Hydraulic Design of Highway Culverts - DOT On-Line Publications

The inlet control equations for tapered inlets are given in Appendix A. The coefficients and
exponents for each control section were developed based on the NBS hydraulic tests. All of the
previously described control sections function in a manner similar to weirs for unsubmerged flow
conditions, and in a manner similar to orifices for submerged flow conditions. For each section,
there is a transition zone defined by an empirical curve connecting the unsubmerged and
submerged curves.
a. Side-tapered Inlet. The side-tapered inlet throat should be designed to be the primary control
section for the design range of flows and headwaters. Since the throat is only slightly lower than
the face, it is likely that the face section will function as a weir or an orifice with downstream
submergence within the design range. At lower flow rates and headwaters, the face will usually
control the flow.
b. Slope-tapered Inlet. The slope-tapered inlet throat can be the primary control section with the
face section submerged or unsubmerged. If the face is submerged, the face acts as an orifice
with downstream submergence. If the face is unsubmerged, the face acts as a weir, with the
flow plunging into the pool formed between the face and the throat. As previously noted, the
bend section will not act as the control section if the dimensional criteria of this publication are
followed. However, the bend will contribute to the inlet losses which are included in the inlet loss
coefficient, ke.
2. Outlet Control. When a culvert with a tapered inlet performs in outlet control, the hydraulics
are the same as described in Chapter III for all culverts. The factors influencing flow in outlet
control are shown in Table 1 (Chapter 1). The inlet area is the area of the face section, the inlet
edge configuration describes the type of tapered inlet as well as the face edge conditions, and
the shape is either circular or rectangular. The barrel characteristics refer to the barrel portion of
the culvert, downstream of the throat section, except that the barrel length includes the length of
the tapered inlet, and the barrel slope may be flatter than the natural stream bed slope.
Equation (5) in Chapter III describes the losses in outlet control. The tapered inlet entrance loss
coefficient (ke) is 0.2 for both side-tapered and slope-tapered inlets. This loss coefficient
includes contraction and expansion losses at the face, increased friction losses between the
face and the throat, and the minor expansion and contraction losses at the throat.
The headwater depth in outlet control is measured from the invert of the culvert exit. Equation
(5) or the outlet control nomograph for the appropriate barrel size is used to determine the total
losses through the culvert. Equation (7) is then used to calculate the headwater depth, where
the tailwater (TW) is taken to be either (dc + D)/2 or the downstream channel depth, whichever
is larger.
3. Outlet Velocity. Outlet velocities for culverts with tapered inlets are determined in the same
manner as described in Chapter III. Note that when a FALL is used at the inlet, the barrel slope
is flatter than the stream slope and is calculated as follows.
S
EL − EL
t o = (11)
La
− L1
S is the approximate barrel slope, m/m (ft/ft)
ELt is the invert elevation at the throat, m (ft)
ELo is the invert elevation at the outlet, m (ft)
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