Velocity-Area Flowmetering
Flow rate or discharge in an open conduit, channel or river can be calculated with the velocity-area principle.
The velocity-area 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
qn = vn an (1)
where
qn = flow rate or discharge in section n (m3/s, ft3/s)
vn = measured velocity in section n (m/s, ft/s)
an = area of section n (m2, ft2)
One simple way to express the section area is
an = dn (ln+1 - ln-1) / 2 (2)
The total flow in the stream can be summarized to
Q = Σ1n vn an (3)
where
Q = summarized flow rate or discharge in the conduit (m3/s, ft3/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 (m2) | q (m3/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
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:
Simple Average Method
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)
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 cross-sectional area. The section flow rate can be expressed as
qn = vn (((ln - ln-1) + (ln+1 - ln)) / 2) dn (5)
