For a river flow such as the one shown below an average velo

For a river flow such as the one shown below, an average velocity in vertical elevation can be estimated by the arithmetic average of the velocities at 0.2 and 0.8 of total depth d. Measurements at station distance 80 ft are 1.2 ft/s at 0. 2 d & 2.0 ft/s at 0.8d, and at station distance 100 ft are 0.8 ft/s and 1.3 ft/s. Breaking up the cross-section into two rectangles of area approximately the same area as the sections 73-87 ft and 87-113 ft, estimate the bankfull stage volumetric flow rate of the river.

Solution

The average velocity of low at the station 80 ft = V₈₀ = (1.2+2)/2 = 1.6 ft/s

The average velocity of low at the station 100 ft = V₁₀₀ = (0.8+1.3)/2 = 1.05 ft/s

The depth at the section 87 ft = 99.1- 97.2 = 1.9 ft

So, the average depth = 1.9 ft

Width of bankfull stage = 40 ft

Area of the cross section, A = 40*1.9 = 76 ft²

The average velocity of flow, V_avg = (1.6 + 1.05)/2 = 1.3 ft/s

Hence, the volumetric flow rate of the river = A* V_avg = 76*1.3 = 98.8 ft³/s