DrainageCalculators

Gradually Varied Flow Calculator

Calculate water surface profiles using the Direct Step Method. Analyze backwater and drawdown curves with automatic profile classification (M1, M2, S1, etc.) for open channels.

What This Solves

Computes water surface profiles in open channels where depth changes gradually along the reach, classifying profile types (M1, M2, S1, S2, etc.) using the Direct Step Method.

Best Used When

  • You need to calculate backwater effects upstream of a dam, bridge, or culvert
  • You want to determine how far upstream a downstream control affects water levels
  • You are analyzing drawdown curves approaching a free overfall or steep reach

Do NOT Use When

Key Assumptions

  • Flow is steady (not changing with time) but non-uniform (depth changes with distance)
  • Channel slope, roughness, and cross-section change gradually (no abrupt transitions)
  • Energy slope is approximated using Manning's equation at each step
  • The channel is prismatic or varies gradually between cross-sections
  • No lateral inflow or outflow along the reach

Input Quality Notes

The starting depth (boundary condition) must be known — typically normal depth or critical depth at a control section. Step size affects accuracy; use smaller steps where depth changes rapidly.

Water Surface Profile Classifications

Mild Slope (yn > yc)

  • M1: Backwater (y > yn)
  • M2: Drawdown (yc < y < yn)
  • M3: Supercritical (y < yc)

Steep Slope (yn < yc)

  • S1: Backwater (y > yc)
  • S2: Drawdown (yn < y < yc)
  • S3: Backwater (y < yn)

Other Classifications

  • C1, C3: Critical slope
  • H2, H3: Horizontal bed
  • A2, A3: Adverse slope

Input Parameters

Flow Parameters

cfs

Roughness coefficient

Channel Geometry

ft
:1 (H:V)

0 for rectangular

ft/ft

Profile Computation

ft

Known depth at control section

ft

Target depth for computation

Computation increments

ft

Reference location

Velocity distribution correction (typically 1.0)

Ready to Calculate

Enter channel parameters and depth range to compute the water surface profile.

Disclaimer & Terms of Use

Educational Purpose: The calculations provided by DrainageCalculators.com are for informational and educational purposes only. While we strive for accuracy, these tools do not substitute for professional engineering judgment or designs stamped by a licensed Professional Engineer (PE) where required by law.

Professional Certification: Users are solely responsible for verifying all calculations, confirming compliance with local codes and regulations, and determining the appropriateness of any methodology for their specific application. Critical infrastructure and public safety projects require review and certification by a licensed Professional Engineer.

Limitation of Liability: DrainageCalculators.com, its owners, operators, and contributors assume no liability for damages or losses arising from the use of these calculators. By using this tool, you acknowledge that you have read, understood, and agreed to these terms.

This disclaimer applies to the Gradually Varied Flow Calculator calculator and all associated calculations.

PE Stamp Required: Many jurisdictions require drainage designs to be reviewed and stamped by a licensed Professional Engineer. Check your local requirements before using these calculations for construction or permit applications.

Professional Review: For projects requiring regulatory approval or where public safety is involved, have your calculations reviewed and stamped by a licensed Professional Engineer (PE).

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Last verified: February 2026

Disclaimer & Terms of Use

Educational Purpose: The calculations provided by DrainageCalculators.com are for informational and educational purposes only. While we strive for accuracy, these tools do not substitute for professional engineering judgment or designs stamped by a licensed Professional Engineer (PE) where required by law.

Professional Certification: Users are solely responsible for verifying all calculations, confirming compliance with local codes and regulations, and determining the appropriateness of any methodology for their specific application. Critical infrastructure and public safety projects require review and certification by a licensed Professional Engineer.

Limitation of Liability: DrainageCalculators.com, its owners, operators, and contributors assume no liability for damages or losses arising from the use of these calculators. By using this tool, you acknowledge that you have read, understood, and agreed to these terms.

PE Stamp Required: Many jurisdictions require drainage designs to be reviewed and stamped by a licensed Professional Engineer. Check your local requirements before using these calculations for construction or permit applications.