Water Discharge Calculator

Solve discharge with flexible hydraulic input options. Switch units, inspect formulas, and read sample tables. Get dependable outputs for coursework, checks, and planning today.

Calculation Inputs

Choose a hydraulic relation matching your available measurements.
Used for widths, depths, heads, and diameters.
Needed for weir equations. Keep standard gravity unless required otherwise.
Enter measured cross-sectional flow area.
Area conversion is applied automatically.
Use measured mean flow velocity.
Velocity is converted into metres per second.
Top width of the flowing rectangular section.
Average flow depth across the section.
Internal diameter of the flowing pipe.
Set 1 for full flow. Use a lower share for reduced effective area.
Width of the rectangular weir opening.
Measure steady upstream head relative to crest or notch apex.
Typical field estimates vary by geometry and calibration.
Enter the included V-notch angle.

Plotly Graph

This chart compares standard example discharges in m³/s and adds your latest computed result when available.

Chart unit: cubic metres per second

Formula Used

This calculator supports several standard discharge relationships so you can work from measured area, channel dimensions, pipe geometry, or weir head.

Method Formula Meaning
Area × Velocity Q = A × V Discharge equals flow area multiplied by average velocity.
Rectangular Channel Q = b × y × V Area is width times depth, then multiplied by mean velocity.
Circular Pipe Q = (πD²/4) × k × V Full pipe area is adjusted by an effective area factor.
Rectangular Weir Q = (2/3) × Cd × b × √(2g) × h3/2 Head-driven overflow relation for a sharp-crested rectangular weir.
V-Notch Weir Q = (8/15) × Cd × tan(θ/2) × √(2g) × h5/2 Common low-flow notch relation using head and notch angle.

How to Use This Calculator

  1. Select the method that matches your available field or study data.
  2. Choose the correct units before entering measurements.
  3. Enter positive values for area, dimensions, velocity, head, and coefficients.
  4. Click the calculate button to display discharge above the form.
  5. Review the converted units, steps, and notes for reasonableness.
  6. Use the CSV or PDF buttons to keep a clean record.

Example Data Table

Scenario Key Inputs Output (m³/s) Output (L/s)
Area × Velocity A = 2.4 m², V = 1.8 m/s 4.32 4,320
Rectangular Channel b = 1.5 m, y = 0.8 m, V = 1.4 m/s 1.68 1,680
Circular Pipe D = 0.6 m, k = 0.9, V = 2.2 m/s 0.559831 559.831
Rectangular Weir b = 1.2 m, h = 0.35 m, Cd = 0.62 0.45484 454.84
V-Notch Weir h = 0.28 m, θ = 90°, Cd = 0.58 0.056833 56.833

Why discharge estimation matters

Water discharge is the volumetric flow rate moving through a channel, pipe, or control section per unit time. In design work, even a small input error can shift computed capacity by several percentage points. Engineers, students, and field technicians use discharge estimates to size drainage, review pumping performance, and verify open-channel measurements under repeatable conditions.

Area and velocity relationship

The most direct equation is Q = A × V, where area and average velocity determine flow. If the wetted area is 2.4 square metres and the mean velocity is 1.8 metres per second, discharge becomes 4.32 cubic metres per second. This method is efficient when cross-sectional surveys and velocity readings are already available from current meters or flow sensors.

Channel and pipe interpretation

For rectangular channels, width and flow depth establish area before velocity is applied. A 1.5 metre width with 0.8 metre depth gives 1.2 square metres of area. At 1.4 metres per second, discharge becomes 1.68 cubic metres per second. In circular pipes, diameter controls full area, while an effective area factor adjusts for partially full conditions and nonuniform flow profiles.

Weir-based low and moderate flow checks

Weirs are practical when velocity measurement is difficult but head can be observed reliably. A rectangular weir with 1.2 metre crest width, 0.35 metre head, and coefficient 0.62 produces about 0.45484 cubic metres per second. A 90 degree V-notch with 0.28 metre head and coefficient 0.58 yields about 0.056833 cubic metres per second, which suits smaller controlled flows.

Unit conversion and reporting quality

Reporting the same result in multiple units improves communication across teams. One cubic metre per second equals 1000 litres per second and 3600 cubic metres per hour. Conversions are not new calculations, but they reduce transcription mistakes when comparing pump sheets, environmental reports, laboratory notes, and maintenance records that use different hydraulic conventions or regional preferences.

Improving result reliability

Accurate discharge estimation depends on representative measurements, stable approach conditions, and coefficients. Depth should be measured where surface disturbance is limited, while velocity should represent the bulk flow rather than isolated points. For coursework, show units and intermediate steps. For field practice, repeat measurements, compare methods when possible, and document assumptions before using the result for decisions.

FAQs

1. What does water discharge measure?

Water discharge measures the volume of water passing a section each second or hour. It is commonly expressed in m³/s, L/s, m³/h, ft³/s, or US gallons per minute.

2. When should I use area multiplied by velocity?

Use it when you already know the flow cross-sectional area and the representative average velocity. It is the fastest method for surveyed sections and instrument-based velocity readings.

3. Why does the pipe method use an effective area factor?

The factor adjusts full pipe area for partially full flow or reduced effective section. A value of 1 means full flow, while smaller values reduce the active area.

4. Why are weir coefficients required?

Coefficients account for real flow effects such as crest shape, contraction, and installation conditions. Using a realistic coefficient improves agreement between theoretical and observed discharge values.

5. Are unit conversions changing the physical result?

No. Conversions only restate the same discharge in other units. They help teams compare results across field notes, reports, equipment manuals, and regional conventions.

6. How can I improve accuracy in practice?

Measure dimensions carefully, use stable flow conditions, repeat readings, and document assumptions. When possible, compare more than one method to confirm that the final discharge is reasonable.

Related Calculators

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.