The Annulus Pipe component models an annulus pipe with losses. The pressure drop is computed with the Darcy equation. When the Reynolds number is greater than the maximum value for laminar flow but less than the minimum value for turbulent flow, the friction factor is determined using linear interpolation.

$q\=q_A\=-q_B\=\mathrm{Re}A\frac{\mathrm{\nu }}{{\mathrm{D}}_h}$

$p\=p_A-p_B\=\frac{1}{2}L\mathrm{\rho }\frac{{\mathrm{\nu }}^2}{{\mathrm{D}}_h^3}\mathrm{Re}\{\begin{array}{cc}{f}_{\mathrm{Colebrook}}\left(\left|\mathrm{Re}\right|\,\frac{\mathrm{\epsilon }}{{\mathrm{D}}_h}\right)\left|\mathrm{Re}\right|& \mathrm{mode}\=\mathrm{+turbulent}\vee \mathrm{mode}\=\mathrm{-turbulent}\\ \left(f_L\+\frac{f_T-f_L}{{\mathrm{Re}}_T-{\mathrm{Re}}_L}\left(\left|\mathrm{Re}\right|-{\mathrm{Re}}_L\right)\right)\left|\mathrm{Re}\right|& \mathrm{mode}\=\mathrm{+mixed}\vee \mathrm{mode}\=\mathrm{-mixed}\\ \mathrm{AnnulusShapeFactor}\left({\mathrm{D}}_i\,{\mathrm{D}}_0\right)& \mathrm{otherwise}\end{array}$

$\mathrm{mode}\&equals;\{\begin{array}{cc}\mathrm{+turbulent}& {\mathrm{Re}}_T<\mathrm{Re}\\ \mathrm{-turbulent}& {\mathrm{Re}}_T<-\mathrm{Re}\\ \mathrm{+mixed}& {\mathrm{Re}}_L<\mathrm{Re}\\ \mathrm{-mixed}& {\mathrm{Re}}_L<-\mathrm{Re}\\ \mathrm{laminar}& \mathrm{otherwise}\end{array}$

${\mathrm{D}}_h\&equals;{\mathrm{D}}_o-{\mathrm{D}}_{i}A\&equals;\frac{\mathrm{\pi }}{4}\left({\mathrm{D}}_o^2-{\mathrm{D}}_i^2\right)$

$f_{\mathrm{Colebrook}}\&equals;\left(\mathrm{Re}\&comma;{\mathrm{\epsilon }}_{\mathrm{D}}\right)\to {\left(1.8{{\log }_{10}\left(\frac{6.9}{\mathrm{Re}}\&plus;\left(\frac{{\mathrm{\epsilon }}_{\mathrm{D}}}{3.7}\right)\right)}^{1.11}\right)}^{\mathrm{-2}}$