Water Flow Resistance - MapleSim Help
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Water Flow Resistance

Flow resistance, based on Handbook of Hydraulic Resistance, I.E. Idelchik [1]

 Description The Water Flow Resistance component models a flow resistance which is caused by bending of flow for the lumped thermal fluid simulation of Water. This component calculates mainly pressure difference and mass flow rate.

Equations

The calculation is changed based on parameter values of Type of Resistance and Dynamics of mass in the Water Settings component.

The definition of Inner hydraulic diameter and Flow area and Geometrical coefficient for laminar flow, and the heat transfer coefficient calculation are explained in the following:

Reynolds number for Friction factor calculation is defined with:

$\mathrm{Re__target}=\mathrm{max}\left(\frac{{\begin{array}{cc}\mathrm{ρ__a}& \mathrm{dp}\ge 0\\ \mathrm{ρ__b}& \mathrm{others}\end{array}\cdot \left|v\right|\cdot \mathrm{D__h_act}}{{\begin{array}{cc}\mathrm{μ__a}& \mathrm{dp}\ge 0\\ \mathrm{μ__b}& \mathrm{others}\end{array}},0.1\right)$

$\frac{ⅆ\mathrm{Re}}{ⅆt}=\frac{\left(\mathrm{Re__target}-\mathrm{Re}\right)}{\mathrm{T__const}}$

 Type of Resistance = General Inner hydraulic diameter is defined with: $\mathrm{D__h_act}=\mathrm{D__h}$ Flow area is defined with: $\mathrm{A__act}=\mathrm{A__cir}$ Geometrical coefficient for laminar flow is defined with: $\mathrm{Geo__act}=1$ Geometrical length for Bend to get the values from tables: $\mathrm{D0__Bend}=0$ Total loss coefficient:
 Type of Resistance = Elbow with sharp corner (Circular) : (*) Reference[1] : page.365-366.   Inner hydraulic diameter is defined with: $\mathrm{D__h_act}=\mathrm{D__h}$ Flow area is defined with: $\mathrm{A__act}=\mathrm{A__cir}$ Geometrical coefficient for laminar flow is defined with: $\mathrm{Geo__act}=1$ Geometrical length for Bend to get the values from tables: $\mathrm{D0__Bend}=\mathrm{D__h}$ Local resistance is defined with: $\mathrm{zeta__loc}=\mathrm{A__loc_Elbow}\cdot \mathrm{C__loc}\cdot \mathrm{max}\left({10}^{-8},0.95\cdot \mathrm{sin}{\left(\frac{\mathrm{θ}}{2}\right)}^{2}+2.05\cdot \mathrm{sin}{\left(\frac{\mathrm{θ}}{2}\right)}^{4}\right)$ Correction factor C is defined with: $\mathrm{C__loc}=1$ Correction factor A is defined with: $\mathrm{A__loc_Elbow}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{θ}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A_Elbow}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Friction resistance is defined with: $\mathrm{zeta__fri}=\mathrm{k__δ}\cdot \mathrm{k__Re}\cdot \mathrm{zeta__loc}$ Correction factor k_delta (Roughness dependency) is defined with: $\mathrm{k__δ}=\mathrm{min}\left(1.5,\mathrm{max}\left(1.0,1.0+500\cdot \frac{\mathrm{roughness}}{\mathrm{D__h_act}}\right)\right)$ Correction factor k_Re (Reynolds number dependency) is defined with: $\mathrm{k__Re}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{Re}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__k_Re_Elbow}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Total resistance is defined with: $\mathrm{zeta__act}=\mathrm{zeta__fri}$
 Type of Resistance = Elbow with sharp corner (Rectangular): (*) Reference: page.365-366 in [1].   Inner hydraulic diameter is defined with: $\mathrm{D__h_act}=\frac{2}{\frac{1}{\mathrm{a__rec}}+\frac{1}{\mathrm{b__rec}}}$ Flow area is defined with: $\mathrm{A__act}=\mathrm{A__rec}$ Geometrical coefficient for laminar flow is defined with: $\mathrm{Geo__act}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{b__rec}}{\mathrm{a__rec}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__geo_rec}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Geometrical length for Bend to get the values from tables: $\mathrm{D0__Bend}=\mathrm{a__rec}$ Local resistance is defined with: $\mathrm{zeta__loc}=\mathrm{A__loc_Elbow}\cdot \mathrm{C__loc}\cdot \mathrm{max}\left({10}^{-8},0.95\cdot \mathrm{sin}{\left(\frac{\mathrm{θ}}{2}\right)}^{2}+2.05\cdot \mathrm{sin}{\left(\frac{\mathrm{θ}}{2}\right)}^{4}\right)$ Correction factor C is defined with: $\mathrm{C__loc}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{b__rec}}{\mathrm{a__rec}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__C_Elbow}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor A is defined with: $\mathrm{A__loc_Elbow}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{θ}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A_Elbow}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Friction resistance is defined with: $\mathrm{zeta__fri}=\mathrm{k__δ}\cdot \mathrm{k__Re}\cdot \mathrm{zeta__loc}$ Correction factor k_delta (Roughness dependency) is defined with: $\mathrm{k__δ}=\mathrm{min}\left(1.5,\mathrm{max}\left(1.0,1.0+500\cdot \frac{\mathrm{roughness}}{\mathrm{D__h_act}}\right)\right)$ Correction factor k_Re (Reynolds number dependency) is defined with: $\mathrm{k__Re}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{Re}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__k_Re_Elbow}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Total resistance is defined with: $\mathrm{zeta__act}=\mathrm{zeta__fri}$
 Type of Resistance = Bend (Circular) : The following diagram shows... (*) Reference[1] : page.357-339.   Inner hydraulic diameter is defined with: $\mathrm{D__h_act}=\mathrm{D__h}$ Flow area is defined with: $\mathrm{A__act}=\mathrm{A__cir}$ Geometrical coefficient for laminar flow is defined with: $\mathrm{Geo__act}=1$ Geometrical length for Bend to get the values from tables: $\mathrm{D0__Bend}=\mathrm{D__h}$ Local resistance is defined with: $\mathrm{zeta__loc}={\begin{array}{cc}\mathrm{k__Re}\cdot \mathrm{k__δ}\cdot \mathrm{A1__loc_Bend}\cdot \mathrm{B__loc_Bend}\cdot \mathrm{C__loc}& \mathrm{Re}>10000\\ \frac{\mathrm{A2__loc_Bend}}{\mathrm{max}\left(3000,\mathrm{Re}\right)}+\mathrm{A1__loc_Bend}\cdot \mathrm{B__loc_Bend}\cdot \mathrm{C__loc}& \mathrm{Re}\le 10000\end{array}$ Correction factor C is defined with: $\mathrm{C__loc}=1$ Correction factor A1 is defined with: $\mathrm{A1__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{θ}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A1_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor A2 is defined with: $\mathrm{A2__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{R0}}{\mathrm{D0__Bend}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A2_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor B is defined with: $\mathrm{B__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{R0}}{\mathrm{D0__Bend}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__B_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor k_delta (Roughness dependency) is defined with: $\mathrm{k__δ}={\begin{array}{cc}\mathrm{min}\left(1.5,1.0+0.001\cdot \frac{\mathrm{roughness}}{\mathrm{D__h_act}}\right)& \frac{\mathrm{R0}}{\mathrm{D0__Bend}}\le 0.55\\ \mathrm{min}\left(2.0,\mathrm{max}\left(1.0,\frac{\mathrm{λ__tur_roughness}}{\mathrm{λ__tur_smooth}}\right)\right)& \frac{\mathrm{R0}}{\mathrm{D0__Bend}}>0.55\end{array}$   Friction coefficient of smooth pipe for k_Re calculation is defined with: $\mathrm{λ__tur_smooth}=0.25\cdot {\left(\frac{1}{\mathrm{log10}\left(\frac{5.74}{\mathrm{max}{\left(\mathrm{Re},1.0\right)}^{0.9}}\right)}\right)}^{2}$ Friction coefficient of rough pipe for k_Re calculation is defined with  (Swamee and Jain's approximation[2]): $\mathrm{λ__tur_roughness}=0.25\cdot {\left(\frac{1}{\mathrm{log10}\left(\frac{\frac{\mathrm{roughness}}{\mathrm{D__h_act}}}{3.7}+\frac{5.74}{\mathrm{max}{\left(\mathrm{Re},1.0\right)}^{0.9}}\right)}\right)}^{2}$   Correction factor k_Re (Reynolds number dependency) is defined with: $\mathrm{k__Re}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{Re}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__k_Re_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Friction resistance is defined with: $\mathrm{zeta__fri}=\mathrm{θ}\cdot \mathrm{λ}\cdot \frac{\mathrm{R0}}{\mathrm{D__h_act}}$ The friction factor of flow is calculated with: $\mathrm{λ}=\mathrm{HeatTransfer.Functions.lambda_Re}\left(\mathrm{Re},\mathrm{roughness},\mathrm{D__h_act},\mathrm{Re__CoT},\mathrm{IF__speed},\mathrm{Geo__act}\right)$ (*) The above function $\mathrm{HeatTransfer.Functions.lambda_Re}$ is to calculated friction factor for Laminar and Turbulent flow.      Regarding the implementation of the friction factor calculation, see the reference section below.   Total resistance is defined with: $\mathrm{zeta__act}=\mathrm{zeta__loc}+\mathrm{zeta__fri}$
 Type of Resistance = Bend (Rectangular): (*) Reference[1]: page.357-339.   Inner hydraulic diameter is defined with: $\mathrm{D__h_act}=\frac{2}{\frac{1}{\mathrm{a__rec}}+\frac{1}{\mathrm{b__rec}}}$ Flow area is defined with: $\mathrm{A__act}=\mathrm{A__rec}$ Geometrical coefficient for laminar flow is defined with: $\mathrm{Geo__act}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{b__rec}}{\mathrm{a__rec}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__geo_rec}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Geometrical length for Bend to get the values from tables: $\mathrm{D0__bend}=\mathrm{a__rec}$ Local resistance is defined with: $\mathrm{zeta__loc}={\begin{array}{cc}\mathrm{k__Re}\cdot \mathrm{k__δ}\cdot \mathrm{A1__loc_Bend}\cdot \mathrm{B__loc_Bend}\cdot \mathrm{C__loc}& \mathrm{Re}>10000\\ \frac{\mathrm{A2__loc_Bend}}{\mathrm{max}\left(3000,\mathrm{Re}\right)}+\mathrm{A1__loc_Bend}\cdot \mathrm{B__loc_Bend}\cdot \mathrm{C__loc}& \mathrm{Re}\le 10000\end{array}$ Correction factor C is defined with: $\mathrm{C__loc}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{b__rec}}{\mathrm{a__rec}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__C_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor A1 is defined with: $\mathrm{A1__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{θ}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A1_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor A2 is defined with: $\mathrm{A2__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{R0}}{\mathrm{D0__Bend}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__A2_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor B is defined with: $\mathrm{B__loc_Bend}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\frac{\mathrm{R0}}{\mathrm{D0__Bend}}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__B_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Correction factor k_delta (Roughness dependency) is defined with: $\mathrm{k__δ}={\begin{array}{cc}\mathrm{min}\left(1.5,1.0+0.001\cdot \frac{\mathrm{roughness}}{\mathrm{D__h_act}}\right)& \frac{\mathrm{R0}}{\mathrm{D0__Bend}}\le 0.55\\ \mathrm{min}\left(2.0,\mathrm{max}\left(1.0,\frac{\mathrm{λ__tur_roughness}}{\mathrm{λ__tur_smooth}}\right)\right)& \frac{\mathrm{R0}}{\mathrm{D0__Bend}}>0.55\end{array}$   Friction coefficient of smooth pipe for k_Re calculation is defined with: $\mathrm{λ__tur_smooth}=0.25\cdot {\left(\frac{1}{\mathrm{log10}\left(\frac{5.74}{\mathrm{max}{\left(\mathrm{Re},1.0\right)}^{0.9}}\right)}\right)}^{2}$ Friction coefficient of rough pipe for k_Re calculation is defined with  (Swamee and Jain's approximation[2]): $\mathrm{λ__tur_roughness}=0.25\cdot {\left(\frac{1}{\mathrm{log10}\left(\frac{\frac{\mathrm{roughness}}{\mathrm{D__h_act}}}{3.7}+\frac{5.74}{\mathrm{max}{\left(\mathrm{Re},1.0\right)}^{0.9}}\right)}\right)}^{2}$   Correction factor k_Re (Reynolds number dependency) is defined with: $\mathrm{k__Re}=\mathrm{MapleSim.Interpolate1D}\left(\mathrm{data},\mathrm{Re}\right)$ (*) $\mathrm{MapleSim.Interpolate1D}$ is the function of Lookup table of 1D. (*) data is specified with:      - If data_source = inline, parameter $\mathrm{table__k_Re_Bend}$.      - If data_source = attachment, an attached file (.csv and .xls, .xlsx) is used.      - If data_source = file, need to specify the path of file (.csv and .xls, .xlsx).   Friction resistance is defined with: $\mathrm{zeta__fri}=\mathrm{θ}\cdot \mathrm{λ}\cdot \frac{\mathrm{R0}}{\mathrm{D__h_act}}$ The friction factor of flow is calculated with: $\mathrm{λ}=\mathrm{HeatTransfer.Functions.lambda_Re}\left(\mathrm{Re},\mathrm{roughness},\mathrm{D__h_act},\mathrm{Re__CoT},\mathrm{IF__speed},\mathrm{Geo__act}\right)$ (*) The above function $\mathrm{HeatTransfer.Functions.lambda_Re}$ is to calculated friction factor for Laminar and Turbulent flow.      Regarding the implementation of the friction factor calculation, see the reference section below.   Total resistance is defined with: $\mathrm{zeta__act}=\mathrm{zeta__loc}+\mathrm{zeta__fri}$
 (Reference) Detailed implementation of Friction factor calculation Friction factor of Laminar flow is calculated with: $\mathrm{λ__lam}=\mathrm{Geo__act}\cdot \frac{64}{\mathrm{Re}}$ And, Turbulent flow's friction factor is defined with (Swamee and Jain's approximation[2]): $\mathrm{λ__tur}=\frac{0.25}{\mathrm{log}{\left(\frac{\frac{\mathrm{roughness}}{\mathrm{D__h_act}}}{3.7}+\frac{5.74}{{\mathrm{Re}}^{0.9}}\right)}^{2}}$ Intermittency is defined with: $\mathrm{κ}=\frac{\mathrm{tanh}\left(\frac{\mathrm{IF__speed}\cdot \left(\mathrm{Re}-\mathrm{Re__CoT}\right)}{2}\right)+1}{2}$ So, the friction factor is calculated with: $\mathrm{λ}=\left(1-\mathrm{κ}\right)\cdot \mathrm{λ__lam}+\mathrm{κ}\cdot \mathrm{λ__tur}$ The following plot is Reynolds number vs Friction factor, and $\frac{\mathrm{roughness}}{\mathrm{D__h_act}}=0.001$, $\mathrm{IF__speed}=0.007$, $\mathrm{Re__CoT}=3500$, $\mathrm{Geo__act}=1$.

The definition of Flow calculation is the following and:

 Dynamics of mass = Static Pressure difference is calculated with Darcy–Weisbach equation: $\mathrm{dp}=\frac{1}{2}\cdot \mathrm{zeta__act}\cdot \frac{1}{{\mathrm{A__act}}^{2}\cdot {\begin{array}{cc}\mathrm{ρ__a}& \mathrm{dp}\ge 0\\ \mathrm{ρ__b}& \mathrm{others}\end{array}}\cdot {\mathrm{mflow}}^{2}\cdot \mathrm{sign}\left(\mathrm{mflow}\right)$
 Dynamics of mass = Dynamic In theory, Mass flow rate is calculated with Darcy–Weisbach equation: $\mathrm{mflow}=\sqrt{\frac{2\cdot {\mathrm{A__act}}^{2}}{\mathrm{zeta__act}}}\cdot \sqrt{{\begin{array}{cc}\mathrm{ρ__a}& \mathrm{dp}\ge 0\\ \mathrm{ρ__b}& \mathrm{others}\end{array}\cdot \left|\mathrm{dp}\right|}\cdot \mathrm{sign}\left(\mathrm{dp}\right)$ In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation: $\mathrm{mflow}=\sqrt{\frac{2\cdot {\mathrm{A__act}}^{2}}{\mathrm{zeta__act}}}\cdot \mathrm{HeatTransfer.Functions.regRoot2}\left(\mathrm{dp},\mathrm{dp_small},\mathrm{ρ__a},\mathrm{ρ__b},\mathrm{true},\mathrm{sharpness}\right)$ (*) $\mathrm{HeatTransfer.Functions.regRoot2}$ is the same function as $\mathrm{Modelica.Fluid.Utilities.regRoot2}$. To check the details of the package and view the original documentation, which includes author and copyright information, click here.

Definitions related to Mass flow rate and pressure:

$\mathrm{dp}=\mathrm{port_a.p}-\mathrm{port_b.p}$

$v=\frac{\mathrm{mflow}}{{\begin{array}{cc}\mathrm{ρ__a}& \mathrm{dp}\ge 0\\ \mathrm{ρ__b}& \mathrm{others}\end{array}\cdot \mathrm{A__act}}$

$\mathrm{port_a.mflow}=\mathrm{mflow}$

$\mathrm{port_b.mflow}=-\mathrm{mflow}$

Specific enthalpy is defined with:

$\mathrm{port_a.hflow}=\mathrm{inStream}\left(\mathrm{port_b.hflow}\right)$

$\mathrm{port_b.hflow}=\mathrm{inStream}\left(\mathrm{port_a.hflow}\right)$

Density is calculated with:

$\mathrm{ρ__a}=\mathrm{inStream}\left(\mathrm{port_a.rho}\right)$

$\mathrm{ρ__b}=\mathrm{inStream}\left(\mathrm{port_b.rho}\right)$

If Fidelity of properties = Constant, properties $\mathrm{μ}$ and $\mathrm{c__p}$ and $k$ are constants and properties at each ports are:

$\mathrm{μ__a}=\mathrm{μ}$

$\mathrm{μ__b}=\mathrm{μ}$

(*) Regarding the value of properties for Constant, see more in Air Settings.

If Fidelity of properties = Ideal Gas (NASA Polynomial), properties are calculated with:

$\mathrm{μ__a}=\mathrm{Function__vis}\left(\mathrm{inStream}\left(\mathrm{port_a.T}\right)\right)$

$\mathrm{μ__b}=\mathrm{Function__vis}\left(\mathrm{inStream}\left(\mathrm{port_b.T}\right)\right)$

(*) The properties are defined with NASA polynomials and coefficients, see more in Air Settings.

Port's variables are defined with:

$\mathrm{port_a.rho}=\mathrm{inStream}\left(\mathrm{port_b.rho}\right)$

$\mathrm{port_b.rho}=\mathrm{inStream}\left(\mathrm{port_a.rho}\right)$

$\mathrm{port_a.T}=\mathrm{inStream}\left(\mathrm{port_b.T}\right)$

$\mathrm{port_b.T}=\mathrm{inStream}\left(\mathrm{port_a.T}\right)$

 References [1] : Idelchik,I.E.: Handbook of hydraulic resistance. Jaico Publishing House, Mumbai, 3rd edition, 2006. [2] : Swamee P.K., Jain A.K. (1976): Explicit equations for pipe-flow problems. Proc. ASCE, J.Hydraul. Div., 102 (HY5), pp. 657-664.

Variables

 Symbol Units Description Modelica ID $\mathrm{dp}$ $\mathrm{Pa}$ Pressure difference p $\mathrm{mflow}$ $\frac{\mathrm{kg}}{s}$ Mass flow rate mflow $\mathrm{ρ__a}$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density at port_a rho_a $\mathrm{ρ__b}$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density at port_b rho_b $\mathrm{μ__a}$ $\mathrm{Pa}\cdot s$ Dynamic viscosity at port_a vis_a $\mathrm{μ__b}$ $\mathrm{Pa}\cdot s$ Dynamic viscosity at port_b vis_b $v$ $\frac{m}{s}$ Velocity of flow v $\mathrm{Re}$ $-$ Reynolds number for Friction factor calculation Re $\mathrm{Re__target}$ $-$ Targeted Reynolds number for Friction factor calculation Re_target $\mathrm{λ}$ $-$ Friction factor lambda $\mathrm{zeta__loc}$ $-$ Local resistance zeta_loc $\mathrm{zeta__fri}$ $-$ Friction resistance zeta_fri $\mathrm{zeta__act}$ $-$ Actual loss coefficient zeta_act $\mathrm{C__loc}$ $-$ Correction factor C for Elbow and Bend C_loc $\mathrm{A__loc_Elbow}$ $-$ Correction factor A for Elbow A_loc_Elbow $\mathrm{A1__loc_Bend}$ $-$ Correction factor A1 for Bend A1_loc_Bend $\mathrm{A2__loc_Bend}$ $-$ Correction factor A2 for Bend A3_loc_Bend $\mathrm{B__loc_Bend}$ $-$ Correction factor B for Bend B_loc_Bend $\mathrm{k__Re}$ $-$ Correction factor k_Re, Reynolds number dependency k_Re $\mathrm{k__δ}$ $-$ Correction factor k_delta, Roughness dependency K_delta $\mathrm{λ__tur_smooth}$ $-$ Friction coefficient of smooth pipe for k_Re calculation lambda_tur_smooth $\mathrm{λ__tur_roughness}$ $-$ Friction coefficient of rough pipe for k_Re calculation lambda_tur_roughness $\mathrm{D__h_act}$ $m$ Inner hydraulic diameter used for Fluid simulation Dh_act $\mathrm{A__act}$ ${m}^{2}$ Flow area used for Fluid simulation A_act $\mathrm{Geo__act}$ $-$ Geometrical coefficient used for Fluid simulation Geo_act $\mathrm{D0__Bend}$ $-$ Geometrical length for Bend to get values from tables D0_Bend

Connections

 Name Condition Description Modelica ID $\mathrm{port__a}$ Air Port $\mathrm{port_a}$ $\mathrm{port__b}$ Air Port $\mathrm{port_b}$ $\mathrm{zeta_in}$ if Use zeta as input = true Resistance coefficient input $\mathrm{zeta_in}$

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{WaterSettings1}$ $-$ Specify a component of Water simulation settings Settings $\mathrm{General}$ $-$ Select pipe type  - General  - Elbow with sharp corner (Circular)  - Elbow with sharp corner (Rectangular)  - Bend (Circular)  - Bend (Rectangular) TypeOfResistance $\mathrm{D__h}$ $0.1$ $m$ Internal hydraulic diameter if Type of Resistance is General or Elbow with sharp corner (Circular) or Bend (Circular). Dh $\mathrm{a__rec}$ $0.2$ $m$ Horizontal length if Type of Resistance = Elbow with sharp corner (Rectangular) or Bend (Rectangular). a_rec $\mathrm{b__rec}$ $0.1$ $m$ Vertical length if Type of Resistance = Elbow with sharp corner (Rectangular) or Bend (Rectangular). b_rec $\mathrm{A__cir}$ $\frac{1}{4}\cdot \mathrm{Pi__}\cdot {\mathrm{D__h}}^{2}$ ${m}^{2}$ Flow area if Type of Resistance is General or Elbow with sharp corner (Circular) or Bend (Circular). A_cir $\mathrm{A__rec}$ $\mathrm{a__rec}\cdot \mathrm{b__rec}$ ${m}^{2}$ Flow area if Type of Resistance = Elbow with sharp corner (Rectangular) or Bend (Rectangular). A_rec $\mathrm{R0}$ $0.1$ $m$ Radius of Neutral axis. R0 $\mathrm{θ}$ $\frac{30}{180}\cdot \mathrm{Pi}$ $\mathrm{rad}$ Angle of elbow/bend. theta $\mathrm{roughness}$ $0.000025$ $m$ Absolute roughness of pipe, with a default for a smooth steel pipe roughness $\mathrm{false}$ $-$ If true, use input for Resistance coefficient only if Type of Resistance is General. use_in_zeta $\mathrm{zeta}$ $0.15$ $-$ Resistance coefficient only if Type of Resistance is General and Use zeta as input = true zeta $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__rec}$ inline - See Data Source Options section above. DSM_geo_rec $\mathrm{table__rec}$ $\left[\begin{array}{cc}0& 1.5\\ 0.1& 1.323\\ 0.2& 1.192\\ 0.3& 1.094\\ 0.4& 1.023\\ 0.5& 0.9716\\ 0.6& 0.9360\\ 0.7& 0.9120\\ 0.8& 0.8983\\ 0.9& 0.8909\\ 1.0& 0.8887\end{array}\right]$ $-$ Geometrical coefficient for Rectangular pipe, if  = inline. [1] : b_rec / a_rec [2] : Geometrical coefficient table_geo_rec $\mathrm{data__rec}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_geo_rec $\mathrm{columns__rec}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_geo_rec 0 - Number of rows that are skipped from the top of the data table. skiprows_geo_rec $\mathrm{smoothness__rec}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_geo_rec $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__C_Elbow}$ inline - See Data Source Options section above. DSM_C_Elbow $\mathrm{table__C_Elbow}$ $\left[\begin{array}{cc}0.25& 1.10\\ 0.50& 1.07\\ 0.75& 1.04\\ 1.00& 1.00\\ 1.50& 0.95\\ 1.00& 0.90\\ 3.00& 0.83\\ 4.00& 0.78\\ 5.00& 0.75\\ 6.00& 0.72\\ 7.00& 0.71\\ 8.00& 0.70\end{array}\right]$ $-$ Correction factor C for Elbow, if  = inline. [1] : b_rec / a_rec [2] : Correction factor C table_C_Elbow $\mathrm{data__C_Elbow}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_C_Elbow $\mathrm{columns__C_Elbow}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_C_Elbow $\mathrm{skiprows__C_Elbow}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_C_Elbow $\mathrm{smoothness__C_Elbow__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_C_Elbow $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__A_Elbow}$ inline - See Data Source Options section above. DSM_A_Elbow $\mathrm{table__A_Elbow}$ $\left[\begin{array}{cc}0& 2.50\\ \frac{20}{180}\cdot \mathrm{Pi}& 2.50\\ \frac{30}{180}\cdot \mathrm{Pi}& 2.22\\ \frac{45}{180}\cdot \mathrm{Pi}& 2.87\\ \frac{60}{180}\cdot \mathrm{Pi}& 1.50\\ \frac{75}{180}\cdot \mathrm{Pi}& 1.28\\ \frac{90}{180}\cdot \mathrm{Pi}& 1.2\\ \frac{110}{180}\cdot \mathrm{Pi}& 1.2\\ \frac{130}{180}\cdot \mathrm{Pi}& 1.2\\ \frac{50}{180}\cdot \mathrm{Pi}& 1.2\\ \mathrm{Pi}& 1.2\\ & \end{array}\right]$ $-$ Correction factor A for Elbow, if  = inline. [1] : theta[rad] [2] : Correction factor A table_A_Elbow $\mathrm{data__A_Elbow}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_A_Elbow $\mathrm{columns__A_Elbow}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_A_Elbow $\mathrm{skiprows__A_Elbow}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_A_Elbow $\mathrm{smoothness__A_Elbow__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_A_Elbow $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__k_Re_Elbow}$ inline - See Data Source Options section above. DSM_k_Re_Elbow $\mathrm{table__k_Re_Elbow}$ $\left[\begin{array}{cc}10000& 1.4\\ 14000& 1.33\\ 20000& 1.26\\ 30000& 1.19\\ 40000& 1.14\\ 60000& 1.09\\ 80000& 1.06\\ 100000& 1.04\\ 140000& 1.00\\ 200000& 1.00\end{array}\right]$ $-$ Correction factor k_Re for Elbow, if  = inline. [1] : Reynolds number [2] : Correction factor k_Re table_k_Re_Elbow $\mathrm{data__k_Re_Elbow}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_k_Re_Elbow $\mathrm{columns__k_Re_Elbow}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_k_Re_Elbow $\mathrm{skiprows__k_Re_Elbow}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_k_Re_Elbow $\mathrm{smoothness__k_Re_Elbow__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_k_Re_Elbow $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__C_Bend}$ inline - See Data Source Options section above. DSM_C_Bend $\mathrm{table__C_Bend}$ $\left[\begin{array}{cc}0.25& 1.30\\ 0.50& 1.17\\ 0.75& 1.09\\ 1.00& 1.00\\ 1.50& 0.90\\ 1.00& 0.85\\ 3.00& 0.85\\ 4.00& 0.90\\ 5.00& 0.95\\ 6.00& 0.98\\ 7.00& 1.00\\ 8.00& 1.00\end{array}\right]$ $-$ Correction factor C for Bend, if  = inline. [1] : b_rec / a_rec [2] : Correction factor C table_C_Bend $\mathrm{data__C_Bend}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_C_Bend $\mathrm{columns__C_Bend}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_C_Bend $\mathrm{skiprows__C_Bend}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_C_Bend $\mathrm{smoothness__C_Bend__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_C_Bend $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__A1_Bend}$ inline - See Data Source Options section above. DSM_A1_Bend $\mathrm{table__A1_Bend}$ $\left[\begin{array}{cc}0& 0\\ \frac{20}{180}\cdot \mathrm{Pi}& 0.31\\ \frac{30}{180}\cdot \mathrm{Pi}& 0.45\\ \frac{45}{180}\cdot \mathrm{Pi}& 0.60\\ \frac{60}{180}\cdot \mathrm{Pi}& 0.78\\ \frac{75}{180}\cdot \mathrm{Pi}& 0.90\\ \frac{90}{180}\cdot \mathrm{Pi}& 1.00\\ \frac{110}{180}\cdot \mathrm{Pi}& 1.13\\ \frac{130}{180}\cdot \mathrm{Pi}& 1.20\\ \frac{50}{180}\cdot \mathrm{Pi}& 1.28\\ \mathrm{Pi}& 1.40\\ & \end{array}\right]$ $-$ Correction factor A1 for Bend, if  = inline. [1] : theta[rad] [2] : Correction factor A1 table_A1_Bend $\mathrm{data__A1_Bend}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_A1_Bend $\mathrm{columns__A1_Bend}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_A_1Bend $\mathrm{skiprows__A1_Bend}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_A1_Bend $\mathrm{smoothness__A1_Bend__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_A1_Bend $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__A2_Bend}$ inline - See Data Source Options section above. DSM_A2_Bend $\mathrm{table__A2_Bend}$ $\left[\begin{array}{cc}0.50000& 4000\\ 0.55000& 4000\\ 0.55001& 6000\\ 0.70000& 6000\\ 0.70001& 4000\\ 1.00000& 2000\\ 1.00001& 1000\\ 2.00000& 1000\\ 2.00001& 600\\ 2.50000& 600\end{array}\right]$ $-$ Correction factor A2 for Bend, if  = inline. [1] : R0 / Dh [2] : Correction factor A2 table_A2_Bend $\mathrm{data__A2_Bend}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_A2_Bend $\mathrm{columns__A2_Bend}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_A2_Bend $\mathrm{skiprows__A2_Bend}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_A2_Bend $\mathrm{smoothness__A2_Bend__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_A2_Bend $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__B_Bend}$ inline - See Data Source Options section above. DSM_B_Bend $\mathrm{table__B_Bend}$ $\left[\begin{array}{cc}0.50& 1.18\\ 0.60& 0.77\\ 0.70& 0.51\\ 0.80& 0.37\\ 0.90& 0.28\\ 1.00& 0.21\\ 1.25& 0.19\\ 1.50& 0.17\\ 2.00& 0.15\\ 4.00& 0.11\\ 6.00& 0.09\\ 8.00& 0.07\\ 10.00& 0.07\end{array}\right]$ $-$ Correction factor B for Bend, if  = inline. [1] : R0 / Dh [2] : Correction factor B table_B_Bend $\mathrm{data__B_Bend}$ $2$ - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_B_Bend $\mathrm{columns__B_Bend}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_B_Bend $\mathrm{skiprows__B_Bend}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_B_Bend $\mathrm{smoothness__B_Bend__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_B_Bend $\mathrm{data}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{source__k_Re_Elbow}$ inline - See Data Source Options section above. DSM_k_Re_Elbow $\mathrm{table__k_Re_Elbow}$ $\left[\begin{array}{ccccccccccccccc}0.00000& 999& 1000& 1400& 2000& 3000& 4000& 6000& 8000& 10000& 14000& 20000& 30000& 40000& 40001\\ 0.50000& 1.40& 1.40& 1.33& 1.26& 1.19& 1.14& 1.09& 1.06& 1.04& 1.00& 1.00& 1.00& 1.00& 1.00\\ 0.55000& 1.40& 1.40& 1.33& 1.26& 1.19& 1.14& 1.09& 1.06& 1.04& 1.00& 1.00& 1.00& 1.00& 1.00\\ 0.55001& 1.67& 1.67& 1.58& 1.49& 1.40& 1.34& 1.26& 1.21& 1.19& 1.17& 1.14& 1.06& 1.00& 1.00\\ 0.70000& 1.67& 1.67& 1.58& 1.49& 1.40& 1.34& 1.26& 1.21& 1.19& 1.17& 1.14& 1.06& 1.00& 1.00\\ 0.70001& 2.00& 2.00& 1.89& 1.77& 1.64& 1.56& 1.46& 1.38& 1.30& 1.15& 1.02& 1.00& 1.00& 1.00\\ 0.70002& 2.00& 2.00& 1.89& 1.77& 1.64& 1.56& 1.46& 1.38& 1.30& 1.15& 1.02& 1.00& 1.00& 1.00\end{array}\right]$ $-$ Correction factor k_Re for Elbow, if  = inline. [u:column] :R0 / Dh [v:row] : Reynolds number [value] : Correction factor k_Re table_k_Re_Elbow $\mathrm{data__k_Re_Elbow}$  - Geometrical coefficient for Rectangular pipe, if  =file or attachment. You can specify data by using an attached file or specifying the path of file (.csv and .xls, .xlsx) data_k_Re_Elbow $\mathrm{columns__k_Re_Elbow}$ $\left[2\right]$ - Determines which columns of the data table will be used to interpolate. For example, in an Excel spreadsheet, column A corresponds with 1, column B corresponds with 2, and so on. columns_k_Re_Elbow $\mathrm{skiprows__k_Re_Elbow}$ 0 - Number of rows that are skipped from the top of the data table. skiprows_k_Re_Elbow $\mathrm{smoothness__k_Re_Elbow__}$ Table points are linearly interpolated - Determines whether the data points will be interpolated linearly or with a cubic spline. smoothness_k_Re_Elbow $\mathrm{dp__small}$ $0.1$ $\mathrm{Pa}$ Approximation of function for |dp| <= dp_small dp_small $\mathrm{sharpness}$ $1.0$ $-$ Sharpness of approximation for sqrt(dp) and sqrt(rho * dp) sharpness $\mathrm{T__const}$ $0.001$ $s$ Time constant for Reynolds number calculation T_const $\mathrm{Re__CoT}$ $3500$ $-$ Reynolds number of the center of Transition zone Re_CoT $0.007$ $-$ Changing rate of Intermittency factor IF_spread