Problem $4($Ch$.1-4,7)$

a$)$ Using the data in the table to calculate the total rain fall, and the average rain fall intensity for the event $(10\text{'}).$

b$)$ If the net storm rain fall is $1\mathrm{.}2$ inch, determine the exact Phi $()$ index $($in$./$hr$)$ for the drainage basin $($assumed the loss only from infiltration, $15\text{'}).$

$\backslash$table$[[$Time $($hr$),$Incremental Rain Fall $($in$)],[0,0],[0\mathrm{.}5,0\mathrm{.}5],[1,0\mathrm{.}6],[1\mathrm{.}5,0\mathrm{.}4],[2,0\mathrm{.}8],[2\mathrm{.}5,0\mathrm{.}3],[3,0\mathrm{.}5],[3\mathrm{.}5,0\mathrm{.}2]]$

${}_1=\frac{{\displaystyle \underset{i}{\overset{?}{}}}{P}_i-DR}{Nt}=\frac{{\displaystyle \underset{i=1}{\overset{N}{}}}(it)-DR}{Nt}$

${}_2=\frac{{\displaystyle \underset{i=1}{\overset{N}{}}}(it)-DR-{\displaystyle \underset{i=1}{\overset{M^{**}}{}}}(i^{\text{'}}t)}{N^{**}t},it=P_i$

$N=N^{**}+M^{**}$