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Dynamic Similarity Lecture 1 ME EN 412 Andrew Ning aning@byu.edu - - PDF document
Dynamic Similarity Lecture 1 ME EN 412 Andrew Ning aning@byu.edu - - PDF document
Dynamic Similarity Lecture 1 ME EN 412 Andrew Ning aning@byu.edu Outline Motivating Example Dynamic Similarity Some Important Nondimensional Quantities Motivating Example View Jupyter notebook Three basic ways or methods of obtaining
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Three basic ways or methods of obtaining living water from the scriptural reservoir:
- 1. reading the scriptures from beginning to end
- 2. studying the scriptures by topic
- 3. searching the scriptures for connections,
patterns, and themes – Elder Bednar
Dynamic Similarity
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What parameters might you expect the aerodynamic drag of this airfoil to depend on?
V1
2D incompressible Navier-Stokes equation (x-momentum) u∂u ∂x + v∂u ∂y = −1 ρ ∂p ∂x + µ ρ ∂2u ∂x2 + ∂2u ∂y2
- Try to nondimensionalize this equation.
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u∗∂u∗ ∂x∗ + v∗∂u∗ ∂y∗ = −∂p∗ ∂x∗ + µ ρV∞c ∂2u∗ ∂x∗2 + ∂2u∗ ∂y∗2
- where
x∗ = x c , y∗ = y c u∗ = u V∞ , v∗ = v V∞ p∗ = p − p∞ ρV 2
∞
Re ≡ ρV c µ
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The solution, in terms of these nondimensional positions and velocities, will be the same if:
- The nondimensional geometry and boundary
conditions are the same
- The Reynolds number is the same
Cp = f(Re, geometry c )
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Some Important Nondimensional Quantities Reynolds number
Re = ρV l µ
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Mach number
Ma = V a
Froude number
Fr = V √gl
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