VelocityArea Flowmetering
Flow rate or discharge in an open conduit, channel or river can be calculated with the velocityarea principle.
The velocityarea principle is based on velocity measurements in a open flow like a conduit, channel or river.
Velocities and depths across the stream are measured as indicated in the figure above. A partial discharge in a section of the stream can be calculated as
q_{n} = v_{n} a_{n} (1)
where
q_{n} = flow rate or discharge in section n (m3/s, ft3/s)
v_{n} = measured velocity in section n (m/s, ft/s)
a_{n} = area of section n (m^{2}, ft^{2})
One simple way to express the section area is
a_{n} = d_{n} (l_{n+1}  l_{n1}) / 2 (2)
The total flow in the stream can be summarized to
Q = Σ_{1}^{n} v_{n} a_{n} (3)
where
Q = summarized flow rate or discharge in the conduit (m^{3}/s, ft^{3}/s)
The accuracy of estimate depends on the profile of the conduit and the number of measurements. For conduits with regular shapes like rectangular channels a limited number of measurements are required. For irregular shapes  like natural rivers or similar  higher accuracy requires more measurements both horizontal and vertical.
Example  Computing Flow Rate in a Channel
From a conduit we have three measurements:
Measured Values  Calculated Values  

n  v (m/s)  d (m)  l (m)  a (m^{2})  q (m^{3}/s) 
0  0  0  0  
1  3  1  2  2  6 
2  4  1.5  4  3  12 
3  3  0.9  6  1.8  5.4 
4  0  0  8  
Summarized  23.4 
The section areas can be calculated like
a_{1} = (1 m) ((4 m)  (0 m)) / 2
= 2 m^{2}
a_{2} = (1.5 m) ((6 m)  (2 m)) / 2
= 3 m^{2}
a_{3} = (0.9 m) ((8 m)  (4 m)) / 2
= 1.8 m^{2}
The flow rates can be calculated as
q_{1} = (3 m/s) (2 m^{2})
= 6 m^{3}/s
q_{2} = (4 m/s) (3 m^{2})
= 12 m^{3}/s
q_{3} = (3 m/s) (1.8 m^{2})
= 5.4 m^{3}/s
The total flow can be summarized as
Q = (6 m^{3}/s) + (12 m^{3}/s) + (5.4 m^{3}/s)
= 23.4 m^{3}/s
Note  there are alternative ways to calculate the section flow rates:
Simple Average Method
Using the simple average of two successive vertical depths, their mean velocity, and the distance between them can be expressed as
q_{n to n+1 } = [(v_{n} + v_{n+1}) / 2] [(d_{n} + d_{n+1} ) / 2] (l_{n+1}  l_{n}) (4)
Midsection Method
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 crosssectional area. The section flow rate can be expressed as
q_{n} = v_{n} [((l_{n}  l_{n1}) + (l_{n+1}  l_{n})) / 2] d_{n} (5)
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