Basic Hydraulics: Culverts – I

Concepts• A culvert conveys surface water through a roadway

embankment or away from the highway right-of-way (ROW) or into a channel along the ROW

• In addition to the hydraulic function, the culvert must also support construction and highway traffic and earth loads; therefore, culvert design involves both hydraulic and structural design

• Culverts are considered minor structures, but they are of great importance to adequate drainage and the integrity of the facility.

Definitions

• Culvert = relatively short length of conduit used to transport water through an embankment

• Components

• Outlet

• Barrel(s)

• Inlet

Shapes• Typically, several shapes provide hydraulically

adequate design alternatives:

Multiple barrel culverts

Materials• Commonly used culvert materials include concrete

(reinforced and non-reinforced), steel (smooth and corrugated), aluminum (smooth and corrugated), and plastic (smooth and corrugated)

• The selection of material for a culvert depends on:• structure strength, • hydraulic efficiency, • installation, local construction practices, • durability, • cost.

Pertinent dimensions

Circular culvert – diameter

Box culvert – rise & span

Terminology

HW = headwater

TW = tailwater

Headwater• Headwater is the depth of water on the entrance

or upstream side of the culvert as measured from the inlet invert

• The Tailwater is the depth of water on the exit or downstream side of the culvert, as measured from the downstream invert

Culvert hydraulics

• What we need to know:• For given discharge, what size culvert is required

to carry the flow without overtopping embankment?

• For given culvert size, will specified discharge overtop?

• For given culvert size, what is capacity without overtopping?

• To answer these, must compute headwater depth, using principles of hydraulics

What’s in control?

• “Control” of culvert flow may be:• At inlet (inlet control) • At outlet (outlet control).

• Analysis of a culvert requires us to:• Assume inlet control, calculate headwater

depth.• Assume outlet control, calculate headwater

depth for control at outlet.• Pick higher of two values as appropriate

headwater value.

Data needed for culvert analysis

Item Inlet control Outlet control

Inlet area X X

Inlet edge configuration X X

Barrel shape X X

Barrel roughness X

Barrel area X

Barrel length X

Barrel slope X X

Tailwater elevation X

Inlet control

• Occurs when flow capacity of entrance is less than flow capacity of barrel.

• Control section is located just inside culvert entrance.

• Water surface passes through critical depth.• Inlet capacity depends on entrance geometry.

Computing inletcontrol headwater

• Culvert headwater depth for inlet control depends on the inlet shape and efficiency

• Federal Highway Administration (FHWA) developed a series of nomographs for standard culvert shapes that compute headwater depth for inlet control

Using FHWA nomographs

• Identify the culvert type (concrete pipe, box, CMP, etc.).

• Find correct nomograph.• Start on the pipe diameter scale line• Draw a straight line through the discharge scale line• Read the value of HW/D from the appropriate HW/D

scale for the entrance type for your culvert.• Usually two or three “scales” on nomograph that

represent the type of inlet. • For example, on next page, scales for (1) square

edge with head wall; (2) groove end with headwall; (3) groove end projecting

Example of FHWA nomograph

Scale HW/D HW (ft)

(1) 2.5 8.8

(2) 2.1 7.4

(3) 2.2 7.7

Example: D = 42 in. Q = 120 cfs

Entrance treatment

Source: HEC-2 Users Manual

Entrance efficiency

Outlet control

• Occurs when flow capacity is limited by downstream conditions (high-tailwater) or by capacity of the barrel

Outlet control examples

Outlet control computations

• To analyze, use energy equation:

where Zup = upstream invert elevation; HW = depth at inlet; Vup = average velocity upstream; g = acceleration of gravity; Zdown = downstream invert elevation; TW = depth at outlet; Vdown = average velocity downstream; hL = total energy loss through culvert.

• Since Vup Vdown we can simplify the equation

Lupdown hTWZZHW )(

Energy loss equations

• Energy loss is

in which hL= total head loss; he= entrance loss; hf = friction loss; ho= outlet (exit) loss

• Friction loss estimated with Manning’s equation

in which L = culvert length (feet); Q = flow rate in the culvert (cfs); n = Manning's roughness coefficient; A = area of flow (square feet); R = hydraulic radius (feet)

ofeL hhhh

Entrance loss coefficients(For outlet control only)

Type of Structure and Design of Entrance Coefficient, ken

Concrete Pipe Projecting from Fill (no headwall):

Socket end of pipeSquare cut end of pipe

0.20.5

Concrete Pipe with Headwall or Headwall andWingwalls:

Socket end of pipe (grooved end)Square cut end of pipeRounded entrance, with rounding radius = 1/12 of diameter

0.20.50.2

Concrete Pipe:

Mitered to conform to fill slopeEnd section conformed to fill slopeBeveled edges, 33.7 or 45 degree bevelsSide slope tapered inlet

0.70.50.20.2

Corrugated Metal Pipe or Pipe-Arch:

Projected from fill (no headwall)Headwall or headwall and wingwalls square edgeMitered to conform to fill slopeEnd section conformed to fill slopeBeveled edges, 33.7 or 45 degree bevelsSide slope tapered inlet

0.90.50.70.50.20.2

Weir flow

• Flow over the roadway can be computed as weir flow.

• Check the the headwater elevation to see if weir flow occurs.• If headwater elevation is higher than the

roadway, use iterative procedure, balancing weir and culvert flow.

• Solution found when weir flow and culvert flow produce same headwater elevations.

Qtotal = Qweir + Qculvert = Qgiven

Flow analysis for culverts

Flow Rate (cfs)

Roadway Crest

Top of Culvert

Inlet Control

Outlet Control Culvert Plus RoadwayOvertopping

Headw

ate

r Ele

vati

on (

ft)