Unit 3: Channel Capacity and Manning's Equation

Venkatesh Merwade, Purdue University (vmerwade@purdue.edu)
James McNamara, Boise State University (jmcnamar@boisestate.edu)

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Initial Publication Date: December 5, 2019 | Reviewed: June 3, 2022 (see revision history: 2 events)

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.

Geodesy | College Introductory, College Lower (13-14)

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Topics

Geodesy

Grade Level

College Introductory, College Lower (13-14)

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These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below.

Overview

Students apply various geodetically acquired data to measure channel and floodplain geometry. They, then, employ Manning's equation to determine the flowrate of a channel based upon one of a known geometry.

Science and Engineering Practices

Using Mathematics and Computational Thinking: Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3, acre-feet, etc.). HS-P5.5:

Developing and Using Models: Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system HS-P2.3:

Analyzing and Interpreting Data: Apply concepts of statistics and probability (including determining function fits to data, slope, intercept, and correlation coefficient for linear fits) to scientific and engineering questions and problems, using digital tools when feasible. HS-P4.2:

Analyzing and Interpreting Data: Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. HS-P4.1:

Cross Cutting Concepts

Systems and System Models: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. HS-C4.2:

Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:

Structure and Function: The functions and properties of natural and designed objects and systems can be inferred from their overall structure, the way their components are shaped and used, and the molecular substructures of its various materials. HS-C6.2:

Disciplinary Core Ideas

The Roles of Water in Earth's Surface Processes: Water continually cycles among land, ocean, and atmosphere via transpiration, evaporation, condensation and crystallization, and precipitation, as well as downhill flows on land. MS-ESS2.C1:

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Learning Goals

Unit 3 Learning Outcomes

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Show caption

Traditional river surveyors taking measurements of channel and floodplain topography. A variety of surveying methods such as the one shown here are highlighted in this unit. From Steve Holnbeck, Wyoming-Montana Water Science Center.
Provenance: Source: Steve Holnbeck, Wyoming-Montana Water Science Center. https://www.usgs.gov/media/images/ground-point-survey-total-station-measure-depth-streambed
Reuse: This item is in the public domain and maybe reused freely without restriction.

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 the use of $, abs, sum, etc. may need to be reviewed if students are not highly familiar with spreadsheets.

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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.