10.7: Nomenclature
- Page ID
- 53625
Table \(\PageIndex{1}\): Nomenclature
\(A\) | area, \(m^2\), absorption factor |
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\(\mathscr{A}\) | closed surface area of the control volume \(\mathscr{V}\), \(m^2\) |
\(\mathscr{A}_a (t)\) | closed surface area of an arbitrary, moving control volume \(\mathscr{V}_A(t)\), \(m^2\) |
\(A_c\) | area of the entrances and exits for the control volume \(\mathscr{V}\), \(m^2\) |
\(A_c (t)\) | area of the entrances and exits for the control volume \(\mathscr{V}_A(t)\), \(m^2\) |
\(\mathscr{A}_m (t)\) | surface area of a body, \(m^2\) |
\(AW_J\) | atomic mass of the \(J^{th}\) atomic species, g/mol |
\(\mathbf{A}\) | atomic matrix, also identified as \(\begin{bmatrix} N_{JA} \end{bmatrix}\) |
\(\mathbf{A}^*\) | row reduced echelon form of the atomic matrix, also identified as \(\begin{bmatrix} N_{JA} \end{bmatrix}^*\) |
\(\mathbf{B}\) | Bodenstein matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}_B\) |
\(c_A\) | \(\rho_A / MW_A\), molar concentration of species \(A\), mol/\(m^2\) |
\(c\) | \(\sum_{A=1}^{A=N} c_A\), total molar concentration, mol/\(m^3\) |
C | conversion |
\(D\) | diameter, m |
\(\mathbf{f}\) | vector force, N |
\(f\) | magnitude of the force vector, N |
\(\mathbf{g}\) | gravity vector, m/\(s^2\) |
\(g\) | magnitude of the gravity vector, m/\(s^2\) |
\(h\) | height, m |
\(\mathbf{I}\) | unit matrix |
\(K_{eq,A}\) | equilibrium coefficient for species \(A\) |
\(L\) | length, m |
\(m\) | mass, kg |
\(\dot{m}\) | mass flow rate, kg/s |
\(m_A\) | mass of species \(A\), kg |
\(\dot{m}_A\) | mass flow rate of species \(A\), kg/s |
\(\dot{M}_A\) | molar flow rate of species \(A\), mol/s |
\(\dot{M}\) | \(\sum_{A=1}^{A=N} \dot{M}_A\) total molar flow rate, mol/s |
\(MW_A\) | molecular mass of species \(A\), g/mol |
\(\mathbf{M}\) | mechanistic matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}_M\) |
\(\mathbf{n}\) | outwardly directed unit normal vector |
\(n\) | \(\sum_{A=1}^{A=N} n_A\), total number of moles |
\(n_A\) | number of moles of species \(A\) |
\(N\) | number of molecular species in a multicomponent system |
\(N_{JA}\) | number of \(J\)-type atoms associated with molecular species \(A\) |
\(\begin{bmatrix} N_{JA} \end{bmatrix}\) | atomic matrix, also identified as \(\mathbf{A}\) |
\(\begin{bmatrix} N_{JA} \end{bmatrix}^*\) | row reduced echelon form of the atomic matrix, also identified as \(\mathbf{A}^*\) |
\(p\) | \(\sum_{A=1}^{A=N} p_A\) total pressure, N/\(m^2\) |
\(p_A\) | partial pressure of species \(A\), N/\(m^2\) |
\(p_{A,vap}\) | vapor pressure of species \(A\), N/\(m^2\) |
\(p_g\) | \(p - p_o\), gauge pressure, N/\(m^2\) |
\(p_o\) | reference pressure (usually atmospheric), N/\(m^2\) |
\(\mathbf{P}\) | pivot matrix that maps \(\mathbf{R}_P\) onto \(\mathbf{R}_{NP}\) |
\(Q\) | volumetric flow rate, \(m^3\)/s |
\(r\) | radial position, m |
\(R\) | universal gas constant, see Table 5-1 for units |
\(r_A\) | net mass rate of production of species \(A\) per unit volume, kg/\(m^3\)s |
\(R_A\) | \(r_A/ MW_A \), net molar rate of production of species \(A\) per unit volume, mol/\(m^3\)s |
\(\mathbf{R}_M\) | column matrix of all net rates of production, mol/\(m^3\)s |
\(\mathbf{R}\) | column matrix of net rates of production of stable species, mol/\(m^3\)s |
\(\mathbf{r}\) | column matrix of elementary reaction rates, mol/\(m^3\)s |
\(\mathbf{R}_B\) | Bodenstein column matrix of net rates of production of Bodenstein products, mol/\(m^3\)s |
\(\mathbf{R}_P\) | column matrix of net molar rates of production of the pivot species, mol/\(m^3\)s |
\(\mathbf{R}_{NP}\) | column matrix of net molar rates of production of the non-pivot species, mol/\(m^3\)s |
\(\mathscr{R}_A\) | net global molar rate of production of species \(A\), mol/s |
\(\mathbf{S}\) | stoichiometric matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}\) |
S | selectivity |
\(T\) | temperature, K |
\(t\) | time, s |
\(\mathbf{u}_A\) | \(\mathbf{v}_A - \mathbf{v}\), mass diffusion velocity of species \(A\), m/s |
\(\mathbf{u}_A^*\) | \(\mathbf{v}_A - \mathbf{v}^*\), molar diffusion velocity of species \(A\), m/s |
\(\mathbf{v}_A\) | species \(A\) velocity, m/s |
\(\mathbf{v}\) | \(\sum_{A=1}^{A=N} \omega_A v_A\), mass average velocity, m/s |
\(\mathbf{v}^*\) | \(\sum_{A=1}^{A=N} x_A v_A\), molar average velocity, m/s |
\(v\) | magnitude of velocity vector, m/s |
\(\mathbf{v}_r\) | relative velocity, m/ |
\(V_A\) | partial molar volume of species \(A\), \(m^3\) |
\(V\) | volume, \(m^3\) |
\(\mathscr{V}_a (t)\) | volume of an arbitrary moving control volume, \(m^3\) |
\(\mathscr{V} (t)\) | volume of a specific moving control volume, \(m^3\) |
\(\mathscr{V}_m (t)\) | volume of a body which is referred to as a material volume, \(m^3\) |
\(\mathscr{V}\) | volume of a fixed control volume, \(m^3\) |
\(v_x, v_y, v_x\) | components of the velocity vector, \(\mathbf{v} = \mathbf{i}v_x + \mathbf{j}v_y + \mathbf{k}v_z\), m/s |
\(\mathbf{w}\) | velocity of the surface of the arbitrary moving control volume \(\mathscr{V}_a (t)\), m/s |
\(x_A\) | \(c_A/c\), mole fraction of species \(A\) in the liquid phase |
\(y_A\) | \(c_A/c\), mole fraction of species \(A\) in the gas phase |
\(x,y,z\) | rectangular Cartesian coordinates, m |
\(\mathbf{Y}\) | yield |
Greek Letters | |
\(\lambda\) | unit tangent vector. |
\(\gamma\) | \(\rho / \rho_{\ce{H2O}}\), specific gravity |
\(\theta\) | angle, radians |
\(\nu\) | \(\mu / \rho\), kinematic viscosity, \(m^2\)/s |
\(\nu_{A\alpha}\) | stoichiometric coefficient for species \(A\) in the \(\alpha\)-reaction |
\(\rho_A\) | mass density of species \(A\), kg/\(m^3\) |
\(\rho\) | \(\sum_{A=1}^{A=N} \rho_A\), total mass density, kg/\(m^3\) |
\(\omega_A\) | \(\rho_A / \rho\), mass fraction of species \(A\) |
\(\varepsilon\) | void fraction, volume of void space per unit volume |
\(\mu\) | viscosity, \(\mathbf{P}\) |
\(\boldsymbol{\mu}\) | specific growth rate, \((m^3 \ s)^{-1}\) |
\(\sigma\) | surface tension, N/m |
\(\tau\) | residence time, s |