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This is the first course of a two-semester fluid mechanics sequence for graduate students in the thermal sciences. This course deals with solutions of these equations, both exact and approximate. Key points of this lecture are: Laminar Flow Solutions, Propulsion of Fish, Birds, and Sailboats, Nearly Incompressible Laminar Flow, Equations and Solution Technique, Transitional or Turbulent, Conservation of Mass, Momentum Equation, Conservation of Energy, Vorticity Equation, Continuity and Vorticit
Typology: Exercises
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Author: John M. Cimbala, Penn State University Latest revision: 31 October 2007
i
i
u
x
2 i i i i j i j i j j
Du u u (^) p u ρ ρ u ρg μ Dt t x x x x
2
p i i
ρC k Dt x x
, where φ = 2 μ e eij ij.
For ideal gas at very low Ma :
2
p i i
ρC k Dt x x
, or
2
i i
κ Dt x x
p
k κ ρC
≡ = thermal diffusivity).
2 k k k j j j j
Dω u ω ω ν Dt x x x
expansion coefficient,
p
ρ α ρ T
(for an ideal gas,
reference temperature T 0. ( T is assumed to vary only slightly from T 0 , so that density is nearly constant, but does
2
i i i i j i j i j j
Du u u p u ρ ρ u ρ α T T g μ Dt t x x x x
2
0 0
i i i i j i j i j j
Du u u p u u α T T g ν Dt t x ρ x x x
, where
0
μ ν
2
0 p i i
ρ C k Dt x x
For ideal gas at very low Mach number :
2
i i
κ Dt x x
, where
0 p
k κ ρ C
≡ (^) & viscous dissipation is negligible.
buoyancy is important, the energy equation must be solved simultaneously with mass and momentum.)