ABSTRACT
It must be remembered that the potential flow approximation could not be used to calculate velocity profiles, boundary layer thickness, or boundary layer heat and mass transfer phenomena, etc., close to stationary solid objects in the flow field. The potential flow approximation is good for determining the flow patterns sufficiently from stationary solid objects. 3.3.2 Very Slow Motion (Inertia! Forces Arc Neglected, v ~ 0) When the velocity or the fluid is very slow, the inertial force (pv. Vn•) becomes smaller in comparison to the viscous force (M V2 v). For a steady-state flow, if the inertial force is sufficiently smaller than the viscous force, then the inertial force can be neglected and the approximate form of the Navier-Stokes equation [Eq. (I 1 .21)] becomes
v. p = fL '12 1' (11.68)
This is known as the "very small motion" or "creeping motion" approximation. It can be seen from (11.21) that if Land v00 are the characteristic linear dimension
and linear velocity of a given flow system, then inertial and viscous force terms will be proportional to pv;_,; L and 2 , respectively. The ratio of inertial to viscous forces, pv00 L/J1 is the characteristic Reynolds number. Thus, the smaller the Reynolds number, the better will be the approximation of the Navier-Stokes equation by neglecting the inertial force term.
