$$ \newcommand{\partd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\partdd}[2]{\frac{\partial^{2} #1}{\partial {#2}^{2}}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\Int}{\int\limits} \newcommand{\D}{\displaystyle} \newcommand{\dA}{\; \mbox{dA}} \newcommand{\dz}{\; \mbox{dz}} $$

 

 

 

Nomenclature

symbol definition
\( \dot{V} \) 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