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Lift and drag

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The force on a body immersed in a fluid is decomposed into lift and drag. Lift is the component of the force normal to the freestream velocity while drag is the force in the direction of the freestream velocity.

The force on a body B can be obtained by integrating the stress on the surface \partial B of the body and is given by


F_i = \int_{\partial B} \sigma_{ij} n_j dS

where

  • \sigma_{ij} = -p\delta_{ij} + \tau_{ij} is the total stress
  • p is the static pressure
  • \tau_{ij} is the shear stress
  • n_i is the unit normal vector to \partial B

If U_i is the freestream velocity with U = \sqrt{U_i U_i} then the drag force (D) is given by


D := F_i U_i / U

The remaining force can be considered as lift force. For a 3-D slender body the lift force may be broken into a normal force and a side force.

In 2-D, the lift (L) and drag are given by


L = -F_1 \sin\alpha + F_2 \cos\alpha


D = F_1 \cos\alpha + F_2 \sin\alpha

where \alpha is the angle of attack, that is the angle between the freestream velocity and the x_1 axis.

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