Culvert inlet and outlet control on the PE Civil WRE exam

A culvert problem on the Water Resources & Environmental exam usually asks one thing: for this flow, how high does the water stand at the entrance? That headwater depends on which part of the culvert limits the flow, the inlet or the barrel and outlet. The method is to work out the headwater both ways and keep the higher one. The Handbook covers this under Stormwater Collection and Drainage, which has both a USGS method for measuring flow through culverts and the FHWA hydraulic-design relations.

What you actually need to own

• Inlet control. The entrance passes less flow than the barrel could carry. Headwater depends only on the discharge and the inlet: barrel shape and area, and the edge and headwall treatment. Barrel roughness, length and tailwater don't affect it. At low headwater the inlet acts like a weir (unsubmerged). Once the inlet is well submerged it acts like an orifice. The Handbook prints the inlet-control equations for both, with a table of constants by shape and inlet configuration.
• Outlet control. The barrel, the outlet or the tailwater limits the flow. Treat it as an energy balance from the outlet back to the entrance. Headwater = the downstream water level + entrance loss + friction loss + exit loss − the fall through the barrel (length × slope). Now n, length and tailwater matter too, and the barrel slope enters in full through the fall.
• The losses. Entrance loss is k_e · v²/2g. k_e is small for a beveled or well-shaped entrance and large for a thin-walled projecting pipe. A square edge in a headwall is typically about 0.5. Friction loss comes from Manning. The exit loss is usually taken as one velocity head. For a barrel flowing full, these combine into v²/2g multiplied by (1 + k_e + a friction term in n²L/R^(4/3)), which is how the Handbook presents the full-flow case. That bracket already holds the entrance and exit losses, even though the Handbook's heading calls it friction head loss.
• The downstream level. Use the tailwater if it's high enough to control. If the tailwater is low and the barrel isn't flowing full at the outlet, set the outlet water level at (d_c + D)/2 above the outlet invert, and use the tailwater whenever it is higher. This approximation comes from the FHWA culvert design manual. The Handbook prints the energy balance it feeds.
• Check both, keep the larger. Compute the inlet-control headwater and the outlet-control headwater for the same flow. The higher one controls, and that's the headwater you report and check against the allowable (a road shoulder, an upstream property). Steep, short barrels tend to be inlet controlled. Long, flat or rough barrels and high tailwater tend toward outlet control. Confirm by calculation, not by rule of thumb.

Where people lose points

• Checking only one control. A tidy inlet-control answer that ignores a high tailwater gives a headwater that's too low.
• Adding barrel friction to an inlet-control check. Under inlet control, length and n don't appear.
• Counting entrance and exit losses twice. The Handbook's full-flow "friction head loss" bracket, (1 + k_e + 29n²L/R^1.33)·v²/2g, is the entrance, friction and exit losses together. Use it as the whole barrel loss, or add k_e·v²/2g, the Manning friction term and v²/2g separately. Adding k_e and the exit head on top of that bracket double-counts both.
• Dropping the barrel fall, or adding it with the wrong sign, in the outlet-control energy balance.
• Mixing headwater datums. Inlet-control headwater is measured from the invert of the inlet control section, and tailwater from the outlet invert. Convert each to an elevation before comparing the two controls or checking an allowable.
• Forgetting what happens downstream. A supercritical outlet velocity often means a hydraulic jump or a dissipator below the culvert.

A note on standards

FHWA HDS-5 (culverts) and HEC-14 (energy dissipators) become supplied design standards starting with the April 2027 exam. Until then, you work culverts from the Handbook, which already includes the inlet- and outlet-control equations. See the April 2027 change.

How to study it

Pick one culvert and work it at three flows, with low and then high tailwater, and watch control switch. Keep the outlet-control balance written out term by term. It's the same energy bookkeeping as Manning's equation and detention outlet routing.

Part of the Hydraulics–Open Channel area of the PE Civil WRE exam. → Start practicing free — the whole practice bank, free with an account.