# unit_6 - Engi2800(Section I Engineering Thermodynamics I...

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10/05/09 http://jjl.me.dal.ca/Engi2800 1 J.M. Chuang Dalhousie University Dept. of Mechanical Engineering Last Modified: October 5, 2009 Unit #6 ( Textbook Reference: Ch.6 ) First-Law Analysis for a Control Volume Engi2800 (Section I) Engineering Thermodynamics I

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10/05/09 http://jjl.me.dal.ca/Engi2800 2 Contents Control Volume (Open System) Conservation of Energy for a CV Flow Work Steady Flow Process Application of Steady-Flow Energy Equation Procedure of Using Steady-Flow Energy Equation Thermodynamic Devices Nozzle Diffuser Turbine Compressor Throttling Valve Mixing Chamber Heat Exchanger Pipe and Duct Flow Unsteady Flow Process Energy Equation for Unsteady Flow Process
10/05/09 http://jjl.me.dal.ca/Engi2800 3 Control Volume (Open System) (1) Control Volume (CV), a.k.a. Open System: CV is an arbitrary volume in space of interest for a particular study. CV may move in space, and change its shape and size, CV may move in space. (but our focus is mostly on fixed shape and location). Mass may enter or leave an CV. Control Surface (CS): the boundary of CV CS can be comprised of actual solid an/or imaginary (virtual) surfaces. Two concepts: Steady: No change in time. Uniform: No change with location. Pipe flow CV CS CS CS Pipe flow Pipe flow Non-uniform Uniform CS

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10/05/09 http://jjl.me.dal.ca/Engi2800 4 Control Volume (Open System) (2) Conservation of mass: Mass is neither destroyed nor created; mass is conserved except in nuclear reactions. Energy and mass are related by but, in non-nuclear reactions, the impact of this relationship is negligible. See section 5.9, p.156. in the textbook to verify that this is indeed the case. Conservation of mass for an open system If If If e = mc 2 Total mass entering CV Total mass leaving CV Net change of mass in CV + CV inlet outlet CS ¡ = = ¢ m CV X m in X m out X m in > X m out ¡! ¢ m CV is (+) = ) m CV Increase X m in < X m out ¡! ¢ m CV is ( ¡ ) = ) m CV Decrease X m in = X m out ¡! ¢ m CV is zero = ) m CV Remain Constant Imaginary Boundary Control Volume
10/05/09 http://jjl.me.dal.ca/Engi2800 5 Control Volume (Open System) (3) Mass flow rate, Consider mass flow flowing through a cross section per unit time Mass flow through elemental area Mass flow through cross section Usually, , it follows that where _ m = dm dt V n A Average normal velocity V n = ~ V ¢ ~n = j ~ V jj ~n j cos µ ~n ~n µ Through an imaginary surface dA ~ V dA A ½ = const _ m = Z A ½ ~ V ¢ ~ndA = Z A ½V n dA _ m = Z A ½ ~ V ¢ ~ndA = Z A ½V n dA = ½ Z A V n dA = ½V ave A V ave = 1 A Z A V n dA d _ m = ½ ~ V ¢ ~n dA = ½V n dA Velocity component normal to A

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10/05/09 http://jjl.me.dal.ca/Engi2800 6 Control Volume (Open System) (4) Volume flow rate:
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unit_6 - Engi2800(Section I Engineering Thermodynamics I...

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