Gate Hydraulic Calculation Tool

Gate Hydraulic Analysis Tool - Worksheet

Free & Submerged Flow Principles

1. Flow Conditions
Calculation Mode	Given Head, Find Q Given Q, Find Head
Upstream Depth (y1)		m
-+
Design Discharge (Q)		m3/s
-+
Tailwater Mode	Known / Initial Depth Compute Normal Depth
Tailwater Depth (y3)		m

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

2. Gate Geometry & Sill
Gate Type	Sluice Gate (Vertical) Radial Gate (Tainter)
Bottom Sill / Weir	None (Flat Bed) Broad-Crested Sill Ogee Crest Sharp-Crested Weir
Sill Height (P)		m
Gate Opening (a)		m
-+
Gate Width (B)		m
Contraction Coeff (Cc)		Presets... 0.61 (Sluice) 0.62 (Radial)

* The gate opening (a) is measured vertically from the crest of the sill to the lip of the gate.

Hydraulic Results Summary
Discharge (Q)	Upstream Head (y₁)	Vena Contracta (y₂)	Jump Conjugate (y₂*)	Jump Length (Lj)
0.00 m³/s	0.00 m	0.00 m	0.00 m	0.00 m	FREE
Discharge Coeff (Cd / Cw)	Jet Velocity (V₂)	Froude No. (F₂)	Jump Loss (ΔE)
0.00	0.00 m/s	0.00	0.00 m

Gate Profile Schematic

Rating Curve (y₁ vs Q)

Discharge vs Opening (Q vs a)

Tailwater Effect (Q vs y₃)

Energy Loss & Jump vs Opening

Flow Scenario Analysis (Varying Upstream Head)
Scenario Head	y₁ (m)	Discharge Q (m³/s)	Cd/Cw	y2* (m)	Froude (F2)	Control State

Theoretical Background

1. Sill / Weir Effect: The effective head on the gate is reduced by the sill height (H₁ = y₁ - P). If the upstream water level drops below the gate lip (y₁ < P + a), the gate stops restricting flow, and the system acts entirely as an open weir over the sill. 2. Free Gate Flow Equation: Occurs when the downstream tailwater does not drown the hydraulic jump. Q = Cd · B · a · √(2g · H₁) 3. Submerged Gate Flow Equation: Occurs when the tailwater forces the hydraulic jump back against the gate. Q = Cc · B · a · √(2g · (H₁ - H₃)) 4. Weir Flow Equation (Gate is Open): When the gate lip clears the water surface (or Qweir < Qgate), the sill controls the flow: Q = 2/3 · Cw · B · √(2g) · H₁1.5 Broad-Crested: Cw ≈ 0.60 Ogee Crest: Cw ≈ 0.75 Sharp-Crested (Rehbock Eq): Cw = 0.602 + 0.083·(H₁/P) 5. Submergence & Hydraulic Jump: Weirs: Reduced using Villemonte Eq if H₃/H₁ > 0.67: Qsub = Qfree[1 - (H₃/H₁)1.5]0.385 Gates: Flow transitions to submerged if tailwater (H₃) exceeds the jump conjugate depth (y₂*): y₂* = (y₂ / 2) · [ √(1 + 8 · F₂²) - 1 ]

References & Sources

Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill. (General gate flow equations, hydraulic jump conjugate depth, Manning's equation). [View Archive] Villemonte, J. R. (1947). Submerged Weir Discharge Studies. Engineering News-Record. (Submerged weir capacity reduction factor). [View on Google Scholar] Rehbock, T. (1929). Discussion of 'Precise Weir Measurements'. Transactions of the American Society of Civil Engineers. (Sharp-crested weir discharge coefficient Cw calculation). [View on ASCE] U.S. Bureau of Reclamation (1987). Design of Small Dams (3rd ed.). Water Resources Technical Publication. (Hydraulic jump length approximation Lj ≈ 6y, Ogee crest coefficients). [Download PDF] Henderson, F. M. (1966). Open Channel Flow. Macmillan. (Energy loss formulas and broad-crested sill theory). [View Archive]