# Pipe Culvert Design Spreadsheet Calculations

## Inlet Control and Outlet Control for a Pipe Culvert Design Spreadsheet

One of the general conditions for pipe culvert design calculations is inlet control, in which the flow rate through the culvert is controlled at the inlet end of the culvert by the culvert diameter and other inlet conditions.  The other general condition is outlet control, in which the flow rate is controlled by the outlet conditions and the entire length of the culvert.

## Pipe Culvert Inlet Control Design Spreadsheet Calculations

An equation that relates culvert parameters for inlet control conditions in a pipe culvert design spreadsheet is:

where:

• HW = headwater depth above inlet invert (ft – U.S. or m – S.I.)
• D = inside height of the culvert (ft – U.S. or m – S.I.)
• Q = discharge (cfs – U.S. or m3/s – S.I.)
• A = cross-sectional area of culvert (ft2 – U.S. or m2 – S.I.)
• S = culvert slope (dimensionless)
• K1 = 1.0 for U.S. units or 1.811 for S.I. units
• Ks = slope constant = -0.5 for a non-mitered or + 0.7 for a mitered inlet
• Y and c are constants dependent on the type of culvert and type of inlet.

## Pipe Culvert Outlet Control Design Calculations

An equation that relates culvert parameters for outlet control conditions in a pipe culvert design spreadsheet is:

Where:

• hL = the head loss in the culvert barrel for full pipe flow (ft – U.S. or m – S.I.)
• Ku = 29 for U.S. units or 19.63 for S.I. units
• n = Manning roughness coefficient for the culvert material
• L = length of the culvert barrel (ft – U.S. or m – S.I.)
• R = hydraulic radius of the full culvert barrel = A/P (ft – U.S. or m – S.I.)
• A = cross-sectional area of the culvert barrel (ft2 – U.S. or m2 – S.I.)
• P = perimeter of the culvert barrel, ft or m
• V = velocity in the culvert barrel, ft/sec or m/s
• Ke = loss coefficient for pipe entrance

## A spreadsheet screenshot for pipe culvert design calculations

The Excel spreadsheet screenshot below shows part of a spreadsheet for circular culvert design calculations based on inlet control.   Based on the indicated input values, the spreadsheet will calculate the minimum required pipe culvert diameter and the headwater depth for the next larger standard culvert diameter.