The section areas can be calculated like
a1 = (1 m) ((4 m) - (0 m)) / 2
= 2 m2
a2 = (1.5 m) ((6 m) - (2 m)) / 2
= 3 m2
a3 = (0.9 m) ((8 m) - (4 m)) / 2
= 1.8 m2
The flow rates can be calculated as
q1 = (3 m/s) (2 m2)
= 6 m3/s
q2 = (4 m/s) (3 m2)
= 12 m3/s
q3 = (3 m/s) (1.8 m2)
= 5.4 m3/s
The total flow can be summarized as
Q = (6 m3/s) + (12 m3/s) + (5.4 m3/s)
= 23.4 m3/s
Note - there are alternative ways to calculate the section flow rates:
Using the simple average of two successive vertical depths, their mean velocity, and the distance between them can be expressed as
qn to n+1 = [(vn + vn+1) / 2] [(dn + dn+1 ) / 2] (ln+1 - ln) (4)
With the midsection method, the depth and mean velocity are measured for each number of verticals along the cross section. The depth at a vertical is multiplied by the width, which extends halfway to the preceding vertical and halfway to the following vertical, to develop a cross-sectional area. The section flow rate can be expressed as
qn = vn [((ln - ln-1) + (ln+1 - ln)) / 2] dn (5)
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