The Manning Equation

Paul Butler
The Evergreen State College
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This material was originally developed by Spreadsheets Across the Curriculum as part of its collaboration with the SERC Pedagogic Service.


In this Spreadsheets across the Curriculum activity, students investigate the relationship between discharge and culvert diameter, given various culvert materials and slope angles. To begin, students are given the culvert diameter, material and gradient, and use the Manning equation to determine velocity and then discharge. Next, students determine culvert size to convey a specified discharge. These activities allow students to graph the relationship between culvert diameter and discharge.

Learning Goals

Students will:
  • Create and work with spreadsheets in Excel.
  • Create graphs within Excel.
  • Gain experience with foward modeling.
  • Gain experience with solving an inverse problem using the iterative process.
  • Gain experience working with power functions and fractional exponents.
  • Gain experience with manipulating algebraic equations.
In the process, the students will:
  • Use the Manning equation to solve for culvert radius and gradient.
  • Graphically examine the relationship of culvert diameter to velocity and discharge.

Context for Use

This module is designed for use in upper division geology or hydrology courses.

Description and Teaching Materials

PowerPoint SSAC2005.TC401.PB1.1-student version (PowerPoint 99kB May2 07)

The module is a PowerPoint presentation with embedded spreadsheets.

If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher ( by filling out and submitting the Instructor Module Request Form.

Teaching Notes and Tips

The module is intended as a stand-alone or homework assignment. It can be completed in a single 2-hour computer lab session.


The last two slides of the module contain 4 "end-of-module" questions that allow the instructor to assess student learning.

References and Resources