## Boundary Conditions |

To develop a water surface profile (WSP) through the culvert using Gradually Varied Flow calculations one or more boundary condition must be defined. A boundary condition is a section of the channel where the depth of flow is known at a given flow rate. For culverts, these boundary conditions occur at or near the inlet and outlet.

For backwater calculations (WSP calculated from downstream
to upstream) a downstream boundary condition is necessary. When
performing frontwater calculations WSP calculated going downstream) an
upstream boundary condition is required. Determining the type of
boundary condition and calculation (backwater verses frontwater) needed
is a function of the __hydraulic slope__
and tailwater depth.
In FishXing the tailwater depth is defined by one of the available Tailwater Methods.

Boundary Conditions used by FishXing for Gradually Varied Flow Calculations are illustrated below.

Where:

yTW = Tailwater depth, measured from outlet bottom (negative below bottom, positive above bottom)

yc = Critical depth

yn = Normal depth

yfs = __Free
surface depth__, a function of (0.71*Ac)

A_{c} = Cross sectional area at
critical depth

H_{L}
= Inlet headloss

GVF = Gradually Varied Flow (arrow shows the direction of calculation)

RVF = Rapidly Varied Flow (arrow shows the direction of calculation)

**Inlet
Boundary Conditions Used in FishXing**

In FishXing, inlet boundary conditions are only required for hydraulically Steep sloping culverts (yc > yn).

__Steep
Slopes __

**GVF Boundary Conditions
= Critical Depth at inlet.**

Frontwater GVF Calculations begin at critical depth at inlet and end at outlet

**Outlet
Boundary Conditions Used in FishXing**

Outlet boundary conditions required on non-Steep slopes or on Steep slopes with tailwater depth > critical depth (yTW > yc ).

__Mild,
Horizontal, Adverse, Critical Slopes__

**Type 1: GVF Boundary
Condition = Tailwater Depth**

When the Tailwater Depth (yTW) is greater than Critical Depth (yc ) the culvert is controlled by the downstream water surface. Backwater GVF calculations begin at the outlet and proceed upstream to the inlet.

**Type 2: GVF Boundary
Condition = Critical Depth**

When Tailwater Depth (yTW) is less than the Free Surface Depth (yfs) the flow is passing through Critical Depth (yc ) and entering a zone of Rapidly Varied Flow. RVF is approximated linearly by drawing the flow profile from critical depth at a distance of 4yc from the outlet through yfs at the outlet. When yTW is negative, an outlet plunge exists.

**Type 3: GVF Boundary
Condition = Critical Depth**

When Tailwater Depth (yTW) is less than the Critical Depth (yc ) and greater than Free Surface Depth (yfs) the flow is passing through critical and entering a zone of Rapidly Varied Flow. The water surface within the RVF zone is approximated by drawing the flow profile from the tailwater elevation at the outlet to critical depth at a distance of 4yc upstream from the outlet.

__Steep
Slopes __

For Steep slope culverts, a downstream boundary condition is only needed if a backwater calculation is required.

In this case the Tailwater Depth (yTW) is below critical depth, so no backwater calculation is required.

**Type 4: Steep Slope
with GVF Boundary Condition = Tailwater Depth**

For hydraulically Steep slopes, if the Tailwater
Depth (yTW) is greater than
the Critical Depth (yc ) then
the downstream boundary condition is yTW
and a backwater calculation is performed. In addition, for all Steep
sloping culverts a frontwater calculation is also performed. Determine
the extent the flow profile is influenced by the tailwater depth requires
comparing the frontwater and backwater generated profiles and identifying
the location of a __hydraulic jump__,
if one exists.

See: Outlet Plunge, Outlet Drop, Tailwater Calculations, Hydraulic Jumps,