200
P. Liu
direction
P 1 + W sin θ − P 2 − F f = 0
Because of the steady uniform flow, P 1 = P 2 simplified as
W sin θ = F f
It shows that in the steady uniform flow of the open channel, the frictional
resistance between the wall surface and the component force of the water
gravity in the flow direction is balanced.
The shape, size, and bottom slope of the open channel have an important
effect on the flow regime. Common artificial open channel sections have rectangular, trapezoidal, and circular geometries, and natural river channels will
show irregular shapes. For a rectangular section as shown in Fig. 3.28, let the
water depth be h and the channel width be b, then the hydraulic radius R is
R =
A
P
=
bh
b + 2h
The degree of a longitudinal inclination of the open channel bottom is
called the bottom slope. The bottom slope is usually expressed as i = sinθ.
i > 0 for down slope channel, i < 0 for reverse slope channel, i = 0 for flat
slope channel. The uniform flow characteristics of the open channel are as
follows:
Fig. 3.28 Rectangular section of open channel