Table 2.

The cubic polynomials used for designing the convergent section of nozzle².

$\frac{r-r_{\mathit{Th}}}{r_{\mathit{In}}-r_{\mathit{Th}}}=1-\frac{1}{X_m^2}{\left(\frac{x}{L}\right)}^3\left(\frac{X}{L}\le X_m\right)$	Bi-cubic curve	(12)
$\frac{r-r_{\mathit{Th}}}{r_{\mathit{In}}-r_{\mathit{Th}}}=1-\frac{1}{{\left(1-X_m\right)}^2}{\left(1-\frac{x}{L}\right)}^3\left(\frac{x}{L}>X_m\right)$
$r=\frac{r_{\mathit{Th}}}{\sqrt{1-\left[1-{\left(r_{\mathit{Th}}/r_{\mathit{In}}\right)}^2\right]\frac{{\left(1-{\left(\frac{x}{L}\right)}^2\right)}^2}{{\left(1+\frac{x^2}{3\times L^2}\right)}^3}}}$	Witoszynski curve	(13)
$\frac{r-r_{\mathit{Th}}}{r_{\mathit{In}}-r_{\mathit{Th}}}=1-10{\left(\frac{x}{L}\right)}^3+15{\left(\frac{x}{L}\right)}^4-6{\left(\frac{x}{L}\right)}^5$	Quintic curve	(14)