Drop Structure and Stilling Basin Design (Hydraulic Jump)

Drop Structure & Stilling Basin Design

Hydraulic Jump & Energy Dissipation

1. Design Flow
Total Discharge (Q)		m³/s
Tailwater Mode	Known / Initial Depth Compute Normal Depth
Tailwater Depth (ytw)		m

Downstream Channel Properties
Channel Shape	Rectangular Trapezoidal
Bottom Width (btw)		m
Side Slope (z)		H:1V
Manning's n
Bed Slope (S0)

2. Structure Geometry
Drop Type	Vertical Drop Ogee Spillway Sloped Chute
Chute Slope (z)		H:1V
Drop Height (Δz)		m
Basin Width (B)		m
Unit Discharge (q)		m³/s/m
Basin Depression (d)		m
Basin Length (Lb)	Auto (USBR) Custom Length
Custom Length		m
Drop Energy Loss %		%

* The basin depression (d) lowers the floor of the stilling basin below the downstream channel invert to ensure the hydraulic jump does not sweep out.

Hydraulic Jump Analysis
Drop Length (Ld)	Critical Depth (yc)	Toe Depth (y₁)	Req. Tailwater (y₂*)	Basin Length (Lb)	Basin Status
0.00 m	0.00 m	0.00 m	0.00 m	0.00 m	CONTAINED USBR Basin: Type III
Upstream Head (H)	Froude No. (F₁)	Velocity at Toe (v₁)	Energy Loss (ΔE)	Actual Depth (yb)
0.00 m	0.00	0.00 m/s	0.00 m	0.00 m

1. Natural Channel (Without Basin, d=0)

2. Designed Structure (With Basin)

3. Stilling Basin Plan View (Top-Down)

Specific Energy Curve (E vs y)

USBR Basin Matrix (Fr vs V)

Froude No.	Velocity	Basin Type	Characteristics
1.0 - 1.7	Any	None	Standing wave. No baffle blocks needed.
2.5 - 4.5	Any	Type IV	Oscillating jump. Requires large deflector blocks.
> 4.5	< 18 m/s	Type III	Stable jump. Uses chute blocks & baffle blocks.
> 4.5	> 18 m/s	Type II	High velocity. Chute blocks & dentated sill only.

Theoretical Background

1. Energy at the Toe (y₁): Water falling over the drop converts potential energy (Δz) into kinetic energy. The depth at the toe (y₁) is found by solving the specific energy equation: E₁ = y₁ + q² / (2g·y₁²) = Δz + 1.5·yc + d - Hloss 2. Conjugate Depth (y₂*): The depth required to force the supercritical jet to jump back to subcritical flow. It depends heavily on the Froude number (F₁). y₂* = (y₁ / 2) · [ √(1 + 8·F₁²) - 1 ] 3. Basin Depression (d): If the natural tailwater (ytw) is less than the required conjugate depth (y₂*), the jump will sweep downstream and cause severe erosion. Lowering the basin floor by depth d ensures containment. Required d ≈ y₂* - ytw 4. Stilling Basin Length (Lb): The natural jump length is Lj ≈ 6(y₂* - y₁). USBR basins use blocks and baffles to shorten the required length of the concrete structure: Type II: Lb ≈ 4.3·y₂* | Type III: Lb ≈ 2.7·y₂* | Type IV: Lb ≈ 6.1·y₂* 5. Impact Distance / Drop Length (Ld): The horizontal distance from the crest to the toe/impact point depends on the structure geometry. For a vertical free overfall, an empirical trajectory formula is used: Vertical: Ld = 4.30·Δz·(yc / Δz)0.81 | Chute: Ld = Δz·z | Ogee: Ld ≈ 0.8·Δz 6. USBR Basin Block & Sill Dimensions: Appurtenances are scaled using the toe depth (y₁) and conjugate depth (y₂) according to standard USBR guidelines: Chute/Floor Blocks (Types II & III): Height = Width = Spacing = y₁ Baffle Blocks (Type III): Height = 1.5·y₁, Width = Spacing = 0.75·y₁ Deflector Blocks (Type IV): Height = 2.0·y₁, Width = 0.75·y₁, Spacing = 2.5·y₁ End Sills: Type II Dentated (h = 0.2·y₂, w = s = 0.15·y₂); Type III Solid (h = 0.2·y₂); Type IV Solid (h = 1.25·y₁)

References & Sources
U.S. Bureau of Reclamation (1987). Design of Small Dams. (Standard Stilling Basin Types II, III, IV design criteria). [Download PDF] Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill. (Specific Energy and Hydraulic Jump derivation). [View Archive]