A rectangular channel with a bottom width b$1=5\mathrm{.}0$ ft transitions to a

downstream trapezoidal channel with a bottom width b$2=7\mathrm{.}5$ ft and

side slopes m$2=2.$ The transition bottom drops $1$ ft from the rectangular upstream channel to the downstream trapezoidal channel. The flow rate

Q $=25$ ft$3/$s$,$ the upstream flow depth y$1=2\mathrm{.}0$ ft and the downstream

flow depth y$2=2\mathrm{.}2$ ft$.$ Calculate the head loss through the transition