# Unit 3: Channel Capacity and Manning's Equation

## Summary

A flood occurs when the flow rate in a river exceeds the capacity of a channel to transmit water downstream within its banks. How much water can a channel transmit? Answering this question requires measurements of channel and floodplain topography, coupled with the application of the physics of flow in channels. These complex concepts are embodied in the well-known Manning's Equation. In this unit, students evaluate the geometry of river channels and floodplains using LIDAR-derived data and compute the depths and velocities of flow rates within channels using Manning's equation.

## Learning Goals

### Unit 3 Learning Outcomes
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Students will be able to:

- Describe geodetic methods used to measure channel and floodplain geometry
- Describe the basic physical concepts underlying Manning's equation
- Apply Manning's equation to compute the flow rate that a channel of known geometry can transmit

## Context for Use

This unit provides basic information about floodplain geometry and Manning's equation. The PowerPoint files provide just enough information to connect Unit 2 on flood frequency analysis with Unit 4: Hydraulic Modeling and Flood Inundation Mapping using HEC-RAS on hydraulic modeling of floodplains. In Unit 4, Manning's equation is embedded inside a rather complex hydraulic model. This unit gives students a chance to compute Manning's equation using real data so that Unit 4 is more understandable. The student exercise could also be used in other classes that go into deeper detail about channel hydraulics and floods such as geoscience courses on geomorphology or engineering courses on open channel flow.

## Description and Teaching Materials

This unit includes two PowerPoint presentations that could be used together in a single class period. The first gives a basic introduction to geodetic methods used in floodplain analysis so that students have an understanding of how the data were collected. The second gives a brief introduction to Manning's equation. Both could be easily expanded by an instructor to tailor the level of detail to a specific course. The student exercise presents a very prescriptive example of how to use Manning's equation with real survey data, and then asks students to repeat the exercise on the other cross-section. Final answers are provided for the first cross-section so that students can check their work and make sure they develop the correct formulae as they work through calculating wetted perimeter and cross-sectional area.

- Presentations
- Presentation on Using Geodesy in Hydrology (PowerPoint 2007 (.pptx) 29.6MB Mar14 23)
- Presentation on Manning's Equation (PowerPoint 2007 (.pptx) 16.6MB Mar14 23)
- Combined Geodesy and River Hydraulics Presentation (PowerPoint 2007 (.pptx) 42.3MB Dec21 18)

- Student exercise files
- Unit 3 Mannings Equation Student Exercise.docx (Microsoft Word 2007 (.docx) 207kB Mar14 23)
- Unit 3 Student Exercise Data File Boise River - some calculations (Excel 2007 (.xlsx) 2.5MB Nov13 18)
- This version has some of the Excel formulae included to give the students more support in doing the exercise.

- Unit 3 Student Exercise Data File Boise River - no calculations (Excel 2007 (.xlsx) 2.5MB Nov13 18)
- This version has no formulae included so the students must develop them themselves. Which file to choose is up to instructor discretion.

- Instructor file
- Unit 3 Student Exercise Data File Instructor Calculations (Excel 2007 (.xlsx) 2.5MB Nov13 18)

## Teaching Notes and Tips

- If students have not used Excel before, they could struggle with some of the computations. Instructors should ensure that the higher learning objectives about understanding Manning's equation and floods are not lost while making the calculations in Excel. Certain Excel functions such as use of $, abs, sum, etc. may need to be reviewed if students are not highly familiar with spreadsheets.

## Assessment

A simple formative assessment is presented in the Manning PowerPoint. Students should complete a Manning's calculation with simple geometry before working through the Excel example. This formative assessment should not be graded, but instructors should ensure that each student understands each variable in Manning's equation. The student exercise forms the summative assessment for this unit. Instructors should just check for completion of the Boise River example, but grade the Wabash project for quality and comprehension.