alleryStart learning →For an INCOMPRESSIBLE Newtonian fluid with constant μ, the Navier-Stokes equation reduces to:
A$\rho D\mathbf{u}/Dt = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{f}$
B$\rho \mathbf{u} = 0$
C$\partial u/\partial t = 0$
D$\nabla p = 0$
Answer & Solution
Correct answer: A. $\rho D\mathbf{u}/Dt = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{f}$
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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