A rectangular concrete channel of width $10$ m and whose slope is $0\mathrm{.}01$ carries a flow of $12$ m$3/$s$.$ Compute the normal depth and the critical depth and determine the flow regime. Now, imagine that an obstruction is placed at the location in the stream causing the water level to rise by $3$ m about the normal depth. Compute the backwater profile until the water depth reaches $10\%$ above the normal depth