Culvert Design Calculator

Inlet and Outlet Control. Flow thru culverts and over road or damHeadwater Depth vs. Discharge graph, chart. Based on HDS-5 methodology. Hydraulic design of culverts

Register to enable "Calculate" button. Demonstration mode for 0.9 m < D < 1.1 m and N<3 where D is pipe diameter, N is number of pipes (cookies must be enabled).

Diagram of Flow through a Culvert

Links on this page:  Introduction   Equations   Variables  Values of Coefficients and Manning n   Error Messages and Validity    References

In the culvert design calculator above:
• Culvert Types:
    "Conc. Sq edge. Wall" = Concrete pipe with square edged inlet and headwall
    "Conc. Groove. Wall" = Concrete pipe with groove end at inlet and headwall
    "Conc. Groove. Proj" = Concrete pipe with groove end projecting at inlet
    "CMP. Headwall" = Corrugated metal pipe with headwall at inlet
    "CMP. Mitered" = Corrugated metal pipe mitered to slope at inlet
    "CMP. Projecting" = Corrugated metal pipe projecting at inlet

• Culvert Design Calculator Units:
m=meters, ft=feet, l/s=liter/sec, cfm=cubic feet per minute, cfs=cubic feet per second, gpm=US gallons per minute, gph=US gallons per hour, gpd=US gallons per day, MGD=Millions of US gallons per day.

• You can enter tailwater depth (Y_t) as a negative number if flow from the culvert drops down to a receiving channel.  You don't need to know the exact elevation drop; entering any negative number for Y_t will have the same effect.

• The phrase "Inlet Control" or "Outlet Control" that appears in the upper right hand corner of the calculation refers to the type of control for the total flow (Q_t) entered in the calculation's upper left hand corner. The graph below the calculation plots headwater depth (Y_h) for the range of minimum Q_t to maximum Q_t entered under the word "GRAPHING:" in the calculation. The type of control may change from one part of the graph to another as Q_t changes.

Introduction
Culverts have been utilized for thousands of years as a means to transmit water under walkways or roads. Often, a culvert is simply installed without much thought to how much water it needs to convey under extreme conditions. If a culvert cannot convey all of the incoming water, then the water will flow over or around the pipe, or simply back up behind the culvert creating a pond or reservoir. If any of these conditions are unacceptable, then the proper culvert diameter and number of culverts must be selected prior to installation in order to convey all of the anticipated water through the pipe(s). This calculation helps the designer size culverts as well as present a headwater depth vs. discharge rating curve.

Culvert design calculator is primarily based on the methodology presented in Hydraulic Design of Highway Culverts by Normann (1985) and published by the U.S. Department of Transportation's Federal Highway Administration. It is also known as HDS-5 (Hydraulic Design Series No. 5). HDS-5 focuses on culvert design. Culvert design is usually based on the maximum acceptable discharge - thus the HDS-5 methodology is geared toward culverts flowing full with water possibly flowing over the road above the culvert. In addition to programming the HDS-5 methodology, LMNO Engineering wished to compute headwater depths for lesser flows. Therefore, in addition to the HDS-5 methodology, we have added the Manning equation for culverts flowing partially full. The HDS-5 methodology also assumes that the user knows the tailwater depth (Y_t) before using the methodology. Though Y_t can be found by field measurements, it is often computed in the office using Manning's equation based on bottom width, side slopes, channel roughness, and channel slope. Therefore, LMNO Engineering added the additional feature of a built-in subroutine for computing Y_t for trapezoidal channels. Note that for the graphing portion of our calculation, Y_t is re-computed for the entire range of flows (Q_t) shown on the graph (unless the user specifically inputs Y_t).

As explained in Normann, 1985 (also known as HDS-5, Hydraulic Design of Highway Culverts), the discharge through a culvert is controlled by either inlet or outlet conditions. Inlet control means that flow through the culvert is limited by culvert entrance characteristics. Outlet control means that flow through the culvert is limited by friction between the flowing water and the culvert barrel. The term "outlet control" is a bit of a misnomer because friction along the entire length of the culvert is as important as the actual outlet condition (the tailwater depth). Inlet control most often occurs for short, smooth, or greatly downward sloping culverts. Outlet control governs for long, rough, or slightly sloping culverts. The type of control also depends on the flowrate. For a given culvert installation, inlet control may govern for a certain range of flows while outlet control may govern for other flowrates. If the flowrate is large enough, water could go over the road (or dam). In this case, the calculation automatically computes the amount of water going over the road and through each culvert, as well as the headwater depth.

If you have surfed around our website, you may have noticed our other calculations for circular culverts. We have a calculation using Manning's equation for design of circular culverts. Since it uses Manning's equation, it assumes the culvert is long enough so that normal depth is achieved. We also have a calculation for computing discharge from the exit depth ("end depth") in a circular culvert - very useful for flow rate measurement in the field. For flows under pressure, we have several calculations listed under the Pipe Flow category on our home page.

Equations and Methodology             Back to calculation
The LMNO Engineering methodology for the culvert design calculator generally follows that of Normann (1985; also known as HDS-5 - Hydraulic Design of Highway Culverts). However, the Normann methodology is mainly for culvert design. Culvert design usually involves the largest expected flowrate. We wanted to write a calculation that also determines headwater depth for small flowrates. Therefore, in addition to the Normann methodology, we have incorporated Manning's equation for outlet control when the headwater depth is less than 0.93 times the culvert diameter. 0.93D is used since it is the depth at which discharge through a partially full circular culvert is a maximum (Chow, 1959). At depths greater than 0.93D and for full flow, the Nomann (1985) equation is used for outlet control. For inlet control, our calculation uses Normann's equations.

Many of the equations shown below for the culvert design calculator are empirical and require U.S. Customary units (feet, seconds, and radians). Some of the equations are based on first principles and are compatible with any consistent set of units (e.g. SI). However, to keep this web page from being "too busy", we have refrained from indicating which equations are empirical and which are fundamental. If you work through the equations by hand, please use feet, seconds, and radians in all of them, to avoid any problem with units. Our calculation (above) allows many different types of units; the units are internally converted before and after using the equations.

Since total flow rate (Q_t) is entered and headwater depth (Y_h) is computed, the equations below are solved simultaneously to determine Y_h. Outlet versus inlet control is determined by the equation resulting in a larger value for Y_h.

All of the variables are defined below in the Variables section. Pipe downstream invert elevation is defined as 0.0.

General Equations
Q_t = Q_r + N Q_p      S_p = S_c - Y_f /L_p      E_i = L_p S_p      E_h = E_i + Y_h      V=Q_p /A_v

Tailwater Depth, Y_t
Y_t can be computed or input.  If it is computed, Manning's equation is used (Chow, 1959):

Since Q_t is input, the above equations are solved numerically (backwards) for Y_t.

Headwater depth, Y_h
Y_h is computed independently based on inlet and outlet control equations. The equation that gives the larger value of Y_h is considered to be the controlling mechanism and is reported.

    Inlet Control (see below for values of constants C₁, C₂, C₃, C₄ , C₅)
Outlet velocity (V) is computed based on what we call the velocity depth, Y_v.  Normann (1985) suggests computing Y_v using the Manning equation.  If Y_v is greater than D, then Y_v is set to D.

        Unsubmerged Inlet (Normann, 1985):

        Submerged Inlet (Normann, 1985):

    Outlet Control
Outlet velocity (V) is computed based on what we call the velocity depth, Y_v. Normann (1985) suggests: If Y_t≤Y_c, then Y_v=Y_c. If Y_c<Y_t<D, then Y_v=Y_t. If Y_t≥D, then Y_v=D.

        If Y_h<0.93D, then Manning's equation (Chow, 1959) is used:

Since Q_p is input, the above equations are solved numerically for Y_h.

        If Y_h≥0.93D, Normann (1985) is used:

Flow over Road (or Dam)
If water flows over the road (or dam), then flow over the road is computed by (Normann, 1985):

Note that, instead of using a constant value of 3, Normann (1985) uses a coefficient that varies from 2.5 to 3.1 depending on the water depth above the road and whether the road is paved or gravel.

Variables             Back to calculation
A=Flow area [ft²].
A_c=Flow area in one pipe based on critical depth [ft²].
A_v=Flow area in one pipe used for computing outlet velocity [ft²].
b=Width of channel bottom [ft]. Used for computing Y_t.
C₁, C₂, C₃, C₄, C₅=Constants for inlet control equations. See values below.
D=Diameter of each pipe (culvert) [ft].
E_h=Headwater elevation relative to invert of pipe outlet [ft]. Pipe outlet invert elevation is defined at 0.0 ft.
E_i=Elevation of pipe inlet invert relative to pipe outlet invert [ft]. Pipe outlet invert elevation is defined at 0.0 ft.
E_r=Elevation of road (or dam) crest relative to pipe outlet invert [ft]. Pipe outlet invert elevation is defined at 0.0 ft.
g=Acceleration due to gravity, 32.174 ft/s².
H=Head loss computed from outlet control equation [ft].
HW=Abbreviation for headwater.
K_e=Minor loss coefficient for pipe inlet (used for outlet control equations). See values below.
L_p=Pipe (culvert) length [ft]. If there is more than one culvert, they all must have the same length. L_p is the length of one of them (not the sum of the lengths).
L_w="Weir" length [ft]. Length of the road (or dam) that water could flow over. L_w is the width that the water sees as it flows over the road.
n_c=Channel Manning n coefficient. See values below.
n_p=Pipe (culvert) Manning n coefficient. See values below.
N=Number of pipes (culverts) next to each other.
P=Wetted perimeter [ft].
Q_p=Flowrate (discharge) through each pipe [cfs, ft³/s].
Q_r=Flow rate (discharge) over the road (or dam) [cfs].
Q_t=Total flowrate (discharge) [cfs]. Sum of flows through pipes plus flow over road.
S_c=Slope of existing channel [elevation change/length]. Longitudinal slope, not side slopes.
S_p=Pipe slope [elevation change/length]. Longitudinal slope, not side slopes.
T_c=Top width of flow in one pipe based on critical depth [ft].
V=Pipe outlet velocity [ft/s].
V_c=Pipe velocity based on critical depth [ft/s].
Y_avg=Average water depth [ft].
Y_c=Critical water depth [ft].
Y_f=Fall [ft]. Vertical distance that inlet pipe invert is lowered below the existing channel bottom.
Y_h=Headwater depth [ft].
Y_o=Water outlet depth [ft].
Y_t=Tailwater depth [ft]. Depth of water in existing channel at culvert outlet.
Y_v=Depth used for computing outlet velocity [ft].
z₁=Left side slope of existing natural channel [horizontal/vertical].
z₂=Right side slope of existing natural channel [horizontal/vertical].
π=Greek letter "pi" = 3.1415926...
θ=Greek letter "theta". Used for partially full pipes.

Values of Coefficients and Manning n                      Back to calculation
Manning n values are from Chow (1950), French (1985), Mays (1999), Normann (1985), and Streeter (1998). C₁ through C₅ and K_e are from Normann (1985).

Error Messages and Validity                              Back to calculation
Input checks on left side of calculation. If one of these messages appears, the calculation and graphing is halted.
"Need 0≤Q_t<10000 m³/s". Total flow cannot be negative or must be less than 10,000 m³/s.
"Need 0<N<1001". Must have at least one pipe, but no more than 1000 pipes.
"Need 0<D<100 m". Pipe diameter must be positive and less than 100 m.
"Need 0<Lp<10000 m". Pipe length must be positive and less than 10,000 m.
"Need 0<Pipe n<0.05". Pipe Manning n must be positive and less than 0.05.
"Need Y_t<E_r". Tailwater depth cannot be higher than the road crest.
"Need E_i+D<E_r". Upstream pipe invert plus culvert diameter cannot exceed road crest elevation. If E_i+D is greater than E_r, then the top of the culvert is pushing through the road, which is unacceptable.
"Need 0<L_w<10000 m". "Weir" length of road (or dam) must be positive and less than 10,000 m.
"Need Y_t<10000 m". Tailwater depth must be less than 10,000 m. Negative values are acceptable. Negatives simulate culverts discharging to a lower channel.
"Need S_c<0.5". Channel bottom slope cannot exceed 0.5 m/m (vertical to horizontal ratio). This is the longitudinal slope, not the side slopes.
"Need S_c>0". Channel cannot be horizontal.
"Need 0<Chan n<0.5". Channel Manning n must be positive and less than 0.5.
"Need 0<b<10000 m". Channel bottom width must be positive and less than 10,000 m.
"Need 0<z₁<10000", "Need 0<z₂<10000". Channel side slopes can be neither exactly vertical (z=0) nor nearly flat (z>10,000). z is defined as horizontal to vertical ratio.
"Need 1e-7<S_p<0.5". Pipe slope must be between these limits.

Input checks for graph and chart (table). If one of these messages appears, the graph and table will not proceed. Note that if any value is out of range in the upper portion of the calculation, a graph will not be shown.
"Need min Q_t≥0". Minimum total flow for graph was entered as a negative number.
"Max Q_t>10000 m³/s". Maximum total flow for graph cannot exceed 10,000 m³/s.
"Min must be < Max". Minimum Q_t entered for graph must be less than maximum Q_t entered for graph.
"Need Min/Max<0.99". Minimum Q_t entered for graph must be less than 0.99 times maximum Q_t entered for graph. Otherwise, the minimum and maximum are too close together to have good axis labels for the graph.

Run-time errors. The following message may be generated by the graphing/table portion of the calculation:
"Y_t>E_r for some Q_t". Tailwater depth exceeds road (or dam) crest for large values of Q_t. Y_h cannot be computed or graphed when Y_t>E_r since the equations are only valid for Y_t≤E_r.

References            Back to calculation
Chow, V. T. 1959. Open-Channel Hydraulics. McGraw-Hill, Inc. (the classic text)

French, R. H. 1985. Open-Channel Hydraulics. McGraw-Hill Book Co.

Mays, L. W. editor. 1999. Hydraulic design handbook. McGraw-Hill Book Co.

Normann, J. M. 1985. Hydraulic design of highway culverts. HDS-5 (Hydraulic Design Series 5). FHWA-IP-85-15. NTIS publication PB86196961. Obtainable at https://www.fhwa.dot.gov/engineering/hydraulics/library_arc.cfm?pub_number=7&id=13.

Streeter, V. L., E. B. Wylie, and K. W. Bedford. 1998. Fluid Mechanics. WCB/McGraw-Hill. 9ed.

© 2001-2024 LMNO Engineering, Research, and Software, Ltd.  All rights reserved.

Please contact us for consulting or questions about culvert design.

LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd.   Athens, Ohio 45701  USA   Phone: (740) 707-2614
LMNO@LMNOeng.com    https://www.LMNOeng.com

To: 
LMNO Engineering home page (more calculations)

Related calculations:

Circular Culvert using Manning Equation

Critical Depth in Circular Culvert

Other:

Unit Conversions

Register