Hydraulic Design of Highway Culverts - DOT On-Line Publications

H
2 2
⎡ V V ⎤ d
= 1.
0 ⎢ − ⎥
⎣ 2g
2g
⎦
o (4c)
Vd is the channel velocity downstream of the culvert, m/s (ft/s)
Equation (4c) may overestimate exit losses, and a multiplier of less than 1.0 can be used. (40)
The downstream velocity is usually neglected, in which case the exit loss is equal to the full flow
velocity head in the barrel, as shown in Equation (4d).
H
o
2
V
= Hv
=
(4d)
2g
Bend losses, junction losses, grate losses and other losses are discussed in Chapter VI. These
other losses are added to the total losses using Equation (1).
Inserting the above relationships for entrance loss, friction loss, and exit loss (Equation 4d) into
Equation (1), the following equation for loss is obtained:
⎡
2
K n L ⎤ 2
U V
H = ⎢1+
k e + ⎥
(5)
1.
33
⎢⎣
R ⎥⎦
2g
Figure III-8--Full Flow Energy and Hydraulic Grade Lines
Figure III-8 depicts the energy grade line and the hydraulic grade line for full flow in a culvert
barrel. The energy grade line represents the total energy at any point along the culvert barrel.
HW is the depth from the inlet invert to the energy grade line. The hydraulic grade line is the
depth to which water would rise in vertical tubes connected to the sides of the culvert barrel. In
full flow, the energy grade line and the hydraulic grade line are parallel straight lines separated
by the velocity head lines except in the vicinity of the inlet where the flow passes through a
contraction.
The headwater and tailwater conditions as well as the entrance, friction, and exit losses are also
shown in Figure III-8. Equating the total energy at sections 1 and 2, upstream and downstream
of the culvert barrel in Figure III-8, the following relationship results:
35