Two canals join to form a larger canal as shown in Video $\backslash (\backslash$underline$\{10\mathrm{.}4\mathrm{.}1\}\backslash )$ and the figure below. Each of the three rectangular canals is lined with the same material and has the same bottom slope. The water depth in each is to be $2$ m $.$

$($a$)$ Determine the width of the merged canal, $\backslash ($ b $\backslash ).$ Explain physically $($i$.$e$.,$ without using any equations$)$ why it is expected that the width of the merged canal is less than the combined widths of the two original canals $($i$.$e$.,\backslash ($ b$<mn>4</mn><mtext></mtext><mi>\backslash </mi>$mathrm$\{$~m$\}+8\backslash$mathrm$\{$~m$\}=12\backslash$mathrm$\{$~m$\}\backslash )).$