3 Hydrodynamics
201
(1) the shape, size, and water depth of the cross-section remain unchanged
along flow direction;
(2) the average velocity and velocity distribution of the cross-section remains
unchanged along the flow direction and the corresponding kinetic energy
correction coefficient and velocity head remain unchanged along the flow
direction;
(3) the total headline, water surface line, and bottom slope line are parallel
to each other.
The main task of hydraulic calculation of open channel is to determine the
velocity and depth of water. According to the Chezy formula, the discharge
of uniform flow is
Q = V A = AC
√
Ri, Q = K
√
i
where K = AC
√
R is called flow modulus (unit: m 3 /s). It comprehensively reflects the influence of the shape, size, and roughness of the open
channel section on the flow discharge. If Manning’s formula is used, the above
formula can be further written as
Q = AC
√
Ri = A
1
n
R
1/6
√
Ri = A
R 2/3
n
√
i =
A 5/3 √
i
n P 2/3
3.5.3 Steady Nonuniform Gradually Varied Flow
(1) Flow pattern of open channel
According to the definition, in the gradually varied flow of open channel, the
streamline is a nearly parallel straight line, that is to say, the included angle
between the streamline is very small and the curvature radius of the streamline is very large. Because the water surface line, the bottom slope line, and
the total water headline are not parallel, the depth and velocity of the gradually varied flow in the open channel vary along the flow direction. In order
to facilitate the analysis, the uniform water depth is often called the normal
water depth, which is expressed by h 0 . The influence of the free surface of
open channel flow on water depth is the main, and the gravity wave propagation of free surface is the key to affect the shape of the water surface. Using
the equation of one-dimensional flow continuity and energy, the propagation
velocity of microgravity wave in the static water of rectangular channel with
a depth of h is V w =
√
gh. When the channel water moves, the relationship
201
(1) the shape, size, and water depth of the cross-section remain unchanged
along flow direction;
(2) the average velocity and velocity distribution of the cross-section remains
unchanged along the flow direction and the corresponding kinetic energy
correction coefficient and velocity head remain unchanged along the flow
direction;
(3) the total headline, water surface line, and bottom slope line are parallel
to each other.
The main task of hydraulic calculation of open channel is to determine the
velocity and depth of water. According to the Chezy formula, the discharge
of uniform flow is
Q = V A = AC
√
Ri, Q = K
√
i
where K = AC
√
R is called flow modulus (unit: m 3 /s). It comprehensively reflects the influence of the shape, size, and roughness of the open
channel section on the flow discharge. If Manning’s formula is used, the above
formula can be further written as
Q = AC
√
Ri = A
1
n
R
1/6
√
Ri = A
R 2/3
n
√
i =
A 5/3 √
i
n P 2/3
3.5.3 Steady Nonuniform Gradually Varied Flow
(1) Flow pattern of open channel
According to the definition, in the gradually varied flow of open channel, the
streamline is a nearly parallel straight line, that is to say, the included angle
between the streamline is very small and the curvature radius of the streamline is very large. Because the water surface line, the bottom slope line, and
the total water headline are not parallel, the depth and velocity of the gradually varied flow in the open channel vary along the flow direction. In order
to facilitate the analysis, the uniform water depth is often called the normal
water depth, which is expressed by h 0 . The influence of the free surface of
open channel flow on water depth is the main, and the gravity wave propagation of free surface is the key to affect the shape of the water surface. Using
the equation of one-dimensional flow continuity and energy, the propagation
velocity of microgravity wave in the static water of rectangular channel with
a depth of h is V w =
√
gh. When the channel water moves, the relationship