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For an INCOMPRESSIBLE Newtonian fluid with constant μ, the Navier-Stokes equation reduces to:
A{'text': '$\\rho D\\mathbf{u}/Dt = -\\nabla p + \\mu \\nabla^2 \\mathbf{u} + \\rho \\mathbf{f}$', 'label': 'A'}
B{'text': '$\\rho \\mathbf{u} = 0$', 'label': 'B'}
C{'text': '$\\partial u/\\partial t = 0$', 'label': 'C'}
D{'text': '$\\nabla p = 0$', 'label': 'D'}
Answer & Solution
Correct answer: A. {'text': '$\\rho D\\mathbf{u}/Dt = -\\nabla p + \\mu \\nabla^2 \\mathbf{u} + \\rho \\mathbf{f}$', 'label': 'A'}
Incompressible + constant μ: $\rho(\partial \mathbf{u}/\partial t + \mathbf{u}\cdot\nabla \mathbf{u}) = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{f}$. LHS = inertial; RHS = pressure + viscous + body force. The famous N-S equation.
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