Problem $3$:

A rectangular weir of height $2\mathrm{.}2ft$ and length $105ft$ is installed in a river that is $125ft$ wide and initially flowing at a velocity of $1\mathrm{.}7f\frac{t}{s}$ and depth of $1\mathrm{.}9ft.$ The weir has $4$ piers each $0\mathrm{.}6ft$ wide. Find the increase in water level due to the installation of the weir. $[10]$

Hint: Remember when a weir is installed the upstream water level will rise while the downstream water level will remain the same. Assess whether it is free weir or submerged and contracted or suppressed weir. The approach velocity is not the same as initial velocity as the upstream depth will rise, the flow area will be $(P+H)W.$ The length to be used must not include piers. The piers will cause contractions and if it is a contracted weir, it will have two additional contractions. The discharge coefficient can be found using the equation for rectangular sharp crested weir.