Question

Please give detailed solution

A long rectangular unfinished concrete channel of width 3.6 m carries a flow of 14 m/s, with an abrupt change in slope from 0.0019 to 0.0180 at the midpoint of the channel. Determine: a) the uniform flow depths upstream and downstream of the change in slope, b) the critical flow depth, and c) the water surface profile types upstream and downstream of the change in slope.

Answer 1

Upstream manning eq. eta = roughness coefficient for unfinished c n = 0.014 Q = 1/n A R^2/3 s^1/2 A = B.middot y , R = B middot y/(3.6 + 2y) = 3.6y/(3.6 - 2y) 14 = 1/0.014 (3.6 y) (3.6y/3.6 + 2y)^2/3 squareroot 0.0019 y = 1.45 m 4/5 normal depth (2) Down stream normal depth Q = 1/n A R^2/3 s^1/2 14 = 1/0.014 (3.6y) (3.6y/3.6 + 2y)^2/3 squareroot 0.0180 y_n = 0.66 m (2) Critical depth (y_c) Q^2 T/A^3 g = 1 rightdoublearrow (1.41^2 times 3.6/(y_c times 3.6)^3 times 9.81 = 1 y_c = 1.16 m at upstream y_n > y_c rightarrow mild slope downstream y_n < y_c rightarrow st slope