Stormwater will be transported through a circular crosssecti

Stormwater will be transported through a circular cross?section (radius = R), finished concrete channel (n = 0.014) that has slope = 0.0025. For a constant flow area (Ac = 0.25 m2 ), examine how the flow rate of water through the channel varies over flow depth?to?radius ratios in the range 0.1 ? y/R ? 1.9. As you increase the ratio y/R, you will need to decrease the channel radius R to maintain a constant flow area.

a. Prepare a table showing the values of y/R (in 0.1 increments) and the corresponding values for the channel radius (R in m) and flow rate (m3 /s).  

b. Prepare a figure showing flow rate (m3 /s) as a function of y/R.  

c. What value of y/R provides the most efficient flow?

Solution

This is derived by formula y=R/2 (1-cos (theta/2) . From this y/R =1/2 (1-cos (theta/2) . Now putting the value of y/R from 0.1 to 1.9 for an increment of 0.1 we can find R . Flow rate can be calculated from formula Q=(k/n )AR^2/3S^1/2 where n is .014 and s is .0025 , A is available so for each value of R from earlier formula , we can computer Q.