$2.(15$ pts$)$ A proposed bridge crossing has a trapezoidal channel approach section with a bottom width of $10$ feet and $3$horizontal:$1$vertical side slopes with an estimated flow depth of $4$ feet for the $200$ ft$3/$s design flood event.$$ The channel through the bridge opening is a rectangular channel section.$$ Assuming a smooth, horizontal transition with no losses, what is the minimum bridge opening width that will not increase the upstream flow depth.