Physics-based open channel flow analysis and primary measurement device sizing for weirs and flumes
Discharge measurement devices (also called primary measurement devices or flow measurement structures) are engineered hydraulic structures installed in open channels to accurately measure water flow rates. These devices work by creating a known relationship between water level (stage) and discharge (flow rate).
Key Applications:
How They Work: By constricting flow through a calibrated geometry (weir notch or flume throat), these devices force a predictable stage-discharge relationship. Measuring water level at a specific location allows precise flow rate calculation using empirical equations validated through decades of research and standardized by organizations like ASTM, ISO, and USGS.
Suppressed & contracted configurations. Ideal for medium flows in rectangular channels. Simple construction, ISO 1438 compliant.
Triangular (90° or 60°) sharp-crested weirs. Excellent for low flows with wide measurement range (25:1). ISO 4360 standard.
Trapezoidal weirs with 1H:4V side slopes. Self-compensating for end contractions. Popular in irrigation and water rights.
Long horizontal crest structures. Used in dam spillways and high-flow applications. Excellent structural stability.
Converging-throat flumes with self-scouring action. ASTM D1941 standard. Best for wastewater and sediment-laden flows.
Smooth-transition flumes with minimal head loss (8-12%). High accuracy for clean industrial and municipal flows.
OpenFlow Measure is a specialized hydraulic engineering tool designed for civil engineers, hydrologists, and water resource professionals. It bridges the gap between channel analysis and measurement structure design through an integrated, two-module approach.
Key Distinction: Unlike standalone calculators, OpenFlow Measure ensures your measurement device is hydraulically compatible with the channel it will be installed in.
Module 1: Channel Definition & Analysis
Module 2: Measurement Device Design
Visual Feedback: Geometric conflicts (e.g., device taller than channel banks) are flagged immediately through the integrated visualization system.
Manning’s Equation is the fundamental relationship for uniform open channel flow, connecting velocity to channel characteristics and slope.
Variables:
Manning’s n Values: Concrete (0.012-0.014), Clean earth (0.022-0.030), Gravel bed (0.025-0.035), Vegetated channels (0.030-0.150)
Discharge Calculation:
Where Q = Discharge (m³/s) and A = Cross-sectional flow area (m²)
The Froude Number determines whether flow is subcritical, critical, or supercritical.
Where:
Flow Classification:
A suppressed weir extends across the full channel width, eliminating side contractions.
Q = Discharge (m³/s)
L = Crest length (m)
H = Head above crest (m)
Limitations:
When the weir is narrower than the channel, side contractions reduce effective length.
Q = Discharge (m³/s)
L = Physical crest length (m)
n = Number of end contractions (typically 2)
H = Head above crest (m)
Note: Each contraction reduces effective length by 0.1H meters
General Formula (Any Angle):
90° V-Notch Simplified (Thomson Equation):
Q = Discharge (m³/s)
Cd = Discharge coefficient (0.58-0.62)
θ = Notch angle (90° or 60° common)
H = Head above weir vertex (m)
g = 9.81 m/s²
Advantages: H2.5 relationship provides excellent sensitivity for low flows (25:1 range)
Trapezoidal weir with side slopes at 1H:4V (14° from vertical).
Q = Discharge (m³/s)
L = Bottom crest length (m)
H = Head above crest (m)
Key Feature: The 1:4 side slopes automatically compensate for end contractions—no correction factors needed
Long crest length (B/H > 2) forces critical flow on the crest.
Q = Discharge (m³/s)
Cd = Discharge coefficient (0.82-0.90)
L = Weir length perpendicular to flow (m)
H = Head above crest (m)
B = Crest width parallel to flow (m)
g = 9.81 m/s²
Free-Flow Equation:
Q = Discharge (m³/s)
K = Throat-specific coefficient
n = Throat-specific exponent
Ha = Head at upstream gauge (m)
Throat-Specific Coefficients (SI Units):
| Throat Width (W) | K | n | Flow Range (m³/s) |
|---|---|---|---|
| 76 mm (3″) | 0.176 | 1.55 | 0.0014 – 0.0085 |
| 152 mm (6″) | 0.381 | 1.58 | 0.0042 – 0.054 |
| 229 mm (9″) | 0.535 | 1.53 | 0.0085 – 0.110 |
| 305 mm (1 ft) | 0.690 | 1.522 | 0.011 – 0.252 |
| 610 mm (2 ft) | 1.426 | 1.547 | 0.028 – 0.937 |
| 914 mm (3 ft) | 2.148 | 1.566 | 0.045 – 1.922 |
Submergence Warning: When Hb/Ha > 0.70, flow becomes submerged and correction factors apply
Q = Discharge (m³/s)
Cd = Discharge coefficient (0.92-0.98)
Wt = Throat width (m)
H = Upstream head above throat invert (m)
g = 9.81 m/s²
Advantages: Head loss: 8-12% (vs. 30-50% for weirs), Accuracy: ±2-4%
Problem: Calculate discharge over a rectangular suppressed weir with detailed step-by-step calculations.
Step 1: Verify Design Constraints
Step 2: Calculate H1.5
Step 3: Apply the Formula
Step 4: Final Answer
Upstream water level = P + H = 0.80 + 0.40 = 1.20 m above channel bed
Problem: Calculate discharge for a contracted weir accounting for end contractions.
Step 1: Calculate End Contraction Reduction
Step 2: Calculate Effective Length
Step 3: Calculate H1.5
Step 4: Apply the Formula
Step 5: Final Answer
End contractions reduced effective length by 7 cm (4%), demonstrating why contracted weirs have slightly lower discharge than suppressed weirs of the same physical length.
Problem: Determine discharge through a triangular V-notch weir using the Thomson equation.
Step 1: Calculate √(2g)
Step 2: Calculate tan(θ/2)
Step 3: Calculate H2.5
Step 4: Calculate (8/15) × Cd
Step 5: Apply the Full Formula
Step 6: Final Answer
For 90° V-notch weirs, you can use the simplified Thomson equation:
(Note: Small difference due to rounding in coefficient derivation)
V-notch weirs excel at low flows due to H2.5 sensitivity. A 10% change in head results in ~25% change in discharge, providing excellent measurement precision.
Problem: Calculate discharge for a trapezoidal (Cipoletti) weir.
Step 1: Verify Side Slope
Step 2: Calculate H1.5
Step 3: Apply the Formula
Step 4: Final Answer
The coefficient 1.859 already accounts for the 1:4 side slope compensation—no end contraction corrections needed! This makes Cipoletti weirs simpler to calculate than contracted rectangular weirs.
At head H = 0.30 m, the top width is:
Problem: Calculate discharge over a broad-crested weir used in a spillway.
Step 1: Verify Broad-Crested Criteria
Step 2: Calculate √(2g)
Step 3: Calculate H1.5
Step 4: Apply the Formula
Step 5: Final Answer
On the broad crest, critical depth occurs:
This ensures the weir operates in the calibrated regime.
Problem: Calculate discharge through a standard 1-ft Parshall flume.
For 305 mm (1 ft) throat: K = 0.690, n = 1.522
Step 1: Identify Throat-Specific Constants
Step 2: Calculate Ha1.522
Alternative calculation using calculator:
Step 3: Apply the Formula
Step 4: Final Answer
If downstream head Hb is measured:
The upstream gauge (Ha) is located at 2/3 of the converging section length from the throat. For a 1-ft flume, this is approximately 0.46 m upstream of the throat.
Problem: Calculate discharge for a smaller 6-inch Parshall flume.
For 152 mm (6″) throat: K = 0.381, n = 1.58
Step 1: Identify Throat-Specific Constants
Step 2: Calculate Ha1.58
Alternative calculation:
Step 3: Apply the Formula
Step 4: Final Answer
Notice that different throat widths have different K and n values. Always use the throat-specific equation! Using the wrong constants will result in significant errors (±20-40%).
Problem: Calculate discharge through a custom Venturi flume with calibrated coefficient.
Step 1: Calculate √(g)
Step 2: Calculate H1.5
Step 3: Calculate Cd × Wt
Step 4: Apply the Formula
Step 5: Final Answer
Venturi flumes have minimal head loss compared to weirs:
The discharge coefficient Cd = 0.95 was determined by site-specific calibration. Without calibration, use Cd = 0.92-0.94 for preliminary design, then field-calibrate for ±2% accuracy.
Problem: Compare head requirements for Q = 0.500 m³/s using three different measurement devices.
Formula: Q = 1.84 × L × H1.5
Step 1: Rearrange for H
Step 2: Calculate Q / (1.84 × L)
Step 3: Apply Exponent 2/3
Formula: Q = 1.38 × H2.5
Step 1: Rearrange for H
Step 2: Calculate Q / 1.38
Step 3: Apply Exponent 0.4
Formula: Q = 1.426 × Ha1.547
Step 1: Rearrange for Ha
Step 2: Calculate Q / 1.426
Step 3: Apply Exponent 0.6464
| Device | Required Head | Head Loss | Best For |
|---|---|---|---|
| Rectangular Weir | 27.5 cm (lowest) | ~11 cm (40%) | Clean water, low head available |
| V-Notch Weir | 64.3 cm (highest) | ~26 cm (40%) | Low flows, not ideal here |
| Parshall Flume | 48.2 cm (moderate) | ~5 cm (10%) | Debris-laden, minimal head loss |
For Q = 0.500 m³/s: Choose Parshall Flume (610 mm throat)
Rationale: Only 5 cm head loss (vs. 11+ cm for weirs), handles sediment well, moderate installation cost, excellent accuracy over wide flow range.
Selecting the appropriate flow measurement device depends on multiple factors including flow characteristics, accuracy requirements, maintenance considerations, and budget constraints.
| Criterion | Rectangular Suppressed | Rectangular Contracted | V-Notch | Cipoletti |
|---|---|---|---|---|
| Best Application | Medium flows, full-width channels | Narrow channels, flexible installation | Low flows, high precision | Irrigation, simplified design |
| Head Loss | High (30-50% of head) | High (35-55% of head) | High (40-60% of head) | High (30-50% of head) |
| Sediment Tolerance | Poor – Sediment ponds | Poor – Sediment ponds | Very Poor – V traps debris | Poor – Sediment ponds |
| Accuracy Range | ±2% to 5% | ±3% to 5% | ±2% to 3% | ±3% to 5% |
| Installation Cost | Low | Low | Very Low | Low |
| Maintenance | Moderate – Regular cleaning | Moderate – Regular cleaning | High – Frequent debris removal | Moderate – Regular cleaning |
| Flow Range | Moderate (8:1 ratio) | Moderate (10:1 ratio) | Wide (25:1 ratio) | Moderate (8:1 ratio) |
| Regulatory Acceptance | Very High (ISO 1438) | High (ISO 1438) | Very High (ISO 4360) | Moderate (Regional standards) |
| Discharge Formula | Q = 1.84·L·H1.5 | Q = 1.84·(L-0.1nH)·H1.5 | Q = 1.38·H2.5 (90°) | Q = 1.859·L·H1.5 |
| Criterion | Broad-Crested Weir | Parshall Flume | Venturi Flume |
|---|---|---|---|
| Best Application | High flows, dam spillways | Wastewater, debris-laden flows | Clean water, industrial flows |
| Head Loss | Moderate (15-25% of head) | Low (10-15% of head) | Low (8-12% of head) |
| Sediment Tolerance | Good – Wide crest area | Excellent – Self-scouring | Good – Smooth transitions |
| Accuracy Range | ±3% to 5% | ±3% to 5% | ±2% to 4% |
| Installation Cost | Moderate | High | Very High |
| Maintenance | Low – Periodic inspection | Very Low – Minimal cleaning | Low – Minimal cleaning |
| Flow Range | Moderate (12:1 ratio) | Very Wide (20:1 ratio) | Wide (15:1 ratio) |
| Regulatory Acceptance | High (ISO 3846) | Very High (ASTM D1941) | High (ISO 4359) |
| Discharge Formula | Q = Cd·L·√(2g)·H1.5 | Q = K·Han | Q = Cd·Wt·√(g)·H1.5 |
Choose Rectangular Suppressed Weir when:
Choose Rectangular Contracted Weir when:
Choose V-Notch Weir when:
Choose Cipoletti Weir when:
Choose Broad-Crested Weir when:
Choose Parshall Flume when:
Choose Venturi Flume when:
Parshall flumes are the industry standard for influent and effluent measurement. Their self-cleaning properties prevent clogging from suspended solids, and the low head loss preserves hydraulic grade line elevation throughout the treatment train. OpenFlow Measure helps verify NPDES permit compliance by ensuring reported flows match installed device capacity.
V-notch weirs are commonly installed in detention/retention pond outlets to:
The high sensitivity of V-notch geometry allows precise measurement of both low baseflow and high storm events.
Rectangular and Cipoletti weirs enforce water rights allocations in distribution canals. OpenFlow Measure assists irrigation districts in:
Environmental regulations (e.g., EPA 40 CFR Part 122) often require continuous flow monitoring for industrial effluent. Engineers use OpenFlow Measure to:
Spillway rating curves, powerhouse discharge calculations, and environmental flow releases all require accurate flow measurement. OpenFlow Measure supports:
Continuous pit dewatering and tailings management require robust flow measurement systems. Flumes are preferred due to:
A weir or flume is an obstruction placed within an existing channel. If the device creates a water surface elevation exceeding the channel bank height, overflow will occur. OpenFlow Measure links Module 1 (channel analysis) and Module 2 (device design) to prevent this hydraulic failure mode by checking compatibility automatically.
A suppressed weir spans the full channel width with no side contractions—the crest length equals channel width. A contracted weir is narrower than the channel, causing lateral flow convergence. This contraction reduces effective discharge area and requires correction factors (e.g., Francis formula includes end contraction coefficients).
The primary focus is open channel (free-surface) flow. However, the Pipe module does support full-pipe pressure flow analysis using the Darcy-Weisbach equation. For partially-filled pipes flowing by gravity, use the Open Channel module with circular geometry.
Click the Download icon (bottom-right of visualization panel) to export high-resolution PNG images. Rating curves can be exported as CSV tables via the “Export Data” button in the results panel.
Weirs require free-falling nappe (jet) conditions to maintain calibrated accuracy. When downstream water level rises and “drowns” the weir crest, the flow transitions to submerged conditions. Standard discharge equations no longer apply, and correction factors (or different measurement approaches) are required. The software alerts you when tailwater elevation approaches critical submergence thresholds.
Manning’s equation is semi-empirical and highly sensitive to the roughness coefficient (n). For natural channels with vegetation, irregular cross-sections, and variable bed material, accuracy typically ranges from ±15% to ±25%. For engineered channels with uniform geometry and lining, accuracy improves to ±5% to ±10%. Always field-calibrate when possible.
Sharp-crested weirs require minimum head typically in the range of 0.05-0.10 m (2-4 inches) to ensure nappe ventilation and avoid surface tension effects. Below this threshold, accuracy degrades significantly. The software displays minimum recommended head values in the device limitations panel.
No. OpenFlow Measure assumes uniform, steady flow conditions. Tidal influence, backwater curves, and gradually varied flow require unsteady flow models or step-backwater calculations (e.g., HEC-RAS). Use this tool only for reaches where normal depth conditions apply.
Channel slope controls the approach velocity and flow depth. Steep slopes create supercritical approach flow, which can cause hydraulic jumps at the device. Mild slopes produce subcritical flow with higher upstream water levels. OpenFlow Measure recalculates the entire hydraulic profile when slope changes to ensure the device operates within its calibrated range.
Yes. OpenFlow Measure is an engineering aid, not a replacement for professional judgment. All designs should be reviewed and stamped by a licensed Professional Engineer (PE) or appropriate regulatory authority. Site-specific conditions (seepage, frost heave, seismic loads) are not modeled and require separate analysis.