Home › GATE ME › Mechanical Engineering › navierstokes › Stokes' hypothesis (often invoked in N-S derivat…
Stokes' hypothesis (often invoked in N-S derivation) relates bulk and shear viscosities by:
A{'text': 'Bulk = shear viscosity', 'label': 'A'}
B{'text': 'Bulk viscosity = $-2/3 \\cdot$ shear viscosity — usually assumed for monatomic gases and many engineering fluids; makes the trace of the deviatoric stress zero', 'label': 'B'}
C{'text': 'They are unrelated', 'label': 'C'}
D{'text': 'Both are zero', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': 'Bulk viscosity = $-2/3 \\cdot$ shear viscosity — usually assumed for monatomic gases and many engineering fluids; makes the trace of the deviatoric stress zero', 'label': 'B'}
Stokes' hypothesis: $\lambda + (2/3)\mu = 0$, where λ is bulk viscosity. Mathematically convenient; physically exact for monatomic gases. Used in the N-S derivation to ensure the deviatoric stress tensor is traceless.
Related questions
Body force $\mathbf{f}$ in the momentum equation typically represents:The DEVIATORIC STRESS TENSOR $ igma_{ij}^d$ in N-S is the part:The CONSERVATION OF CHEMICAL SPECIES (mass fraction Y_α of species α) gives:The class of LINEAR SECOND-ORDER PDEs (parabolic, elliptic, hyperbolic) appearing in heat Conservation of THERMAL ENERGY in a flowing fluid involves which key terms?Re-derive the incompressibility condition: starting from $\partial\rho/\partial t + \nablaThe "substantial derivative" (or material derivative) of a property $\phi$ is:For an INCOMPRESSIBLE Newtonian fluid with constant μ, the Navier-Stokes equation reduces