Weir Hydraulic Calculation Tool

Weir Hydraulic Analysis Tool - Worksheet

Free-Flow Overtopping Principles

1. Flow Conditions
Calculation Mode	Given Head, Find Q Given Q, Find Head
Head over Crest (H)		m
-+
Design Discharge (Q)		m3/s
-+

2. Weir Geometry
Weir Type	Rectangular (Sharp-Crested) Cipolletti (Trapezoidal) V-Notch (Triangular) Broad-Crested Crump (Triangular Profile) Ogee Spillway Labyrinth (Folded Crest)
Crest Length (L)		m
V-Notch Angle (θ)		°
Crest Breadth (Flow Dir.)		m
Physical Channel Width		m
Number of Cycles		-
Design Head (Hd)		m
Up/Down Slopes (H:1)
End Contractions (n)	0 (Suppressed) 1 (One end) 2 (Both ends)	-
Weir Height (P)		m
Discharge Coeff (Cw)		Presets... Sharp Rect Cipolletti V-Notch (90°) Broad-Crested Crump Weir Ogee Labyrinth

* End contractions reduce the effective length of rectangular weirs. For Labyrinth weirs, enter the total folded length as 'L'.

Guide: How to Select C_w

1. Units Matter!
C_w is dimensional. It changes drastically based on units:
• Metric (m^0.5/s): 1.40 to 2.20
• Imperial (ft^0.5/s): 2.50 to 4.00

2. Adjustments by Weir Type

A. Sharp-Crested (Std: 1.84 M / 3.33 I)

• If H/P > 0.5, bump up C_w slightly (~1.95 M / ~3.5 I).
• Nappe MUST be aerated.

B. V-Notch (Std Base: 1.38 M / 2.50 I)

• For narrower angles (60°, 45°), base drops slightly due to boundary friction.

C. Cipolletti (Fixed: 1.86 M / 3.37 I)

• The 1:4 slopes balance end contractions. Keep constant.

D. Broad-Crested (Range: 1.44 - 1.70 M)

• Low head (H/B_c < 0.2): Use lower value (~1.45 M) due to friction.
• Ideal (H/B_c ≈ 0.25 - 0.4): Use average 1.60 M.
• High head (H/B_c > 0.5): Water may detach. Use higher value (~1.70 M).

E. Ogee Spillway (Range: 2.10 - 2.25 M)

• If H == H_d: Use optimal 2.20 M.
• If H < H_d: Efficiency drops. Use ~2.00 M.
• If H > H_d: Efficiency increases (~2.25 M), but risks cavitation.

F. Crump (Std: 1.96 M / 3.55 I)

• Extremely stable. Stick to standard.

G. Labyrinth (Range: 1.40 - 1.70 M)

• Jets collide inside folds. Use ~1.70 M for low heads, dropping to ~1.45 M for high heads.

Hydraulic Results Summary
Discharge (Q)	Head (H)	Water Surface Elev	Critical Depth (yc)	Effective Length (Le)
0.00 m³/s	0.00 m	0.00 m	0.00 m	0.00 m

Weir Profile View

Front Cross-Section View

Weir Rating Curve (H vs Q)

Flow Scenario Analysis
Scenario	Discharge (m³/s)	Head, H (m)	WSEL (m)	yc (m)	Effective Length (m)

Theoretical Background
1. Standard Weir Equation: Applies to Rectangular, Broad-Crested, and Ogee weirs. Q = Cw · Le · H1.5 2. V-Notch (Triangular) Equation: Used for low-flow measurement accuracy. Q = Cw · tan(θ/2) · H2.5 (Cw is the base coefficient, scaled by the notch angle) 3. Specific Weir Types: Cipolletti: Trapezoidal weir with 1:4 side slopes. The slope perfectly offsets end contractions, so Le = L. Crump: Triangular profile (2:1 upstream, 5:1 downstream) ensuring stable hydraulic performance. Labyrinth: Zig-zag / folded crest. Dramatically increases L for a given physical channel width. 4. Effective Length (Francis Formula): Accounts for flow contraction at the edges of rectangular weir openings. Le = L - 0.1 · n · H (where n is the number of end contractions: 0, 1, or 2) 5. Critical Depth (yc): 6. Reference Typical Discharge Coefficients (Cw / Cd): Weir Type Metric (m0.5/s) Imperial (ft0.5/s) Sharp-Crested (Rectangular) 1.80 - 1.95 (Avg: 1.84) 3.26 - 3.53 (Avg: 3.33) Cipolletti 1.86 3.37 Broad-Crested 1.44 - 1.70 (Avg: 1.60) 2.61 - 3.08 (Avg: 2.90) Crump 1.95 - 2.05 3.53 - 3.71 Ogee Spillway 2.10 - 2.25 3.80 - 4.08 Labyrinth 1.40 - 2.10 2.53 - 3.80 V-Notch (Base Cw) ~ 1.38 ~ 2.50 Note on Cw vs. Cd (Weir vs. Discharge Coefficient): Cw (Weir Coefficient): A dimensional parameter (units of L0.5/T) used for open, free-surface flow over a structure. Because it inherently includes the acceleration of gravity, its numerical value heavily changes depending on whether you use Metric or Imperial units. Cd (Discharge Coefficient): A dimensionless ratio (typically 0.6 to 0.8) representing the ratio of actual flow to theoretical flow. It is universally used across both unit systems and is primarily applied to enclosed orifice/pressure flows. For a standard rectangular weir, they are mathematically related by: Cw = (2/3) · Cd · √(2g)
References
USBR Water Measurement Manual (2001). (The definitive guide for standard weir equations, discharge coefficients, and proper installation dimensions). Bos, M. G. (1989). Discharge Measurement Structures. ILRI Publication 20. (Comprehensive international standards for flumes, sharp-crested, and broad-crested weirs). Brater, E. F., & King, H. W. (1976). Handbook of Hydraulics. McGraw-Hill. (Standard reference for Francis equations and empirical coefficient charts). Henderson, F. M. (1966). Open Channel Flow. Macmillan. (Detailed derivation of critical depth, specific energy, and hydraulic nappe behavior).