Open Channel Flow Calculator: Manning's Equation for Channels and Pipes

How It Works

1. Select Channel Shape

   Choose rectangular (vertical walls), trapezoidal (sloped sides with specified z:1 ratio), or circular (partially full pipe). Each shape has different area, wetted perimeter, and hydraulic radius formulas.

2. Enter Channel Dimensions

   Input bottom width and water depth for rectangular/trapezoidal, or pipe diameter and flow depth for circular. For trapezoidal, enter side slope as horizontal to vertical (e.g., 2:1).

3. Enter Slope and Roughness

   Input channel bed slope in ft/ft and Manning's n. Common values: finished concrete 0.012, unfinished concrete 0.014, corrugated metal 0.024, earth channel 0.025-0.035.

4. Review Flow Results

   See flow rate in CFS and GPM, average velocity, Froude number, and flow regime. Fr below 1 is subcritical (stable). Fr above 1 is supercritical (rapid). Most channels target subcritical flow.

Built For

• Civil engineers designing drainage ditches and channels for stormwater conveyance
• Stormwater designers checking capacity of existing channels under new development runoff
• Wastewater operators calculating flow in partially full gravity sewer pipes
• Irrigation engineers sizing canals and delivery channels for agricultural water supply
• Highway engineers checking culvert capacity for road crossing drainage
• Environmental engineers determining flow velocity for erosion control channel design
• Mine dewatering teams sizing drainage channels for surface runoff management

Features & Capabilities

Manning's Equation (US Customary)

Q = (1.486/n) x A x R_h^(2/3) x S^(1/2). Standard open channel flow formula with the 1.486 constant for US units.

Three Channel Shapes

Rectangular, trapezoidal, and circular (partially full pipe). Calculates area, wetted perimeter, and hydraulic radius for each shape.

Froude Number and Flow Regime

Fr = V / sqrt(g x D_h). Classifies flow as subcritical (Fr below 1), critical (Fr = 1), or supercritical (Fr above 1).

Partially Full Pipe

Solves circular pipe geometry for any depth-to-diameter ratio. Shows that maximum flow occurs at about d/D = 0.94, not when full.

Manning's n Reference

Built-in reference table of roughness coefficients for common channel materials from smooth concrete to heavily vegetated floodplains.

PDF Export

Export channel analysis as a branded PDF for engineering reports or permit applications.

Assumptions

• Manning's equation: Q = (1.486/n) x A x R_h^(2/3) x S^(1/2) in US customary units, assuming uniform and steady flow
• Channel cross-section is prismatic (constant shape and slope) along the entire reach being analyzed
• Manning's n value is constant along the channel and across the cross-section (no composite roughness calculation)
• Flow is fully turbulent, which is valid for virtually all practical open channel applications
• Circular pipe calculations assume gravity flow (not pressurized) with a free water surface
• Channel slope entered is the bed slope, which equals the energy grade line slope under uniform flow conditions

Limitations

• Does not model gradually varied flow (backwater curves) or rapidly varied flow (hydraulic jumps, drops) — only uniform flow
• Composite channels (different roughness on bed vs. banks) require weighted n calculations not performed here
• Partially full pipe geometry uses analytical equations that lose accuracy at very shallow depths (d/D below 0.05)
• Does not account for sediment transport capacity, scour velocity limits, or permissible velocity for erodible channels
• Natural channels with irregular cross-sections, vegetation, and meandering cannot be accurately modeled with a single prismatic section
• Does not evaluate freeboard requirements, which depend on flow regime, channel lining, and local design standards
• Supercritical flow results should be used with caution — channel transitions and obstructions can cause hydraulic jumps with significant energy loss

References

• Chow, V.T. — Open-Channel Hydraulics, 1959 (Manning's n tables and uniform flow theory)
• FHWA HDS-4 — Introduction to Highway Hydraulics (open channel flow design for roadway drainage)
• ASCE Manual of Practice No. 77 — Design and Construction of Urban Stormwater Management Systems
• USBR — Design of Small Canal Structures (Manning's equation application for irrigation canals)
• FHWA HEC-15 — Design of Roadside Channels with Flexible Linings (permissible velocity and channel stability)
• Ten States Standards — Recommended Standards for Sewage Works (gravity sewer design criteria using Manning's equation)

Frequently Asked Questions