symbol | definition |
\( m \) | Mass [kg] |
\( \rho \) | Mass density \( [kg/m^3] \) |
\( \mathbf{P} \) | Linear momentum \( [kg\, m/s] \) |
\( \mathbf{v} \) | Velocity or specific linear momentum [m/s] |
\( K \) | Kinetic energy \( [kg\, m^2/s^2] \) |
\( \mathbf{v\cdot v}/2 \) | Specific kinetic energy \( [m^2/s^2] \) |
\( B \) | Generic extensive property |
\( \beta \) | Generic specific intensive property per mass unit |
\( \mathbf{n} \) | Outward unit normal for the surface \( A(t) \) |
\( \mathbf{e}_i \) | Orthogonal unit vectors |
\( T_{ik} \) | Coordinate stresses [Pa] |
\( T \) | Stress matrix |
\( T_{iI} \) | Normal stresses |
\( T_{ij} \) | Shear stresses, when \( i\neq k \) |
\( \mathbf{T} \) | Stress tensor [Pa] |
\( \gamma \) | Shear strain [] |
\( \epsilon_v \) | Volumetric strain [] |
\( \eta \) | Modulus of elasticity [Pa] |
\( \nu \) | Poisson's ratio [] |
\( \varepsilon_v=E_{ii} \) | Voumetric strain |
\( w \) | Stress work per unit volume |
\( \boldsymbol{T}_0 \) | The first Piola-Kirchhoff stress tensor |
PKS | Piola-Kirchhoff stress tensor |
\( \boldsymbol{S} \) | The second Piola-Kirchhoff stress tensor |
\( p \) | Thermodynamical pressure |
\( R \) | Gas constant for a particular gas |
$ \alpha$ | Womersley parameter |
\( pp \) | Pulse pressure [mmHg] |
\( CO \) | Cardiac output [ml/min] |
\( \tau=RC \) | Relaxation time \( s \) |
\( \dot{V} \) | Rate of change in volume |
\( Q_{i} \) | Flow rate into a volume |
\( Q_o \) | Flow rate out of a volume |
\( Q \) | Volumetric flow rate. |
\( \delta \) | Nonlinear velocity profile correction factor |
\( \delta \) | Correction factor |
\( C_1 \) | Arbitrary constant |
\( \delta'=\delta+1 \) | The modified correction factor |
\( Z_c^f \) | Characteristic impedance for a forward traveling wave |
\( Z_c^b \) | Characteristic impedance for a backward traveling wave |
\( \rho_{w} \) | Density of vessel wall |
\( \tau_w = \tau_{rz}\vert_{r=r_i} \) | Wall shear stress |
\( \delta_{ij} \) | Kronecker delta |
\( e_{ijk} \) | Permutation symbol [] |