 4 4 128 128 128 L z z L P P D w L p z g p z g D gh gL D L L = = = + = = Macroscopic Balances for Isothermal Systems z=0 z=L ( ) ( ) ( ) ( ) ( ) ( ) 4 2 4 2 2 where 1 1 3 128 2 128 2 2 2 1 1 2 ln 1 2 efflux C t L R L efflux gh gL D d h Rh dt R L h R h dh gD h L dt L H R L H L dH C H h L H dt H R L H L dH C dt H L R R R R t C L L L L + + = = + + = = + + =...
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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C8_Isothermal_Macroscopic_Balances - Macroscopic Balances...

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