Pre-Analysis & Start-Up

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{\large
\begin{eqnarray*}
\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{v})=0
\end{eqnarray*}
}

However, as blood can be regarded as an incompressible fluid, the rate of density change is zero, thus since we are considering only the steady case, the time-dependent term is zero. Thus, the continuity equation above can be further simplified in the form below:

{\large
\begin{eqnarray*}
\nabla \cdot \textbf{v}=0
\end{eqnarray*}
}

The Navier-Stokes Equation is written as follows:

{\large
\begin{eqnarray*}
\rho (\frac{d \textbf{v}}{dt}+\textbf{v} \cdot \nabla \textbf{v})=- \nabla p + \mu \nabla ^2 \textbf{v} + \textbf{f}
\end{eqnarray*}
}

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Outlets:
The systolic pressure of a healthy human is around 120 mmHg and the diastolic pressure of a healthy human is around 80 mmHg. Thus taking the average pressure of the two phases, we use 100 mmHg (around 13332 Pascal) as the static gauge pressure at the outlets.

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