FLOOD06195

• County: Statewide
• Community: State of Colorado
• Basin: Statewide
• Title: Measurment of Peak Discharge at Culverts by Indirect Methods
• Date: 6/1/1968
• Prepared By: G.L. Bodhaine
• Floodplain - Doc Type: Educational/Technical/Reference Information

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.

.

;

e~

where

MEASUREMENT OF PEAK DISCHARGE AT CULVERTS BY INDIRECT METHODg

fi

O=the discharge coefficient,
A,=the flow area at the control section,
V, = the mean velocity in the approach
section,
a,=the velocity-head coefficient at the
approach section, and
h/,_.=thehead loss due to friction between
the approach section and the inlet
=L~(Q'fK1K,), and
K= conveyance = (1.486fn) R'!3A , (6)

Other notation is evident from figure 1 or it
has been previously explained. The discharge
coefficient, 0, is discussed in detail in the ~ection
entitled "Coefficients of Discharge."

Type 2 "ow

Type 2 flow, as shown on figure 2, passes
through critical depth at the culvert outlet,
The headwater-diameter ratio does not exceed
1.5, and the barrel flows partly full. The slope
of the culvert is less than critical, and the tail-
water elevation does not exceed the elevation of
the water surface at the control section, h,.
The discharge equation is

Q=CA,~2g (hl+ a~" -d,-h"_.-h,,.,} (7)
where

h/,.3=the head loss due to friction in the
culvert barrel=L(Q'fK,J(,),

Flow with backwater

When backwater is the controlling factor in
culvert flow, critical depth cannot occur and the
upstream water-surface elevation for a given
discharge is a function of the surface elevation
of the tailwater. If the culvert flows partly full,
the headwater-diameter ratio is less than 1.5; or
if it flows full, both ends of the culvert are
completely submerged and the headwater-
diameter ratio may be any value greater than
1.0. The two types of flow in this classification
are 3 and 4.
Type 3 flow

Type 3 flow is tranquil throughout the length
of the culvert, as indicated on figure 2. The
headwater-diameter ratio is less than 1.5, and

the culvert barrel flows partly full. The tail-
water elevation does not submerge the cuh-ert
outlet, but it does exceed the elevation of crit.;cal
depth at the terminal section.
The lower limit of tailwater must be such that
(1) if the culvert slope is steep enough that
under free-fall conditions critical depth at the
inlet would result from a given elevation of
headwater, the tailwater must be at an elevation
higher than the elevation of critical depth at tbe
inlet; and (2) if the culvert slope is mild enough
that under free-fall conditions critical depth at,
the outlet would result from a given elevation of
headwater, then the tailwater must be at an
elevation higher than the elevation of critical
depth at the outlet.
The discharge equation for this type of flow is

Q=CA3~2g (h,+ a'~"-h,-h/l-2-h,,_,} (8)

Type 4 flow

In this classification the culvert is submerged
by both headwater and tailwater, as is shown
in figure 2. The headwater-diameter ratio can
be anything greater than 1.0. No differentiation
is made between low-head and high-head flow
on this basis for type 4 flow. The culvert flows
full and the discharge may be computed directly
from the energy equation between sections 1
and 4. Thus,

[h,+h.,=h,+h.,+h'l-2+h,
+h"., +h/3-4 +(h., -h..)],

where

h.=head loss due to entrance contraction.

In the derivation of the discharge formula
shown below, the velocity head at section 1
and the friction loss between sections 1 and 2
and between sections 3 and 4 have been ne-
glected, Between sections 3 and 4 the energy
loss due to sudden expansion is assumed to be
(h.,-h..). Thus,

h,=h.+h.+h,..,+h."

or

Q= OA ~ 2g(h,-h.) , (9)
o 290'n'L
1+ Ro'!3