Culvert Calculator

Inlet control

FHWA HDS-5 (2012) Appendix A. Unsubmerged inlets (Q/AD^0.5 ≤ 3.5) use Form 1, HW/D = H_c/D + K(Q/AD^0.5)^M + K_sS, or Form 2, HW/D = K(Q/AD^0.5)^M; submerged inlets (≥ 4.0) use HW/D = c(Q/AD^0.5)² + Y + K_sS; between them HDS-5 interpolates. K, M, c and Y come from HDS-5 Table A.1 for the inlet you choose.

Outlet control

A water-surface profile is computed through the barrel from the outlet (the tailwater or critical depth, whichever is higher) by the direct-step method. Where the profile reaches the crown, the barrel runs full and the friction slope of full flow applies. The headwater is the inlet depth (or pressure head) plus (1 + k_e)V²/2g, with k_e from HDS-5 Table C.2. This is the profile basis FHWA HY-8 uses, rather than the (d_c + D)/2 shortcut.

Which control governs

The higher of the two headwaters governs. When the barrel is steep and the tailwater is below critical depth, the barrel flows supercritical and outlet control does not govern; the outlet depth then follows the supercritical profile from the inlet.

Flow for a headwater

For an allowable headwater the calculator finds the flow whose governing headwater equals it, so a culvert can be checked against a roadway or property elevation.

Roadway overtopping

FHWA HDS-5 Eq. 3.9: Q_o = C_d L HW_r^1.5, with C_d = k_tC_r. C_r depends on the surface, the depth over the crest HW_r and the crest width L_r, and k_t on how far the tailwater rises above the crest. Both are published only as curves (Figure 3.11), so the calculator uses values read from those curves. The culvert flow and the road flow that give one headwater and add up to the total are found by iteration, the division HDS-5 section 3.1.5 describes.

Identical barrels

Barrels of the same size, material, inverts and inlet share the flow equally, so each is computed with its share and all have the same headwater.

Tailwater from a channel

The tailwater is either a constant elevation or normal depth by Manning’s equation in a trapezoidal, rectangular or triangular channel below the outlet, at the total flow including any flow over the road. Normal depth assumes nothing downstream raises the level; if something does, enter a constant elevation.

The calculator is tested against the cases below every time its code changes.

Tolerances against HY-8: headwater ±2% of the headwater depth; inlet control for the box (chart 8) and corrugated metal projecting (chart 2) inlets ±5%, because HY-8 evaluates inlet control with polynomial fits of the same curves (HDS-5 §A.5) while this calculator uses the HDS-5 equations. Rows HY-8 marks “inlet control shown, profile substantially full flow” are compared on inlet-control depth only. In the crossing cases the culvert flow and road flow are compared within 3% of the total flow, because a small change in headwater moves flow between them.

• Barrels must be identical. Barrels of different sizes or inverts, embedment, arches, pipe-arches, tapered inlets and improved inlets are not computed yet.
• The road is one level crest. A sag curve is represented as HDS-5 Figure 3.12B describes, by one level crest with the top width of the overflow area as its length; a road profile by segments is not computed.
• C_r and k_t are read from the published curves of HDS-5 Figure 3.11, not from equations. They agree with the values FHWA HY-8 applies within about 1%. Past the end of the k_t curve the factor is taken in a straight line to 0 at h_t/HW_r = 1, and the calculator says so.
• Flow over the road is computed as a discharge only. Depth and velocity limits for traffic, and erosion of the embankment, are not checked.
• Tailwater is a constant elevation or normal depth in a prismatic channel; backwater from downstream is not computed.
• Adverse (uphill) barrels are refused.
• Inlet control follows the HDS-5 equations; FHWA HY-8 uses polynomial fits and can differ by a few percent for some inlets (up to about 5% in the cases checked).
• Your city, county or TxDOT may set the design frequency, allowable headwater and outlet velocity limits. Those criteria decide the design.

What are inlet control and outlet control?

In inlet control the entrance limits the flow, and the headwater depends on the inlet shape and edge. In outlet control the barrel limits it, through friction, entrance and exit losses and the tailwater. The calculator computes both by the FHWA HDS-5 method and reports the higher headwater as the one that governs.

How was it checked?

Against fourteen FHWA HY-8 runs. Six cover one barrel (66 flow rates): pipe and box barrels, three inlet types, mild and steep slopes, low and high tailwater; the governing control matched in all 66 rows, outlet-control headwater within 0.3%, and inlet-control headwater within 2% (5% for box and projecting corrugated metal inlets, where HY-8 uses polynomial fits of the HDS-5 charts). Eight cover whole crossings (88 flow rates): identical barrels, paved, gravel and entered road coefficients, a submerged road and a channel tailwater. The Verification tab lists every case.

Does it compute road overtopping?

Yes, for a level road crest. Enter the crest elevation, length and width and the surface; the calculator divides the flow between the culvert and the road at one headwater by FHWA HDS-5 Eq. 3.9, including submergence by the tailwater, and draws the performance curve of the whole crossing. It reports the flow over the road; your agency’s limits on depth over the road decide whether that is acceptable.

Can it size a culvert?

It computes a culvert you describe, so you can try sizes and numbers of identical barrels and compare the headwater. It does not choose a size for you. Barrels of different sizes, arches and improved inlets are not computed yet; the Limits tab lists them.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.