Lecture_7_notes - Chemical Engineering 374 Fluid Mechanics...

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1 1 Chemical Engineering 374 Fluid Mechanics Fall 2011 Integral Energy Balance In this house, we obey the laws of thermodynamics! Homer Simpson 2
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2 Integral Energy Balance • Recall, we are writing balance equations. – Fluid Statics (no flow) – Mass Balance (last time) – Energy Balance (today) – Momentum Balance (later) 3 Reynolds Transport Theorem dB sys dt = d dt CV ρ bdV + CS ρ b v · ndA System of fixed Mass (closed system) Control Volume: Some (usually fixed) region of space 4 Energy of the system: Internal, Kinetic, Potential E = U + 1 2 mv 2 + mgz Conservation law for our system? dE dt = dQ dt + dW dt RTT à B sys = E, b = e ρ edV ρ e v · ndA Volumetric energy Energy flux dQ dt + dW dt = d dt CV ρ ( u + 1 2 v 2 + gz ) dV + CS ρ ( u + 1 2 v 2 + gz ) v · ndA e = u + 1 2 v 2 + gz 1 st Law of thermodynamics
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3 5 Consider Uniform Properties within a control volum, and Uniform Velocities ˙ m dQ dt + dW dt = d dt ± ρ ( u + 1 2 v 2 + gz ) V + ± ρ
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Lecture_7_notes - Chemical Engineering 374 Fluid Mechanics...

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