Hydraulic Jump & Stilling Basin – Theory & Design Notes

1. What is a hydraulic jump?

A hydraulic jump is the rapid transition from supercritical (shallow, fast) flow to subcritical (deeper, slower) flow in an open channel. It dissipates a large portion of the flow’s kinetic energy over a relatively short distance – which is why stilling basins are placed just downstream of spillways, power outlets and sluices.

For a horizontal, rectangular channel the jump is characterised by two conjugate depths: pre‑jump depth y₁ and sequent depth y₂, related through the momentum equation.

2. Basic hydraulic relations used in the tool

3. Energy loss and jump classification

3.1 Specific energy & loss

Specific energy (per unit weight) in a rectangular channel is:

For a classical hydraulic jump in a rectangular channel, ΔE can also be expressed directly in terms of the conjugate depths:

3.2 Qualitative jump type (Fr₁‑based)

The tool labels the jump approximately as:

• Fr₁ ≲ 1.7: weak / undular jump – limited turbulence & energy dissipation.
• 1.7 ≲ Fr₁ ≲ 2.5: oscillating / unstable jump.
• 2.5 ≲ Fr₁ ≲ 4.5: steady jump – typical range for many stilling basins.
• 4.5 ≲ Fr₁ ≲ 9: strong jump – very efficient energy dissipation.
• Fr₁ ≳ 9: very strong / rough jump – high turbulence and structural demands.

4. Jump length correlations & stilling basin length

4.1 Jump length formulas implemented in the tool

There is no single “exact” length for a hydraulic jump – different experiments give different correlations. The tool implements two simple empirical forms and lets you choose which one to adopt:

In the tool, you can select:

• Height‑based: Lj = k_Lj·(y₂ − y₁)
• y₂‑based: Lj = c_y2·y₂
• Conservative: Lj = max{ k_Lj(y₂ − y₁), c_y2y₂ }

4.2 Stilling basin length

Once a jump length Lj is adopted, the “hydraulic” basin length is inflated by a factor k_basin to allow for appurtenances, uncertainties and model bias:

5. USBR stilling basin types – quick guidance

The tool gives a very simplified suggestion for an appropriate USBR stilling basin type, based solely on Fr₁ and V₁. This is for guidance only; final selection must follow USBR EM‑25 and project‑specific analysis.

• Type I – plain slab jump basin for relatively low Froude numbers (roughly Fr₁ ≲ 4). A common rule is
  L ≈ 6 · y₂, tailwater depth ≈ 1.1·y₂.
• Type IV / SAF‑type – transition range Fr₁ ≈ 2.5–4.5, often with modified blocks & end sill. Basin length similar to Type I, but with different internal appurtenances.
• Type III – Fr₁ > 4.5 with moderate velocities (say V₁ up to ~20 m/s). Uses chute blocks plus baffle blocks & end sill to shorten the basin (commonly around 3–4.5 y₂).
• Type II – Fr₁ > 4.5 with very high velocities, where impact on baffle blocks would be excessive. Uses chute blocks and an end sill but omits baffle blocks; basin length ≈ 4.5 y₂.

The suggestion in the tool is deliberately conservative and meant to trigger the right chapter of the design manual – not to replace detailed design.

6. Worked example (matches the quick design tool)

Consider a spillway stilling basin with the following preliminary design values:

Step 1 – Unit discharge and pre‑jump velocity

Unit discharge: q = Q / B = 80 / 10 = 8.0 m²/s.
Pre‑jump velocity: V₁ = q / y₁ = 8.0 / 0.60 ≈ 13.3 m/s.

Step 2 – Upstream Froude number

Fr₁ = V₁ / √(g · y₁) = 13.3 / √(9.81 · 0.60).
√(9.81 · 0.60) ≈ √5.89 ≈ 2.43, so Fr₁ ≈ 13.3 / 2.43 ≈ 5.5 strong jump.

Step 3 – Conjugate depth y₂

Use the Bélanger equation:

So the sequent depth is about y₂ ≈ 4.4 m.

Step 4 – Energy loss

Specific energies:

• E₁ = y₁ + V₁² / (2g) ≈ 0.60 + 13.3² / (2·9.81) ≈ 0.60 + 177 / 19.62 ≈ 0.60 + 9.0 ≈ 9.6 m
• Downstream velocity: V₂ = q / y₂ ≈ 8.0 / 4.4 ≈ 1.8 m/s (roughly).
  E₂ = y₂ + V₂² / (2g) ≈ 4.4 + 1.8² / (2·9.81) ≈ 4.4 + 3.2 / 19.62 ≈ 4.4 + 0.16 ≈ 4.6 m

Energy loss: ΔE ≈ 9.6 − 4.6 ≈ 5.0 m (about half the specific energy is dissipated in the jump).

Step 5 – Jump length & basin length

Height‑based correlation:

y₂‑based correlation:

The two estimates are very similar (≈26 m). If we choose the conservative “max” option, Lj,adopt ≈ 26.4 m. For k_basin = 1.1:

So a stilling basin floor length of about 29 m is indicated for this discharge and depth, before refining the layout with blocks, piers, end sill and detailed code provisions.

Step 6 – USBR type

With Fr₁ ≈ 5.5 and V₁ ≈ 13.3 m/s, the tool will typically suggest a USBR Type III basin (chute blocks + baffle blocks + end sill) as a starting point, or Type II if baffle blocks are not acceptable. A precise choice requires referring to USBR EM‑25.

The example above is intentionally slightly rounded; the tool will compute the same quantities with full precision and show you the detailed intermediate results.

7. How to use this with the online tool

1. Start from your spillway / outlet rating curve to estimate Q, B and y₁ at the basin entrance.
2. Enter these into the Hydraulic Jump & Stilling Basin – Quick Design tool.
3. Inspect Fr₁, y₂, energy loss and jump length.
4. Adjust k_Lj, c_y2 and k_basin to match your design philosophy (plain basin vs. heavily appurtenanced).
5. Check the USBR type suggestion and cross‑reference with the relevant manual chapter.
6. Once a tentative layout is chosen, move on to anti‑scour checks, floor thickness, uplift, key length and downstream river morphodynamics.

This page is intentionally “design‑office friendly”: it shows what the tool is doing, so you can quickly sanity‑check outputs against hand calculations or other software.