Two brass pipes $($a large pipe and a small pipe$)$ are connected with water flowing from the smaller pipe into the larger pipe from left to right $($as shown in the figure below$).$ If the flowrate is $5$ cfs $,$ the length and area of the smaller pipe is ${100}^{\text{'}}$ and $0\mathrm{.}5f{t}^2,$ and the length and area of the larger pipe is ${75}^{\text{'}}$ and $0\mathrm{.}5f{t}^2,$ what is the pressure difference between the two pipes $($i$.$e$.,$ what is $\frac{P_{\text{l}\text{a}\text{r}\text{g}\text{e}\text{P}\text{i}\text{p}\text{e}}}{}-\frac{P_{\text{s}\text{m}\text{a}\text{l}\text{l}\text{p}\text{i}\text{p}\text{e}}}{})?$ Assume the water is at $70F$ and standard pressure.