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Kim H. Parker added There_is_no_reason_why__.tex
about 8 years ago
Commit id: 93a0b106f284d5ab6c947f30091f230171c350d4
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There is no reason why the method cannot be used to obtain a local wave speed by suing the whole of the calculated data, including the transient period at start of the calculation which arises because of the assumption that $P = U = 0$ before the periodic inlet conditions are started at $t = 0$. This portion of the calculation is not very physiological (except possible as a model for restarting the cardiovascular system after bypass surgery). The transient period is governed by the same physical laws and we might expect that the statistical approach to the problem will be valid during transient periods as well.
It turns out that $c_{IT}$ remains an excellent estimate of $$ when the whole of the calculated data is used.
\begin{table}
\begin{tabular}{ccccc}
location & $x/L$ & $$ & $c_{IT}$ & $c_{SS}$ \\
1 & 0 & 5.13 & 5.25 & 4.45 \\
2 & .025 & 5.13 & 5.25 & 4.47 \\
3 & .05 & 5.13 & 5.26 & 4.50 \\
4 & .075 & 5.13 & 5.27 & 4.52 \\
5 & .10 & 5.13 & 5.29 & 4.55 \\
6 & .25 & 5.13 & 5.28 & 4.69 \\
7 & .50 & 5.13 & 5.22 & 4.98 \\
8 & .75 & 5.13 & 5.23 & 5.56 \\
9 & 1 & 5.13 & 5.23 & 6.84 \\
\end{tabular}
\caption{Theoretical and estimated wave speeds for data calculated at different locations in the vessel using all of the data.}
\end{table}
