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Weir Flow Calculator

Calculate flow rate over rectangular, V-notch, and Cipolletti weirs from head measurement. Enter values for instant results with step-by-step formulas.

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Engineering

Weir Flow Calculator

Free online weir flow calculator. Get instant, accurate results with step-by-step explanations.

Last updated: December 2025

Calculator

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Formula

Rectangular: Q = (2/3)Cd ร— L ร— โˆš(2g) ร— H^(3/2) | Triangular (90ยฐ): Q = (8/15)Cd ร— โˆš(2g) ร— tan(ฮธ/2) ร— H^(5/2)

Francis formula for rectangular weirs (Cdโ‰ˆ0.62). Kindsvater-Shen for triangular (V-notch) weirs. g = 9.81 m/sยฒ.

Last reviewed: December 2025

Worked Examples

Example 1: Rectangular weir

L=2m, H=0.3m
Solution:
Q = 0.667ร—0.62ร—2ร—โˆš19.62ร—0.3^1.5 = 0.596 mยณ/s
Result: 0.596 mยณ/s
Expert Insights

Background & Theory

The Weir Flow Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ€” the permanent self-weight of structural elements, finishes, and fixed equipment โ€” and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ€“0.45 typically yields concrete with 28-day compressive strengths of 30โ€“40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ€“2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ€“350 MPa for mild steel) and ultimate tensile strength (typically 400โ€“500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ€“2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.

History

The history behind the Weir Flow Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ€” a mixture of volcanic ash, lime, and seawater โ€” enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ€” including the 1971 San Fernando and 1994 Northridge events โ€” drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.

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Frequently Asked Questions

V-notch (triangular) weirs are more accurate at low flows. Rectangular weirs handle higher flows and are simpler to construct.
For accurate measurements, the approach channel should be straight and at least 10-20 times the maximum head length upstream to allow uniform flow. The weir crest should be level and sharp-edged, and the nappe (water sheet) must spring clear of the weir plate. The head should be measured at least 3-4 times the maximum head distance upstream to avoid the drawdown zone near the weir. Submerged tailwater conditions invalidate standard weir formulas and require correction factors.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

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Formula

Rectangular: Q = (2/3)Cd ร— L ร— โˆš(2g) ร— H^(3/2) | Triangular (90ยฐ): Q = (8/15)Cd ร— โˆš(2g) ร— tan(ฮธ/2) ร— H^(5/2)

Francis formula for rectangular weirs (Cdโ‰ˆ0.62). Kindsvater-Shen for triangular (V-notch) weirs. g = 9.81 m/sยฒ.

Frequently Asked Questions

How do I interpret the result?

Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.

Can I use the results for professional or academic purposes?

You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.

How do I get the most accurate result?

Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.

How do I verify Weir Flow Calculator's result independently?

The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.

How accurate are the results from Weir Flow Calculator?

All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.

Why might my result differ from another tool or reference?

Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.

Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy