This is applied when the parameter setting is Tee calculation = Constant zeta.

The local resistance $\mathrm{\zeta }$ is defined by a parameter $\mathrm{\ζ\_\_constant}$.

$\mathrm{\ζ}\left[1\right]\=\mathrm{\ζ\_\_constant}\left[1\right]$

$\mathrm{\zeta }\left[2\right]\=\mathrm{\ζ\_\_constant}\left[2\right]$

$\mathrm{\zeta }\left[3\right]\=\mathrm{\ζ\_\_constant}\left[3\right]$

Note : [1] port_a, [2] port_b, [3] port_c (branch)

This is applied when the parameter setting is Tee calculation = Idelchik with design point, or Idelchik with actual flow ratio.

The following equations are defined in Idelchik's method for each case. The calculation uses Volume flow rate $\mathrm{vflow}$.

Note : [1] port_a, [2] port_b, [3] port_c (branch)

If Tee calculation = Idelchik with design point, these volume flow rates are specified by parameter values,

$\mathrm{vflow}\left[1\right]\=\mathrm{vflow\_\_dp}\left[1\right]$

$\mathrm{vflow}\left[2\right]\=\mathrm{vflow\_\_dp}\left[2\right]$

$\mathrm{vflow}\left[3\right]\=\mathrm{vflow\_\_dp}\left[3\right]$

And, if Idelchik with actual flow ratio, the actual calculated volume flow rates are used for $\mathrm{vflow}$.  

Converging 1 : port_a and port_c to port_b

$\mathrm{\ζ}\left[1\right]\=\frac{1.55\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}-{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)}^2}{{\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\=0$

$\mathrm{\zeta }\left[3\right]\=\frac{\(\{\begin{array}{cc}1.0& \frac{\mathrm{A\_\_s}}{\mathrm{A\_\_m}}\le 0.35\\ \{\begin{array}{cc}0.9\cdot \left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)& \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\le 0.4\\ 0.55& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}\)\cdot \left(1\+\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)-2\cdot {\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)}^2\right)}{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}$

Converging 1 : port_b and port_c to port_a

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\=\frac{1.55\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}-{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)}^2}{{\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\=\frac{\(\{\begin{array}{cc}1.0& \frac{\mathrm{A\_\_s}}{\mathrm{A\_\_m}}\le 0.35\\ \{\begin{array}{cc}0.9\cdot \left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)& \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\le 0.4\\ 0.55& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}\)\cdot \left(1\+\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)-2\cdot {\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)}^2\right)}{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}$

Converging 3 : port_a and port_b to port_c

$\mathrm{\ζ}\left[1\right]\=\mathrm{zeta\_\_con\_in}$

$\mathrm{\zeta }\left[2\right]\=\mathrm{zeta\_\_con\_in}$

$\mathrm{\zeta }\left[3\right]\=0$

Diverging 1 : port_a to port_b to port_c

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\=\frac{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)}^2\cdot \(\{\begin{array}{cc}0.4& \frac{\mathrm{A\_\_s}}{\mathrm{A\_\_m}}\le 0.4\\ \{\begin{array}{cc}2\cdot \left(2\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}-1\right)& \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\le 0.5\\ 0.3\cdot \left(2\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}-1\right)& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}\)}{{\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\=\frac{1\+0.3\cdot {\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[1\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}$

Diverging 2 : port_b to port_a to port_c

$\mathrm{\ζ}\left[1\right]\=\frac{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)}^2\cdot \(\{\begin{array}{cc}0.4& \frac{\mathrm{A\_\_s}}{\mathrm{A\_\_m}}\le 0.4\\ \{\begin{array}{cc}2\cdot \left(2\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}-1\right)& \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\le 0.5\\ 0.3\cdot \left(2\cdot \frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}-1\right)& \mathrm{otherwise}\end{array}& \mathrm{otherwise}\end{array}\)}{{\left(1-\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\=0$

$\mathrm{\zeta }\left[3\right]\=\frac{1\+0.3\cdot {\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}{{\left(\frac{\mathrm{vflow}\left[3\right]}{\mathrm{vflow}\left[2\right]}\cdot \frac{\mathrm{A\_\_m}}{\mathrm{A\_\_s}}\right)}^2}$

Diverging 3 : port_c to port_a to port_b

$\mathrm{\ζ}\left[1\right]\=\mathrm{\ζ\_\_div\_ex}$

$\mathrm{\zeta }\left[2\right]\=\mathrm{\ζ\_\_div\_ex}$

$\mathrm{\zeta }\left[3\right]\=0$

Other : pressure difference ports and junction are close to zero [Pa] ($\left|\mathrm{dp}\right|\le \frac{\mathrm{dp\_\_small}}{2}$)

$\mathrm{\ζ}\left[1\right]\=\mathrm{\ζ\_\_0}$

$\mathrm{\zeta }\left[2\right]\=\mathrm{\ζ\_\_0}$

$\mathrm{\zeta }\left[3\right]\=\mathrm{\ζ\_\_0}$

This is applied when the parameter setting is Tee calculation = Rennels with design point, or Rennels with actual flow ratio.

The following equations are defined in Idelchik's method for each case. The calculation uses Mass flow rate $\mathrm{mflow}$.

Note : [1] port_a, [2] port_b, [3] port_c (branch)

If Tee calculation = Rennels with design point, these mass flow rates are specified by parameter values

$\mathrm{mflow}\left[1\right]\=\mathrm{mflow\_\_dp}\left[1\right]$

$\mathrm{mflow}\left[2\right]\=\mathrm{mflow\_\_dp}\left[2\right]$

$\mathrm{mflow}\left[3\right]\=\mathrm{mflow\_\_dp}\left[3\right]$

And, if Rennels with actual flow ratio, the actual calculated mass flow rates are used for $\mathrm{mflow}$.  

Converging 1 : port_a and port_c to port_b

$\mathrm{\ζ}\left[1\right]\=\left(0.54-1.12\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.28\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-2}\+\left(0.38\+0.42\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.56\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-1}-0.88\+0.7\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-0.84\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[2\right]\=0$

$\mathrm{\zeta }\left[3\right]\=\left(-1.92\+1.4\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-0.84\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\+\left(3.46-2.7\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.12\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-1}\+\left(-0.92\+0.2\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.07\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-2}\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^4\+1.0-0.5\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^{\left(1\+\mathrm{D\_\_side}\/\mathrm{D\_\_main}\right)}$

Converging 1 : port_b and port_c to port_a

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\=\left(0.54-1.12\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.28\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-2}\+\left(0.38\+0.42\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.56\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-1}-0.88\+0.7\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-0.84\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[3\right]\=\left(-1.92\+1.4\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-0.84\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\+\left(3.46-2.7\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.12\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-1}\+\left(-0.92\+0.2\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.07\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-2}\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^4\+1.0-0.5\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^{\left(1\+\mathrm{D\_\_side}\/\mathrm{D\_\_main}\right)}$

Converging 3 : port_a and port_b to port_c

$\mathrm{\ζ}\left[1\right]\=\left(0.81-1.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.5\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-2}-\left(0.95-1.65\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-1}\+1.34-1.69\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[2\right]\=\left(0.81-1.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.5\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-2}-\left(0.95-1.65\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-1}\+1.34-1.69\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[3\right]\=0$

Diverging 1 : port_a to port_b to port_c

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\=0.62-0.98\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-1}\+0.36\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-2}\+0.04\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[1\right]}\right)}^6$

$\mathrm{\zeta }\left[3\right]\=0.81-\left(1.13-0.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-1}\+\left(1.00-0.24\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[1\right]}\right)}^{-2}\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^4\+1.08\cdot \left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)-1.06\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^3\+\mathrm{zeta\_\_entrance}$

$\mathrm{zeta\_\_entrance}\=0.57-1.07\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-2.13\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\+8.24\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^{3\/2}-8.48\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^2\+2.90\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^{5\/2}$

Diverging 2 : port_b to port_a to port_c

$\mathrm{\ζ}\left[1\right]\=0.62-0.98\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-1}\+0.36\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-2}\+0.04\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[2\right]}\right)}^6$

$\mathrm{\zeta }\left[2\right]\=0$

$\mathrm{\zeta }\left[3\right]\=0.81-\left(1.13-0.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-1}\+\left(1.00-0.24\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\right)\cdot {\left(\frac{\mathrm{mflow}\left[3\right]}{\mathrm{mflow}\left[2\right]}\right)}^{-2}\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^4\+1.08\cdot \left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)-1.06\cdot {\left(\frac{\mathrm{D\_\_side}}{\mathrm{D\_\_main}}\right)}^3\+\mathrm{\ζ\_\_entrance}$

$\mathrm{\ζ\_\_entrance}\=0.57-1.07\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-2.13\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\+8.24\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^{3\/2}-8.48\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^2\+2.90\cdot {\left(\frac{r}{\mathrm{D\_\_side}}\right)}^{5\/2}$

Diverging 3 : port_c to port_a to port_b

$\mathrm{\ζ}\left[1\right]\=0.59\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-2}\+\left(1.18-1.84\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[1\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-1}-0.68\+1.04\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[2\right]\=0.59\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-2}\+\left(1.18-1.84\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{\mathrm{mflow}\left[2\right]}{\mathrm{mflow}\left[3\right]}\right)}^{-1}-0.68\+1.04\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)$

$\mathrm{\zeta }\left[3\right]\=0$

Other : pressure difference ports and junction are close to zero [Pa] ($\left|\mathrm{dp}\right|\le \frac{\mathrm{dp\_\_small}}{2}$)

$\mathrm{\ζ}\left[1\right]\=\mathrm{\ζ\_\_0}$

$\mathrm{\zeta }\left[2\right]\=\mathrm{\ζ\_\_0}$

$\mathrm{\zeta }\left[3\right]\=\mathrm{\ζ\_\_0}$

This is applied when the parameter setting is Tee calculation = Blevins with design point, or Blevins with actual flow ratio.

The following equations are defined in Idelchik's method for each case. The calculation uses flow velocity $v$.

Note : [1] port_a, [2] port_b, [3] port_c (branch)

If Tee calculation = Blevins with design point, these flow velocities are specified by parameter values

$v\left[1\right]\=\mathrm{v\_\_dp}\left[1\right]$

$v\left[2\right]\=\mathrm{v\_\_dp}\left[2\right]$

$v\left[3\right]\=\mathrm{v\_\_dp}\left[3\right]$

And, if Blevins with actual flow ratio, the actual calculated flow velocity are used for $v$.  

Converging 1 : port_a and port_c to port_b

$\mathrm{\ζ}\left[1\right]\=\frac{0.045\+\left(1.38-1.94\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.34\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[3\right]}{v\left[2\right]}\right)-\left(0.90-0.95\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.23\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[3\right]}{v\left[2\right]}\right)}^2}{{\left(1-\frac{v\left[3\right]}{v\left[2\right]}\cdot \frac{\mathrm{A\_\_side}}{\mathrm{A\_\_main}}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\=0$

$\mathrm{\zeta }\left[3\right]\=\frac{1.09-0.8\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-\left(0.53\+1.27\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-1.86\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[1\right]}{v\left[2\right]}\right)-\left(1.48-2.28\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.80\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[1\right]}{v\left[2\right]}\right)}^2}{\frac{v\left[3\right]}{v\left[2\right]}}$

Converging 1 : port_b and port_c to port_a

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\=\frac{0.045\+\left(1.38-1.94\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.34\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[3\right]}{v\left[1\right]}\right)-\left(0.90-0.95\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.23\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[3\right]}{v\left[1\right]}\right)}^2}{{\left(1-\frac{v\left[3\right]}{v\left[1\right]}\cdot \frac{\mathrm{A\_\_side}}{\mathrm{A\_\_main}}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\=\frac{1.09-0.8\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-\left(0.53\+1.27\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-1.86\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[2\right]}{v\left[1\right]}\right)-\left(1.48-2.28\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+1.80\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[2\right]}{v\left[1\right]}\right)}^2}{\frac{v\left[3\right]}{v\left[1\right]}}$

Converging 3 : port_a and port_b to port_c

$\mathrm{\ζ}\left[1\right]\=\frac{\left(1.19-1.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.46\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)-1.73\cdot \left(1.0-\left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[1\right]}{v\left[3\right]}\right)\+\left(1.34-1.69\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[1\right]}{v\left[3\right]}\right)}^2}{{\left(\frac{v\left[1\right]}{v\left[3\right]}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\=\frac{\left(1.19-1.16\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\+0.46\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)-1.73\cdot \left(1.0-\left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[2\right]}{v\left[3\right]}\right)\+\left(1.34-1.69\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[2\right]}{v\left[3\right]}\right)}^2}{{\left(\frac{v\left[2\right]}{v\left[3\right]}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\=0$

Diverging 1 : port_a to port_b to port_c

$\mathrm{\ζ}\left[1\right]\=0$

$\mathrm{\zeta }\left[2\right]\&equals;\&lpar;\&lcub;\begin{array}{cc}1.55\cdot {\left(0.22-\frac{v\left[3\right]}{v\left[1\right]}\right)}^2-0.03& \frac{v\left[3\right]}{v\left[1\right]}<0.22\\ 0.65\cdot {\left(\frac{v\left[3\right]}{v\left[1\right]}-0.22\right)}^2-0.03& \mathrm{otherwise}\end{array}\&rpar;\cdot \frac{1}{{\left(1-\frac{v\left[3\right]}{v\left[1\right]}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\&equals;\frac{0.99-0.23\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-\left(0.82\&plus;0.29\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;0.3\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[3\right]}{v\left[1\right]}\right)\&plus;\left(1.02-0.64\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;0.76\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[3\right]}{v\left[1\right]}\right)}^2}{{\left(\frac{v\left[3\right]}{v\left[1\right]}\right)}^2}$$$

Diverging 2 : port_b to port_a to port_c

$\mathrm{\&zeta;}\left[1\right]\&equals;\&lpar;\&lcub;\begin{array}{cc}1.55\cdot {\left(0.22-\frac{v\left[3\right]}{v\left[2\right]}\right)}^2-0.03& \frac{v\left[3\right]}{v\left[2\right]}<0.22\\ 0.65\cdot {\left(\frac{v\left[3\right]}{v\left[2\right]}-0.22\right)}^2-0.03& \mathrm{otherwise}\end{array}\&rpar;\cdot \frac{1}{{\left(1-\frac{v\left[3\right]}{v\left[2\right]}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\&equals;0$

$\mathrm{\zeta }\left[3\right]\&equals;\frac{0.99-0.23\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}-\left(0.82\&plus;0.29\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;0.3\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[3\right]}{v\left[2\right]}\right)\&plus;\left(1.02-0.64\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;0.76\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[3\right]}{v\left[2\right]}\right)}^2}{{\left(\frac{v\left[3\right]}{v\left[2\right]}\right)}^2}$$$

Diverging 3 : port_c to port_a to port_b

$\mathrm{\&zeta;}\left[1\right]\&equals;\frac{0.59\&plus;\left(1.18-1.84\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[1\right]}{v\left[3\right]}\right)-\left(0.68-1.04\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[1\right]}{v\left[3\right]}\right)}^2}{{\left(\frac{v\left[1\right]}{v\left[3\right]}\right)}^2}$

$\mathrm{\zeta }\left[2\right]\&equals;\frac{0.59\&plus;\left(1.18-1.84\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot \left(\frac{v\left[2\right]}{v\left[3\right]}\right)-\left(0.68-1.04\cdot \sqrt{\frac{r}{\mathrm{D\_\_side}}}\&plus;1.16\cdot \left(\frac{r}{\mathrm{D\_\_side}}\right)\right)\cdot {\left(\frac{v\left[2\right]}{v\left[3\right]}\right)}^2}{{\left(\frac{v\left[2\right]}{v\left[3\right]}\right)}^2}$

$\mathrm{\zeta }\left[3\right]\&equals;0$

Other : pressure difference ports and junction are close to zero [Pa] ($\left|\mathrm{dp}\right|\le \frac{\mathrm{dp\_\_small}}{2}$)

$\mathrm{\&zeta;}\left[1\right]\&equals;\mathrm{\&zeta;\_\_0}$

$\mathrm{\zeta }\left[2\right]\&equals;\mathrm{\&zeta;\_\_0}$

$\mathrm{\zeta }\left[3\right]\&equals;\mathrm{\&zeta;\_\_0}$

The calculation method can be specified with 3 options.

Friction calculation = Constant

If this option is selected, the friction coefficient $\mathrm{\&lambda;}$ is specified by a parameter $\mathrm{\&lambda;\_\_constant}$.

$\mathrm{\&lambda;}\&equals;\mathrm{\&lambda;\_\_constant}$

Friction calculation = Darcy-Weisbach with Constant velocity (Design point)

If this option is selected, the friction coefficient $\mathrm{\&lambda;}$ is calculated with a parameter of velocity at design point $\mathrm{v\_\_design\_f}$.

$\mathrm{Re}\&equals;\max \left(\frac{\&lcub;\begin{array}{cc}\mathrm{\&rho;\_\_a}& \mathrm{dp}\ge 0\\ \mathrm{\&rho;\_\_b}& \mathrm{others}\end{array}\cdot \mathrm{v\_\_design\_f}\cdot \mathrm{D\_\_h\_act}}{\&lcub;\begin{array}{cc}\mathrm{\&mu;\_\_a}& \mathrm{dp}\ge 0\\ \mathrm{\&mu;\_\_b}& \mathrm{others}\end{array}}\&comma;0.1\right)$

$\mathrm{\lambda }\&equals;\mathrm{`HeatTransfer.Functions.lambda\_Re`}\left(\mathrm{Re}\&comma;\mathrm{roughness}\&comma;\mathrm{D\_\_h\_act}\&comma;\mathrm{Re\_\_CoT}\&comma;\mathrm{IF\_\_speed}\&comma;\mathrm{Geo\_\_act}\right)$

$\mathrm{\&rho;\_\_a}$, $\mathrm{\&rho;\_\_b}$ are density at each port of flow components. $\mathrm{\&mu;\_\_a}$, $\mathrm{\&mu;\_\_b}$ are dynamic viscosity at each port of flow components. This means, one is at port of Water Tee junction, and the another is at the junction node. $\mathrm{D\_\_h\_act}$ is the diameter of flow components. $\mathrm{Re}$ is Reynolds number. $\mathrm{roughness}$ is pipe roughness of flow components.

Friction calculation = Darcy-Weisbach

If this option is selected, the friction coefficient $\mathrm{\&lambda;}$ is calculated with the following equations:

$\mathrm{Re\_\_target}\&equals;\max \left(\frac{\&lcub;\begin{array}{cc}\mathrm{\&rho;\_\_a}& \mathrm{dp}\ge 0\\ \mathrm{\&rho;\_\_b}& \mathrm{others}\end{array}\cdot \left|v\right|\cdot \mathrm{D\_\_h\_act}}{\&lcub;\begin{array}{cc}\mathrm{\&mu;\_\_a}& \mathrm{dp}\ge 0\\ \mathrm{\&mu;\_\_b}& \mathrm{others}\end{array}}\&comma;0.1\right)$

$\frac{\&DifferentialD;\mathrm{Re}}{\&DifferentialD;t}\&equals;\frac{\left(\mathrm{Re\_\_target}-\mathrm{Re}\right)}{\mathrm{T\_\_const}}$

$\mathrm{\lambda }\&equals;\mathrm{`HeatTransfer.Functions.lambda\_Re`}\left(\mathrm{Re}\&comma;\mathrm{roughness}\&comma;\mathrm{D\_\_h\_act}\&comma;\mathrm{Re\_\_CoT}\&comma;\mathrm{IF\_\_speed}\&comma;\mathrm{Geo\_\_act}\right)$

$\mathrm{\&rho;\_\_a}$, $\mathrm{\&rho;\_\_b}$ are density at each port of flow components. $\mathrm{\&mu;\_\_a}$, $\mathrm{\&mu;\_\_b}$ are dynamic viscosity at each port of flow components. $\mathrm{D\_\_h\_act}$ is the diameter of flow components. $\mathrm{Re}$ is Reynolds number. $\mathrm{roughness}$ is pipe roughness of flow components.

(*) The above function $\mathrm{`HeatTransfer.Functions.lambda\_Re`}$ is to calculated friction factor for Laminar and Turbulent flow.
The fundamental implementation is based on the following equations. Especially, the equation of Turbulent flow is Swamee and Jain's approximation[1] .

You can find more information in the Water Detailed Flow help page.