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Abstract
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In classical fluid mechanics, variational principles have been applied to derive the Navier–Stokes equations with relativesuccess. The common procedure uses indirect and semi-direct methods with nonstandard Lagrangians. In this paper, the standard Lagrangian is used to derive the Navier–Stokes equations. In this regard, a Lagrangian potential function related to an isotropic tensor field is introduced. For compressible flow, another Lagrangian potential function related to the viscosity coefficients is defined. The Navier–Stokes equations are then derived from Lagrange’s equations. It is shown that in derivation of governing equations of viscous flow the standard Lagrangian is more efficient than nonstandard Lagrangians. Energy and Hamiltonian rate equations that may be used in fluid mechanics are also proposed.
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