Added eq:kappa and renamed indices of eq:Phi(_mn)
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lrftubes.lyx
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lrftubes.lyx
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@ -2343,8 +2343,8 @@ Dynamic viscosity of a gas mixture
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\end_layout
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\begin_layout Standard
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The dynamic viscosity of a gas mixture can be derived from the dynamic viscosity
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of pure gases as
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The dynamic viscosity of a gas mixture can be derived from the dynamic viscositi
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es of pure gases as
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\begin_inset CommandInset citation
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LatexCommand cite
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after "p. 27"
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@ -2356,42 +2356,42 @@ literal "false"
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:
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\begin_inset Formula
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\begin{equation}
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\mu_{\mathrm{mix}}=\sum_{n=0}^{N-1}\frac{x_{n}\mu_{n}}{\sum_{m=0}^{N-1}\Phi_{nm}x_{m}},\label{eq:mumix}
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\mu_{\mathrm{mix}}=\sum_{α=0}^{N-1}\frac{x_{α}\mu_{α}}{\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}},\label{eq:mumix}
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\end{equation}
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\end_inset
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where
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\begin_inset Formula $\mu_{n}$
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\begin_inset Formula $\mu_{α}$
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\end_inset
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denotes the pure substance dynamic viscosity of species
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\begin_inset Formula $n$
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is the dynamic viscosity of pure chemical species
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\begin_inset Formula $α$
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\end_inset
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, and
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\begin_inset Formula $x_{n}$
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and
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\begin_inset Formula $x_{α}$
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\end_inset
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denotes its mole fraction in the mixture.
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\begin_inset Formula $\Phi_{mn}$
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\begin_inset Formula $\Phi_{αβ}$
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\end_inset
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is defined as:
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\begin_inset Formula
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\begin{equation}
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\Phi_{mn}=\frac{1}{\sqrt{8}}\left(1+\frac{M_{n}}{M_{m}}\right)^{-1/2}\left[1+\left(\frac{\mu_{n}}{\mu_{m}}\right)^{1/2}\left(\frac{M_{m}}{M_{n}}\right)^{1/4}\right]^{2},
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\Phi_{αβ}=\frac{1}{\sqrt{8}}\left(1+\frac{M_{α}}{M_{β}}\right)^{-1/2}\left[1+\left(\frac{\mu_{α}}{\mu_{β}}\right)^{1/2}\left(\frac{M_{β}}{M_{α}}\right)^{1/4}\right]^{2},\label{eq:Phi_mn}
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\end{equation}
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\end_inset
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where
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\begin_inset Formula $M_{i}$
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\begin_inset Formula $M_{α}$
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\end_inset
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is the molar mass of species
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\begin_inset Formula $i$
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\begin_inset Formula $α$
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\end_inset
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.
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@ -2407,7 +2407,7 @@ reference "eq:mumix"
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\end_inset
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can efficiently be solved by noting that
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\begin_inset Formula $d_{n}=\sum_{m=0}^{N-1}\Phi_{nm}x_{m}$
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\begin_inset Formula $d_{α}=\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}$
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\end_inset
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is a matrix-vector product, which can be written as
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@ -2417,6 +2417,65 @@ reference "eq:mumix"
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.
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\end_layout
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\begin_layout Subsubsection
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Thermal conductivity of a gas mixture
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\end_layout
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\begin_layout Standard
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The thermal conductivity of a gas mixture can be derived from the thermal
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conductivities of pure gases as
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\begin_inset CommandInset citation
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LatexCommand cite
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after "p. 276"
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key "bird_transport_2007"
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literal "false"
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\end_inset
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:
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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k_{mix}=\sum_{α=0}^{N-1}\frac{x_{α}k_{α}}{\sum_{β=0}^{N-1}\Phi_{αβ}x_{β}}\label{eq:kappamix}
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\end{equation}
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\end_inset
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\end_layout
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\begin_layout Standard
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where
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\begin_inset Formula $k_{α}$
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\end_inset
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is the thermal conductivity of pure chemical species
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\begin_inset Formula $α$
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\end_inset
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and
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\begin_inset Formula $x_{α}$
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\end_inset
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denotes its mole fraction in the mixture and
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\begin_inset Formula $\Phi_{αβ}$
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\end_inset
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is identical to that appearing in the viscosity equation, see
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "eq:Phi_mn"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\end_layout
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\begin_layout Subsection
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Combustion
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\end_layout
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@ -7015,6 +7074,27 @@ Membrane
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A membrane is a mechanical
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\end_layout
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\begin_layout Section
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Hole
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\end_layout
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\begin_layout Standard
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series_impedance.py/class CircHoleNeck(SeriesImpedance)
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\end_layout
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\begin_layout Standard
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Behaves like an acoustic mass with losses.
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It represents holes in sheet material, which can form the neck of a Helmholtz
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resonator.
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Hole-hole interaction is neglected.
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The resistance term is an approximation.
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\end_layout
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\begin_layout Standard
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Usable for connecting volumes to eachother or volumes to ducts, to form
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Helmholtz resonators.
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\end_layout
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\begin_layout Section
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End corrections and discontinuities
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\begin_inset CommandInset label
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@ -9606,7 +9686,7 @@ n
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\end_layout
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\begin_layout Standard
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The coarse 0impedance of a Helmholtz resonator repeated here:
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The coarse impedance of a Helmholtz resonator repeated here:
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\begin_inset Formula
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\begin{equation}
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Z(\omega)=\underbrace{i\omega m_{A}+R_{v}}_{Z_{h}}+\frac{\rho_{0}c_{0}^{2}}{i\omega V},
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