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Lecture_33_notes

# Lecture_33_notes - Chemical Engineering 374 Fluid Mechanics...

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1 1 Chemical Engineering 374 Fluid Mechanics Fall 2011 Exam 3 Review Exam Review, By Content/Lectures • Classes 25-32 (plus review) • Chapter 6.1-6.4 Momentum Balance • Chapter 9.1-9.2, 9.4-9.6 Differential Balances • Chapter 10.6 Boundary Layers • Chapter 14.1-14.5 Pumps and Turbines • HW 19-26 2

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2 Class 25—Integral Momentum Balance Force Balance – mdot is not a vector – Forces are external: body and surface (esp. P) – Decompose into scalar directions • One equation in one unknown (force, etc.) • Signs matter! Pick control volume intelligently Pressure surface forces should be gauge (unless account for full absolute pressure (including atm) on all surfaces.) For nonuniform flows, may have to integrate to get the full terms in the force balance, but the principle is the same. 3 X ± F = dm ± v dt + X m ± v ) out - X m ± v ) in Class 26—Differential Balances Mass Balance Momentum Balance Derived from the RTT Continuity Equation – Used as a constraint for velocity – Book/handouts give expanded forms for Cartesian, Cylindrical, Spherical coordinates. – Incompressible (const ρ ) means rate in = rate out. – If rate in = is not rate out then the density is changing. Momentum equation: just a differential force balance – (accum) = (in)-(out) + (body and surface forces) – Book/handouts give expanded forms in three coordinates – Again, use to find velocity field or pressure field. 4 ⇥ρ t + · ( ρ⇤ v )=0 · ± v =0
3 Class 27—Navier-Stokes Equations Incompressible, Newtonian, vector The equations look scary, but we seriously simplify them Know how to drop out terms: Solution procedure: Is it steady? (usually, here), is it compressible (no, usually here const

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Lecture_33_notes - Chemical Engineering 374 Fluid Mechanics...

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