Lecture 9 Conservation of Mass and Energy

# Lecture 9 Conservation of Mass and Energy - Thermal and...

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Lecture 9 –Conservation Principles in Open Systems Open and Closed Systems Open System – mass crosses boundary Closed System – no mass crosses boundary Compression stroke Exhaust stroke Closed system Open system Conservation of Mass – Open System Lecture 9 Page 1

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski total total net change of mass entering mass leaving mass in cv ⎛⎞ −= ⎜⎟ ⎝⎠ i e system mmm ∑∑ For flowing streams n V – normal velocity Critical notation: m – mass which enters cv in time t V – volume V – volume of m – velocity v – specific volume mV ρ ∆=∆ Vx ∆= ∆∆ A n x t = n Vt ∆= ∆ A n mt A Lecture 9 Page 2
Thermal and Fluids Engineering I Prof. Deborah A. Kaminski n m A t ρ =∆ V In the limit as 0 t ∆→ n dm md dt == ± A m ± – mass flow rate kg s For flow over a finite area, assuming does not vary over the area nn Ad ∫∫ ± VV A A avg m = ± where avg is average velocity real, turbulent flow approximate flow Now focus on the volume of fluid entering the cv n Vt ∆= ∆ A n V A t as 0 t n V ± A where V is volumetric flow rate, ± 3

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Lecture 9 Conservation of Mass and Energy - Thermal and...

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