HydroCAD® Stormwater Modeling - Since 1986

## Culvert Modeling

A culvert outlet on a pond is one of several options provided by HydroCAD for modeling pipe flow.

HydroCAD supports a wide range of culvert shapes including round, box, arch, and elliptical shapes.

The culvert outlet screen (shown at far right) lets you configure the parameters for each culvert, such as the barrel dimensions, length, slope, and Manning's number.

Since a full culvert analysis must also consider entrance conditions, the entrance energy loss Ke and contraction coefficient Cc must also be specified.  Advanced conditions, such as internal fill, can also be specified as required.

Depending on the selected routing procedure, the culvert calculations can also accommodate tailwater conditions.

These factors mean that culvert flow is considerably more complex than traditional pipe flow, and that different results are to be expected.  Inlet losses can reduce the capacity below simple Manning's flow, while headwater can produce a greater flow.  See below for details.

## Culvert Calculations

When evaluating a culvert, HydroCAD checks multiple flow conditions in order to determine the prevailing control at each elevation. This is based on six types of culvert flow identified in Culverts - Hydrology & Hydraulics by Jerome Norman as listed below:

Flow   Tailwater   Type of

Type Inlet Outlet Slope  Type   Dependent?  Control

1a   SUB.  SUB.   ANY    PIPE       YES    OUTLET

1b   SUB.  FREE   MILD   PIPE       NO     OUTLET (barrel)

1c   SUB.  FREE   ANY    CHANNEL    NO     INLET (orifice)

2a   FREE  TW>Yc  MILD   CHANNEL    YES    OUTLET

2b   FREE  TW<Yc  MILD   CHANNEL    NO     OUTLET (barrel)

2c   FREE  TW<Yc  STEEP  CAHNNEL    NO     INLET (weir)

SUB.=Submerged, TW=Tailwater, Yc=Critical Depth

For type 1b, assuming that the culvert is full along its entire length:

2    H - D + S L

V = -----------------

Ke+1   n²L

---- + --- 4/3

2g     C R

and Q = A V

Where:

V=Average velocity of flow

H=Head (above inlet invert elevation)

D=Depth of flow (=culvert height)

S=Slope [rise/run]

L=Length

Ke=Entrance energy loss coefficient

g=Gravitational constant

n=Manning's number

C=2.22 for US, 1 for metric

R=Hydraulic radius [feet]

A=Cross-sectional area [sq-feet]

Type 2b discharge is the same as type 1b except that the depth (D) is less than the culvert height. Under these conditions, open channel flow exists and backwater calculations must be performed to precisely determine the depth. To reduce calculation time, the depth is approximated by:

D = 3/4 H

Rather than directly determining whether type 1b or 2b flow exists, HydroCAD uses the lesser of this depth and the culvert height. This also ensures continuity between the two flow conditions, with the cross over occurring when the head is 4/3 of the culvert height.

Types 1a and 2a are similar to types 1b and 2b, except for the tailwater dependency. This is accommodated by setting D equal to the tailwater depth (above the outlet invert) when this exceeds the estimated culvert flow depth. (Note that the cross-sectional flow area is not increased and continues to be calculated based on 3/4H.)

Types 1c and 2c operate under inlet control, and the discharge is determined with the circular or rectangular orifice equations. (For an arch or elliptical culvert, the weir flow is determined by integration over the flow depth, similar to a custom weir/orifice.) The orifice discharge coefficient is given by:

Cc

Cd = --------

1 + Ke

Where:

Cc=Contraction coefficient (default is .90)

(Note that for Ke=.5 this yields Cd=.6, which is the default discharge coefficient for a sharp-edged orifice.)

The final determination of culvert discharge is made by calculating the type 1a/2a, 1b/2b and 1c/2c flows as described above. The least of these values (a, b, and c) is then used as the final discharge for a given head.

### Applicability

The approximations used for culvert discharge have generally been found to provide sufficient accuracy for most hydrograph routing purposes; however, it is strongly recommended that the resulting stage-discharge curve be verified using independent culvert data. If a significant discrepancy is found, the desired discharge data can be entered directly as a Special Outlet instead of using the built-in culvert equations.

### For further reading

Also see the HydroCAD Reference Manual and Standard Handbook for Civil Engineers by Frederick Merrit.