ChannelFlow: Culvert
Input Parameters:
name Text of up to 10 characters. Blanks are not allowed. This is in order to preserve the tabular printout, which can be read back into the program.
Q# Flow in section. This can reference a flow computed on a "Qcia" line.
D Inside diameter.
h Vertical inside height, used only for box culverts. It is ignored for equation numbers less than 6, and a circular pipe culvert is assumed.
InvIn Elevation or invert of the pipe at the inlet. It can be left zero. The inverts are used only with the length to compute the slope. If a slope is given, they are unnecessary for computation.
InvOut Elevation or invert of the pipe at the outlet. It can be left zero. The inverts are used only with the length to compute the slope. If a slope is given, they are unnecessary for computation.
L Length of the pipe. It can be left zero. It is used only with the inverts to compute the slope. If a slope is given, length is unnecessary for computation.
S Slope of the pipe. If inverts and length are given, this value will be computed.
n Manning's roughness coefficient. Suggested values are given with the Open Channel formulas.
Ke Inlet loss coefficient. Usually assumed to be 0.5.
tw Tailwater elevation at the pipe outlet, measured from the invert out.
eq Equation constant set from the table given below. This defines what type of culvert is being computed.
Output:
tg This it the given tailwater elevation. It is not actually computed output, but is given so the program can read it back in, and because it is often replaced by the actual tailwater.
tw The actual tailwater used. In the case of a free fall outlet, this may be the critical depth of flow in the pipe. In most cases, the culvert is under inlet control, and the tailwater value is unused, except for computing exit velocity.
V The average exit velocity of flow from the culvert.
HW The headwater, measured from the inlet invert. Immediately after the value, the control designation is printed: "is" for inlet control submerged, "iu" for inlet control unsubmerged, "of" for outlet control full flow, or "pf" for outlet control partially full flow.

The empirical formulas developed by the Federal Highway Administration, and listed in Hydraulic Design Series No. 5, are used to compute culvert flow. These formulas are the basis for most commonly used nomographs, and they simplify the problem by breaking culvert performance into three basic flow types; inlet control unsubmerged, inlet control submerged, and outlet control with both ends submerged. The formulas and constants which have been used in the program are listed below. Refer to the figures below for examples of the various types of flow control. These formulas are applicable to U.S. units only.

A = full area      D = interior culvert height

S = slope    {- (0.5)S should be replaced with + (0.7)S for mitered inlets}

Hc = dc + Vc2/2g    (head at critical depth)

TW = tailwater      HW = headwater

(1) unsubmerged inlet control

HW/D = Hc/D + K[Q/(AD0.5)]M - (0.5)S     for Q/(AD0.5) less or equal to 3.5 approx.

(2) also unsubmerged inlet control

HW/D = K[Q/(AD0.5)]M     for Q/(AD0.5) less or equal to 3.5 approx.

(3) submerged inlet control

HW/D = c[Q/(AD0.5)]2 + Y - (0.5)S     for Q/(AD0.5) > 4.0 approx.

(4) full flow outlet control

HW = (1 + Ke + [29n2L/(d/4)4/3]) Q2 / (2gA2) + TW  

 

Equation constants from HDS NO. 5 K M c Y
0) RCP, square edge with headwall 0.0098 2.00 0.0398 0.67
1) RCP, groove end with headwall 0.0078 2.00 0.0292 0.74
2) RCP, groove end projecting 0.0045 2.00 0.0317 0.69
3) CMP, with headwall 0.0078 2.00 0.0379 0.69
4) CMP, mitered to slope 0.0210 1.33 0.0463 0.75
5) CMP, projecting 0.0340 1.50 0.0553 0.54
6) Rectangular Box, 30-75 degree wingwalls 0.0026 1.00 0.0385 0.81
7) Rectangular Box, 90, 15 degree wingwalls 0.0061 0.75 0.0400 0.80
8) Rectangular Box, 0 degree wingwalls 0.0061 0.75 0.0423 0.82


Inlet control examples (HDS5 p.26)


Outlet control examples (HDS5 p.32)

The value of HW(inlet control unsubmerged) is handled a bit differently in the program. If the depth of normal pipe flow would be higher, the normal pipe flow depth is used. Also, for HW(outlet control full), full flow is assumed when the normal pipe flow depth is up to 90% of pipe diameter. However, if a constant tailwater value is specified, that will govern. If it is less than the pipe diameter, the full flow case will never come up.

Theoretically, the cases left out are under outlet control with the outlet unsubmerged, some examples of which are shown above. These occur when flow is subcritical, and not full. A detailed hydraulic gradeline computation starting at the tailwater elevation is used. As a warning, this computation is not thoroughly verified, as these cases are extremely rare.

(return)