Determine the dimension of the vertical side walls for a rectangular open channel designed to convey 150 cfs of storm water runoff. The runoff is collected in the parking lots and roofs of a 5 acre shopping mall. The open channel is six foot wide and is to be constructed out of cast-in-place concrete. The roughness coefficient for the rough formed new concrete is 0.016. The bottom of the channel is placed at a 1.25 % slope to direct the flow to a nearby river. The designed side wall dimension must allow for a 2 foot freeboard at a flow rate of 150 cfs to prevent the storm water from flowing out of the channel and flood the adjacent field.  

Solution:

Step 1: Use the Chezy-Manning Eqn. and determine the depth of flow for 150 cfs.  

Q = (1.49/n) (A)(R)^.67(S)^.5 = 150 cfs =(1.49/0.016)(A)(R)^.67(0.0125)^.5

Cannot determine A and R without depth.                      Channel width = 6 ft

A = 6d             R = A/P            P = 2d + 6          R = 6d/(2d + 6)  

Step 2: Determine (A)(R)^.67 from the known values. 

 (A)(R)^.67 = (Q)(n)/(1.49)(S)^.5 = (150)(0.016)/(1.49)(0.0125)^.5 = 14.4  

Step 3: Trial and Error solution using a table:

Step 4: Flow depth = 2.1 ft plus 2 ft freeboard = 4.1 ft