# HY8:Exit Loss Options

### Introduction

HY-8 version 7.1 incorporates an alternative modified equation for defining culvert exit loss. The method described in HDS-5 uses the energy equation and several assumptions to compute the exit loss for a culvert. The equation that is given in HDS-5 ignores the velocity head downstream from a culvert barrel and is given as the following:

${\displaystyle H_{0}=k_{0}{\frac {V^{2}}{2g}}}$

where ${\displaystyle k_{0}^{}=1.0}$

Where Ho is the exit loss, V is the velocity inside the culvert barrel, and g is gravity. However, exit losses obtained from this expression do not match exit losses obtained from experimental studies by the researchers at Utah State University. USU has formulated an alternative expression for determining exit losses that uses the “Borda-Carnot equation”. This equation was originally developed for sudden expansions in pressurized pipes, but was found to give an accurate representation of culvert exit losses by USU’s experimental studies. Two useful forms of this expression are:

${\displaystyle H_{0}=1.0{\frac {(V_{p}-V_{c})^{2}}{2g}}}$

and

${\displaystyle H_{0}=k_{0}{\frac {V_{p}^{2}}{2g}}}$

where

${\displaystyle k_{0}=\left(1-{\frac {A_{p}}{A_{c}}}\right)^{2}}$

Where Ho is the exit loss, Vp is the velocity inside the culvert barrel, Vc is the velocity in the downstream channel, and g is gravity. In HY-8, we need to use the first form of the equation (${\displaystyle H_{0}=1.0{\frac {V^{2}}{2g}}}$) to compute the exit loss and the corresponding outlet control depth. The only additional value required between this equation and the previous equation is the velocity in the downstream channel. We already compute the downstream channel velocity in HY-8, so we can just use this computed velocity with the Borda-Carnot equation to compute the modified exit loss.

### Modified Exit Loss Option

To access this equation in HY-8 use Exit Loss combo box in the Macros toolbar in HY-8. This combo box will have two options:

1. Standard Method
2. USU Method

If the Standard Method is selected, HY-8 will use the current method for computing exit losses. If the USU Method is selected, HY-8 will use the USU (Borda-Carnot) equation to compute exit losses.