Chapter 3 - Ideal Fluid Flow

We define Ideal fluid as inviscid ($\nu = 0$) and incompressible ( $\frac{D\rho}{Dt} = 0$). The Reynolds number is defined as the ration between the inertial and viscous forces, so

\begin{displaymath}R_e = \frac{\mbox{inertia}}{\mbox{viscous}} = \frac{UL}{\nu }.
\end{displaymath}

For `typical' problems we are interested in (for example, $ L \ge
1m, U \ge 1m/s$ and $\nu _{water} = 10^{ - 6}{m^2}/s$) we have that

\begin{displaymath}\frac{\nu }{UL} = R_e^{ - 1} < < 1 ( \le 10^{ - 6}).
\end{displaymath}

In other words, the viscous effect are much smaller than the inertial effects, and under certain circunstances (streamlined bodies), the viscous effects are restricted to a thin layer (boundary layer) around the boundaries of the flow (surfaces of streamlined bodies and their wake, for example). Therefore, outside this thin layer, ideal fluid is a good approximation. (Movie to illustrate the boundary layer along body surfaces and how its thickness depends on the Reynolds number)

 

Karl P Burr
2003-07-07