Table 10 Comparison of \(L/\rho\) between the impulse equation and OpenFOAM results for a NACA 0012 airfoil at \(\alpha =10^{\circ }\) having BC-3 and \(A=30\). \(L/\rho\) from Eq. (19) is 1,421.41866, and \(L/\rho\) calculated by OpenFOAM is 1,421.47316

\(\varvec{U}_{\varvec{\infty }}\varvec{\Gamma }\)

\(-\int _{\varvec{I}} \varvec{x}\varvec{(U}_{\varvec{\infty }}\varvec{+u)\Omega } \textbf{d}\varvec{y}\)

\(\int _{\varvec{T}} \frac{\varvec{1}}{\varvec{2}}\varvec{u}^{\varvec{2}} \textbf{d}\varvec{x}\)

\(-\int _{\varvec{O}} \varvec{uv}\textbf{d}\varvec{y}\)

\(\int _{\varvec{O}} \varvec{x(U}_{\varvec{\infty }}\varvec{+u)\Omega } \textbf{d}\varvec{y}\)

\(-\int _{\varvec{B}} \frac{\varvec{1}}{\varvec{2}}\varvec{u}^{\varvec{2}} \textbf{d}\varvec{x}\)