Table 9 The detailed formulas for different kinds of pressure loss

\(\Delta P_{{i,{\text{diffusion}}}}\)

\(\rho \lambda_{i} \frac{{l_{i} }}{{\overline{d}_{i} }}\frac{{U_{i}^{2} }}{2}\)

\(\lambda_{i} = {{64} \mathord{\left/ {\vphantom {{64} {\text{Re}}}} \right. \kern-0pt} {\text{Re}}}_{i}\)

\(\Delta P_{{i,{\text{constriction}}}}\)

\(\rho \varsigma_{2i} \frac{{U_{i}^{2} }}{2}\)

\(\varsigma_{2i} = \left\{ \begin{gathered} \frac{{\lambda_{i} }}{{8\sin ({{\theta_{{\text{c}}} } \mathord{\left/ {\vphantom {{\theta_{{\text{c}}} } {2)}}} \right. \kern-0pt} {2)}}}}\left[ {1 - \left( {\frac{{A_{2} }}{{A_{1} }}} \right)^{2} } \right],\;\theta_{{\text{c}}} < 30^\circ \hfill \\ \frac{{\lambda_{i} }}{{8\sin ({{\theta_{{\text{c}}} } \mathord{\left/ {\vphantom {{\theta_{{\text{c}}} } {2)}}} \right. \kern-0pt} {2)}}}}\left[ {1 - \left( {\frac{{A_{2} }}{{A_{1} }}} \right)^{2} } \right] + \frac{{\theta_{{\text{c}}} }}{1000},\;30^\circ \le \theta_{{\text{c}}} < 90^\circ \hfill \\ \end{gathered} \right.\)

\(\Delta P_{{i,{\text{expansion}}}}\)

\(\rho \varsigma_{3i} \frac{{U_{i}^{2} }}{2}\)

\(\varsigma_{3i} = \frac{{\lambda_{i} }}{{8\sin ({{\theta_{{\text{e}}} } \mathord{\left/ {\vphantom {{\theta_{{\text{e}}} } {2)}}} \right. \kern-0pt} {2)}}}}\left[ {1 - \left( {\frac{{A_{1} }}{{A_{2} }}} \right)^{2} } \right] + \sin (\theta_{E} )\left[ {1 - \left( {\frac{{A_{1} }}{{A_{2} }}} \right)} \right]^{2}\)

\(\Delta P_{{i,{\text{bifurcation}}}}\)

\(\rho \varsigma_{4i} \frac{{U_{i}^{2} }}{2}\)

\(\varsigma_{4i} = 0.1\)

\(\Delta P_{{i,{\text{bend}}}}\)

\(\rho \varsigma_{5i} \frac{{U_{i}^{2} }}{2}\)

\(\varsigma_{5i} = \left[ {0.131 + 0.163\left( \frac{d}{R} \right)^{3.5} } \right]\frac{{\theta_{{\text{b}}} }}{90^\circ }\)

\(\Delta P_{{i,{\text{convection}}}}\)

\(\rho \left( {\frac{{U_{{i,{\text{outlet}}}}^{2} }}{2} - \frac{{U_{{i,{\text{inlet}}}}^{2} }}{2}} \right)\)

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