FLOOD06423

• County: Statewide
• Community: State of Colorado
• Basin: Statewide
• Title: Preparation of Input Data for Automatic Computation of State-Discharge Relations at Culverts
• Date: 1/1/2000
• Prepared By: Matthai, Stull, Davidian
• Floodplain - Doc Type: Educational/Technical/Reference Information

4

TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

of flow at the barrel entrance.

for the highest tailwater elevation selected
to submerge both the inlet and outlet.

If no results -are obtained in step I, the
sequence is:

2. Solve for hI by both the type 5 and

type 6 flow equations if the piezometric head
at section 1 is greater than 1. 5 D + z, or
solve for hl by the tyPe 3 flow: equation as

indicated, if supercl'itical flow occurred in
the section.

3. Solve for hI by the type 4 now equation

for the highest tailwater elevation, a-elected
to submerge both the inlet and outlet.

An outline of the computer program steps
for each type of flow is given below. For
now types 1-5, the sum of the potential and
kinetic heads at the upstreaIIl section are
equated to the Bum Qf the potential and kinetic
heads at the control section downstream plus
the friction and entrance losses between the
two sections.

Type 1 Flow

Critical depth OCcurs at the barrel en-

trance; therefore, the type 1 flow equation is:

2
"'IQ

hi + ----:i = d2 + z +

2gA1

Q2
2
2gA2

+L L+(...!...-l\
w Kl K2 C2 )

Q2
2 .
2gA2

in which h is the piezometric head at the
1
appro&.ch section. section 1, referred to the
elevation of the invert at the culvert outlet;
O'l (alpha) is the velocity-head coefficient at

the approach section; At is area of flow at

the approach section; d2 is .the depth of flow

at the barrel entrance, section 2; z is the
difference in elevation between the entrance
invert and the base (outlet invert) elevation;
L is the length of the reach between the
w
approach section and the barrel entrance;
Kl and K2 are the conveyances at approach

and entrance sections, respectively; C is the
~et discharge coefficient; and A2 is the area

The root of the equation is found by an
iterative process between two extremes,
The lower is the critical depth at the ap-
proach section for the selected discharge.
The elevation is obtained by interpolation be-
tween critical discharges computed in Part 1
for the selected water- sur-face elevations at
the approach section. The upper extreme is
1.5 D + z. If no solution ..esults because the
piezometric head at section 1 is greater than
1. 5 D + z, solutions to flow equations for
types 5, 6, and 4 are attempted.

If no solution results because of super-
critical flow in the approach section. a mes-
sage. "NO SOLUTION TYPE ONE FLOW--
SUPERCRITICAL FLOW AT APPROACH
SECTION,ll is printed. Then solutions for
successive type 3 conditions are tried and an
attempt is made to solve the type 4 flow
equation.

After a successful typ~ 1 solution, flow
equations for types 3 and 4 are solved if that
option is chosen.

Type 2 Flow

Type 2 flow requires two equations for
solution. Critical flow occurs at the barrel
outlet, section 3; therefol:'e, an equation for
flow within the culvert is first solved for
depth at the entrance, d2, This depth is then

used in another equation to solve for the head-
water elevation.

The first type 2 flow equation is

2
d2 + Z + ~
2gA2

2
= d + Q
3 2 A 2
g 3

Q2
+LKK,
2 3

in which d3 is depth of flow at the outlet cor-

responding to the critical discharge, L is the
barref length, and KS is the conveyance at the

outlet section. The root of the equation is
found by iteration between the two extremes,.
d2 = dc and d2 = D.

The second type 2 flow equation is