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Governing Equations in Differential Form

Governing Equations in Differential Form. Take the limit such that the control volume approach to infinitesimal small: consequently, all fluid properties within the volume can be considered constant.

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Governing Equations in Differential Form

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  1. Governing Equations in Differential Form • Take the limit such that the control volume approach to infinitesimal small: consequently, all fluid properties within the volume can be considered constant. • Use the divergence theorem to convert the surface integration term into a volume integration term:

  2. Continuity Equation

  3. Physical Interpretation v(y+Dy) u(x) u(x+Dx) v(y)

  4. Example (suction boundary layer control) A laminar boundary layer can be approximated as having a velocity profile u(x)=Uy/d, where d=cx1/2, c is a constant, U is the freestream velocity, and d is the boundary layer thickness. Determine the v(vertical component) of the velocity inside the boundary layer. d(x)=cx1/2

  5. Example (cont.)

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