Several practical problems of Fluid Dynamics can be solved with the use of the linear momentum balance equation, mostly in integral form. We select an appropriate control volume and evaluate all the forces acting on it, separating the surface forces (acting on the outer surface of the control ...
These include the mass, momentum, and energy equations, as well as thermodynamic principles. The viscosity and thermal conduction enter into the versions of these equations that apply to fluids. Fluids of typical great interest are air and sea water, and consequently this chapter includes asummary...
From the scalar form of the balance of linear momentum above, along with the fact that the basis vectors are everywhere constant (i.e., EA,B=0), the Cartesian vector form of the linear momentum equation (10.105) is (10.114)(tA),A+b=ρ0U¨inB From Eq. (10.108), momentum equation ...
Similarly, the momentum equation can be discretized implicitly as Sign in to download full-size image Figure 8.6. Nodalization for nonlinear stability analysis: (A) clockwise flow and (B) anticlockwise flow. (8.45)ωn+1+pLtΔτ2Ressbωn+12−b=ωn+GrmΔτRess3θI where (8.46)θI=∮...
Therefore, the full equation of the fluid motion is not treated, but either a boundary-layer model is applied to solve the Navier-Stokes equation or a more simplified slot-averaging model is used, in which the flow perturbation is uniform in the direction perpendicular to the main flow. ...
Ch 35. Equilibrium and Momentum Ch 36. Work and Energy Ch 37. Waves Ch 38. Principles of Fluids Ch 39. Gas Laws Ch 40. Electrostatics & Magnetism Ch 41. Electronic Circuit Elements Ch 42. Electrochemistry Ch 43. Sound Ch 44. Light & Geometrical Optics Ch 45. Atomic Structure and Compo...
coupled to a momentum equation for ∂tv $${\rho }_{0}{\partial }_{t}{{{\boldsymbol{v}}}=\langle {\tilde{\mu }}_{{{\rm{c}}}\nabla \psi -\nabla \tilde{f}\rangle +{\Gamma }_{S}{\nabla }^{2}{{{\boldsymbol{v}}}+{{{\boldsymbol{f}}}^{({{{\rm{ext}}})}.$...
A water monolayer squeezed between two solid planes experiences strong out-of-plane confinement effects while expanding freely within the plane. As a consequence, the transport of such two-dimensional water combines hydrodynamic and nanofluidic features,
For a finite Re, we incorporate the inertial terms in the momentum equation within the Schur complement method similar to [40]. Therefore, in addition to solving the flow of inertia-less viscoelastic fluid, our method allows us to access the effects of small to moderate inertia (with or with...
(19), the interaction force F→s is computed on and around the solid object and then is imposed into the momentum equation as a body force at the subsequent time step. (19)F→s=ρsΔt(V→solidn+1−V→n+1) where Vn+1 and Vsolidn+1 are the velocity of the solid object ...