Basics of Fluid Mechanics, 2014a

CHAPTER 10
Inviscid Flow or Potential Flow
10.1 Introduction
The mathematical complication of the Naiver–Stokes equations suggests that a simplified
approached can be employed. N–S equations are a second non–linear partial
equations. Hence, the simplest step will be to neglect the second order terms (second
derivative). From a physical point of view, the second order term represents the viscosity
effects. The neglection of the second order is justified when the coefficient in
front of the this term, after non–dimensionalzing, is approaching zero. This coefficient
in front of this term is 1/Re where Re is Reynold’s number. A large Reynolds number
means that the coefficient is approaching zero. Reynold’s number represents the
ratio of inertia forces to viscous forces. There are regions where the inertia forces are
significantly larger than the viscous flow.
Experimental observations show that when the flow field region is away from a
solid body, the inviscid flow is an appropriate model to approximate the flow. In this
way, the viscosity effects can be viewed as a mechanism in which the information is
transferred from the solid body into depth of the flow field. Thus, in a very close
proximity to the solid body, the region must be considered as viscous flow. Additionally,
the flow far away from the body is an inviscid flow. The connection between these
regions was proposed by Prandtl and it is referred as the boundary layer.
The motivations or benefits for such analysis are more than the reduction of
mathematical complexity. As it was indicated earlier, this analysis provides an adequate
solution for some regions. Furthermore the Potential Flow analysis provides several
concepts that obscured by other effects. These flow patterns or pressure gradients reveal
several “laws” such as Bernoulli’s theorem, vortex/lift etc which will be expanded.
There are several unique concepts which appear in potential flow such as Add Mass,
Add Force, and Add Moment of Inertia otherwise they are obscured with inviscid flow.
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