Capacity Analysis

Last updated: March 16, 2023

When using Capacity Analysis, there are two basic approximate profile cases: the Full Capacity Profile and the Excess Capacity Profile.

Full Capacity Profiles

Full capacity profiles occur when the pipe's actual discharge is greater than or equal to the pipe's full flow capacity (the theoretical capacity based on normal depth being equal to the top of the pipe). In these cases, the downstream depth is taken as the greater of the actual downstream hydraulic grade or the free discharge tailwater elevation. The free discharge tailwater depth is commonly approximated as halfway between the crown of the pipe and the pipe's critical depth (in accordance with the U.S. Federal Highway Administration's HDS-5). Starting from the tailwater elevation, the pipe's full flow friction slope is used to determine the hydraulic grade at the upstream end of the profile.

Excess Capacity Profiles

Excess capacity profiles occur when the full flow capacity of the pipe (again, based on Normal depth equal to the top of the pipe) is greater than the actual flow in the pipe. For these profiles, there are three basic tailwater conditions:

Case 1 - Hydraulic grade downstream less than or equal to normal depth
Case 2 - Hydraulic grade downstream greater than normal depth, and less than or equal to pipe crown
Case 3 - Hydraulic grade downstream greater than or equal to pipe crown

Excess Capacity Profile, Case 1 (Hydraulic Grade <= Normal Depth):

If the downstream depth in the pipe is at or below the pipe's normal depth, normal depth is assumed for the pipe's entire length.

Excess Capacity Profile, Case 2 (Normal Depth < Hydraulic Grade <= Pipe Crown)

When the hydraulic grade is above the pipe's normal depth but below the top of the pipe, a friction slope of zero is assumed until it either intersects the pipe's normal depth or reaches the end of the pipe.

Excess Capacity Profile, Case 3 (Hydraulic Grade >= Pipe Crown)

If the hydraulic grade is above the pipe crown, the hydraulic grade continues upstream following the pipe's full flow friction slope. This slope will continue until it either intersects the pipe crown or reaches the end of the pipe.

Note: If the full friction slope intersects the crown of the pipe, the profile will continue with a Case 2 profile analysis.

Composite Excess Capacity Profiles

An excess capacity profile may actually be a composite of two more simple profiles. Consider the case below, where the tailwater is above the crown of the pipe. In this case, the profile begins as a Case 3 profile. Where the full flow friction slope intersects the crown of the pipe, the profile changes to a Case 2 profile, following a flat slope until it reaches normal depth. Where normal depth is intersected, a Case 1 profile begins, extending all the way to the upstream end of the pipe.