The Manning formula contains a quantity called the hydraulic radius.
2.
In wide rectangular channels, the hydraulic radius is approximated by the flow depth.
3.
For a semicircular channel, the hydraulic radius would simply be the true radius.
4.
The hydraulic radius is " not " half the hydraulic diameter as the name may suggest.
5.
Despite what the name may suggest, the hydraulic diameter is "'not "'twice the hydraulic radius, but four times.
6.
For channels with a lower width-to-depth ratio, a better solution can be found by using the hydraulic radius instead of the above simplification.
7.
This means that side-wall effects can be ignored, and that the hydraulic radius, R _ h, can be assumed to be equal to the channel depth, h.
8.
For calculations involving the outer stream, the equivalent diameter ( or mean hydraulic radius ) is used in place of the geometric diameter, as the cross-sectional area of the annulus is not circular.
9.
Formally, this assumption can generally be held to hold when the width is greater than about 20 times the height; the exact amount of error accrued can be found by comparing the height to the hydraulic radius.
10.
In general, velocity increases with the depth ( or hydraulic radius ) and slope of the river channel, while the cross-sectional area scales with the depth and the width : the double-counting of depth shows the importance of this variable in determining the discharge through the channel.
