Calculator
Example Data Table
| Scenario | Inputs | Computed discharge |
|---|---|---|
| Velocity–Area (rectangular) | b=4.0 m, d=0.6 m, V=0.85 m/s | Q ≈ 2.04 m³/s |
| Velocity–Area (trapezoidal) | b=3.0 m, z=1.5, d=0.8 m, V=0.75 m/s | Q ≈ 2.34 m³/s |
| Weir (rectangular) | Cd=0.62, L=0.60 m, H=0.18 m | Q ≈ 0.052 m³/s |
| Weir (V-notch 90°) | Cd=0.62, θ=90°, H=0.14 m | Q ≈ 0.028 m³/s |
Formulas Used
A from geometry, then multiply by mean velocity V.Q = A · VR = A / PV = (1/n) · R^(2/3) · S^(1/2)Q = (1/n) · A · R^(2/3) · S^(1/2)Q = (2/3) · C_d · L · √(2g) · H^(3/2)Q = (8/15) · C_d · tan(θ/2) · √(2g) · H^(5/2)g = 9.80665 m/s², H is head above crest, L is crest length, and C_d is a calibration coefficient.How to Use
- Select a method that matches your field setup.
- Pick units, then enter geometry and measurement values.
- For Velocity–Area, measure mean velocity or use Float/Manning.
- For weirs, measure head carefully at a stable upstream point.
- Press Calculate; results appear above the form.
- Use Download buttons for CSV and PDF records.
Professional Guide
1) Why stream discharge matters
Stream discharge (Q) links rainfall, catchment response, and channel capacity. It supports flood forecasting, irrigation scheduling, habitat assessment, and sediment transport studies. Typical field targets range from 0.01–0.5 m³/s for small creeks to 10–1,000+ m³/s for major rivers, depending on season and basin size.
2) Choosing the right method
Use Velocity–Area for open reaches with measurable velocity and a stable cross‑section. Choose Weir mode for controlled structures where head can be measured precisely. If you lack a velocity meter, the Float option provides a practical estimate; Manning is best for steady, uniform flow where slope and roughness are defensible.
3) Cross‑section geometry and accuracy
Area errors directly scale discharge. A 5% area overestimate yields ~5% discharge overestimate. Measure width and depth at representative locations, avoid backwater, and keep geometry consistent with flow conditions. Trapezoidal sections are common in lined canals; rectangular is typical for flumes and lab channels.
4) Velocity measurement strategies
For direct velocity, average multiple readings across the section when possible. With the float approach, surface speed is converted to mean speed using k ≈ 0.80–0.90; this calculator defaults to 0.85 when not supplied. Longer float distances reduce timing noise and improve repeatability.
5) Manning estimate for open‑channel flow
Manning velocity uses V = (1/n) R2/3 S1/2. Typical roughness values are 0.010–0.015 for finished concrete, 0.020–0.035 for earth canals, and 0.035–0.070 for natural streams with vegetation. Because Q scales with S1/2, doubling slope increases velocity by ~41%.
6) Weir measurements and best practice
Sharp‑crested weirs are sensitive to head (H). Rectangular weirs follow Q ∝ H3/2, while V‑notch weirs follow Q ∝ H5/2, making small head errors more significant. Measure head upstream where velocity is low, and keep the crest clean and level.
7) Unit handling and reporting
This tool reports discharge in m³/s, L/s, and ft³/s for quick comparison with hydrologic references and local standards. Conversions are internal, so you can enter lengths in meters, feet, or smaller units without manual recalculation.
8) Uncertainty and quality control
Optional uncertainty inputs propagate using root‑sum‑square for key terms. For Velocity–Area, the calculator combines area and velocity percentages; for weirs, it combines coefficient and geometry/head terms. If the uncertainty seems high, repeat measurements, extend float distance, or refine the cross‑section survey.
FAQs
1) What is discharge in simple terms?
Discharge is the volume of water passing a cross‑section per second. It is commonly reported in m³/s, L/s, or ft³/s and represents how much water the stream delivers over time.
2) When should I use Velocity–Area?
Use it when you can estimate cross‑section area and mean velocity reliably. It is ideal for natural reaches, canals, and lab channels where you can measure depth/width and obtain velocity readings or float timing.
3) What k factor should I use for the float method?
k converts surface velocity to mean velocity. Many field surveys use k between 0.80 and 0.90. If you do not have site calibration, 0.85 is a practical default for moderate turbulence.
4) Why does Manning need wetted perimeter?
Manning uses hydraulic radius R = A/P, where P is wetted perimeter. Without P, R cannot be computed, and velocity cannot be estimated. Provide channel geometry or a measured perimeter for best results.
5) Which weir type is better for low flows?
V‑notch weirs are often preferred for low flows because discharge varies strongly with head, improving sensitivity. Rectangular weirs work well at higher flows when head remains within a stable, measurable range.
6) What does the discharge coefficient mean?
The coefficient Cd accounts for real‑world effects like contraction, viscosity, and crest shape. Use values from calibration, standards, or prior site tests. Small errors in Cd directly scale discharge.
7) How do I export my results?
After calculating, use the Download CSV or Download PDF buttons in the Results panel. The exports include method, key inputs, and computed discharge values to support field notes, reporting, and audit trails.