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Sutro Proportional Linear Flow Weir Calculator

Calculates discharge Q and profile notch width x(y) for Sutro proportional weirs where flow rate is directly proportional to water head above datum.

Height of lower rectangular opening before curved flanks begin.

Full crest width of rectangular base section.

Measured upstream water surface head above base weir sill.

Sharp-crested Sutro weir discharge coefficient (typically 0.60 - 0.64).

Calculated Result
175.47 L/s

Discharge (Q)

Flow in m³/s

0.1755 m³/s

Linear Constant K

0.319 m²/s

Notch Top Width

0.2 m

Sensitivity Gain

3.19 L/s per cm

Total Weir Head

0.6 m

Calculation Breakdown

  1. Sutro Proportional Slope FactorK = Cd·b·√(2·g·a) = 0.319 m²/s; Total head = h + a = 0.6 m
  2. Linear Proportional Flow EvaluationQ = K·(h + 2a/3) = 0.1755 m³/s (175.47 L/s)
  3. Curved Notch Surface WidthTop opening width W_top = 2·b·[1 - (2/π)·arctan(√(h/a))] = 0.2 m

Sutro Weir Geometry & Flow

Interactive visualization based on your current inputs

Value
0.03.36.59.813Base Height a (m)Base Width b (m)Head H (m)Discharge (L/s) / 10ParameterValue

What Is the Sutro Proportional Linear Flow Weir Calculator?

Calculates discharge Q and profile notch width x(y) for Sutro proportional weirs where flow rate is directly proportional to water head above datum.

The Sutro Proportional Linear Flow Weir Calculator is an analytical tool in the construction domain designed to evaluate Base Rectangular Crest Height (a), Base Notch Width (b), Total Head Above Crest (H), Discharge Coefficient (Cd) using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Sutro Proportional Linear Flow Weir Calculator Work?

This calculator computes results by taking input values for Base Rectangular Crest Height (a), Base Notch Width (b), Total Head Above Crest (H), Discharge Coefficient (Cd) and applying the governing equation: Calculates linear discharge Q directly proportional to effective head (H - a/3), and computes profile coordinates for fabrication of the curved weir plate.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Sutro Proportional Linear Flow Weir Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Q=Cdb2ga(H−a3),x(y)=b[1−2πarctan⁡ya]Q = C_d b \sqrt{2 g a} \left( H - \frac{a}{3} \right), \quad x(y) = b \left[ 1 - \frac{2}{\pi} \arctan \sqrt{\frac{y}{a}} \right]

Calculates linear discharge Q directly proportional to effective head (H - a/3), and computes profile coordinates for fabrication of the curved weir plate.

How to Use the Sutro Proportional Linear Flow Weir Calculator

  1. Enter your value for Base Rectangular Crest Height (a) in m.
  2. Enter your value for Base Notch Width (b) in m.
  3. Enter your value for Total Head Above Crest (H) in m.
  4. Enter your value for Discharge Coefficient (Cd).
  5. Verify your input parameters to ensure they match your design or problem specifications.
  6. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

Wastewater Grit Chamber Velocity Controller

Input Values:

baseRectangularHeight:0.15
baseRectangularWidth:0.3
headAboveDatum:0.45
dischargeCoeff:0.62
Worked Steps: Validates operating linear head range, discharge flow rate, and notch top width.

Understanding Your Result

The calculated output gives the primary solution for Sutro Proportional Linear Flow Weir under the specified conditions. Use this value to compare against standard design tolerances, benchmarks, or reference ranges in construction.

Factors That Affect the Result

  • Input precision and measurement accuracy of Base Rectangular Crest Height (a), Base Notch Width (b), Total Head Above Crest (H), Discharge Coefficient (Cd).
  • Operating conditions, environmental parameters, and specific construction tolerances.
  • Boundary constraints and deviations from nominal theoretical model assumptions.

When Should You Use This Calculator?

  • When performing technical analysis or dimensioning related to Sutro Proportional Linear Flow Weir.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • The linear proportionality holds strictly when upstream head H exceeds base height a.
  • For heads below a (H < a), discharge follows the standard rectangular orifice/weir equation rather than linear relationship.

Frequently Asked Questions

Why are Sutro weirs essential for grit chambers?+
By placing a Sutro weir at the effluent end of a parabolic channel, the channel flow velocity remains constant (~0.3 m/s) regardless of flow variation, enabling organic solids to stay suspended while dense grit settles.
How is the curved plate constructed?+
The curved flank coordinates x(y) are CNC plasma cut from stainless steel or brass plates following the arctan hyperbolic profile.

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Sutro Proportional Linear Flow Weir Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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