Culvert & Orifice Hydraulics

Source file: culvert_hydraulics.html

Purpose

Estimates the required headwater depth (HW) upstream of a circular pipe culvert operating under inlet control, given a design discharge and culvert geometry — a standard first check in culvert sizing.

Governing Equation

Empirical inlet-control headwater equation (FHWA-style form):

HW = D × [ K × (Q / (A × g^0.5 × D^0.5))^M + 0.5S ]

Where: - HW — required headwater depth above the culvert invert (m) - D — culvert diameter (m) - K — inlet coefficient (depends on inlet edge configuration — e.g., square edge, mitered, beveled) - Q — design discharge (m³/s) - A — culvert cross-sectional (barrel) area = π D² / 4 - g — gravitational acceleration (9.81 m/s²) - S — culvert/bed slope - M — exponent in the inlet-control equation (this implementation uses a fixed exponent of 2, i.e., M = 2, a common simplification of the general FHWA inlet-control form)

Inputs

Solution Method

This is a direct (non-iterative) calculation:

1. Compute barrel area: A = π D² / 4
2. Compute barrel velocity: V = Q / A
3. Compute headwater depth using the formula above, with the discharge term raised to the power M = 2.

Outputs

• Required headwater depth (HW, m)
• Culvert (barrel) flow velocity (V, m/s)

Notes & Limitations

• This is an inlet control check only — it does not evaluate outlet control (which depends on tailwater, barrel friction losses, and exit losses) or compare the two to determine the governing (higher) headwater, as is standard practice in full culvert design (e.g., per FHWA HDS-5).
• The exponent M and coefficient K in the true FHWA method vary by culvert shape/material and inlet edge type and are read from standard charts/tables; here they are simplified to a fixed M = 2 with K as a direct user input — treat results as a preliminary/approximate estimate rather than a final design value.
• Does not check for the culvert flowing full (submerged inlet) versus partially full, nor perform capacity checks against pipe flow limits.