Figure 2.26. Schematic representation of transverse currents in a channel bed.
2.7.3 Subcritical Flow in Bends
Because of the change in flow direction which results in centrifugal forces, there is a
superelevation of the water surface in river bends. The water surface is higher at the outside
bank than at the inside bank. The resulting transverse slope can be evaluated quantitatively.
Using cylindrical coordinates (Figure 2.27), the differential pressure in the radial direction arises
from the radial acceleration or:
2
1 ∂p Vθ
=
(2.157)
ρ ∂r
r
To calculate the total superelevation between the outer and inner bend two assumptions are
made: (1) radial and vertical velocities are small compared to the tangential velocities such that
Vθ ≈ V; and (2) pressure distribution in the bend is hydrostatic, i.e., p = γy.
Figure 2.27. Definition sketch of flow around a bend.
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