Open Channel Hydraulics II – Critical & Non-uniform Flow

Harlan H. Bengtson, Ph.D., P.E.

Course Outline

Open channel flow occurs whenever the flowing liquid has a free surface at atmospheric pressure.  For example, this may be in a natural river channel, in a manmade concrete channel for transporting wastewater, or in a closed conduit, such as a storm sewer, which is flowing partially full.  The driving force for open channel flow must be gravity, since the flow, which is open to the atmosphere, cannot be pressurized.  In contrast, the primary driving force for flow in pressurized, closed conduit flow is usually pressure.  In this course, the parameter called specific energy will be used to introduce the concepts of critical, subcritical, and supercritical flow.  Various calculations related to critical, subcritical and supercritical flow conditions will be presented.  The hydraulic jump as an example of rapidly varied non-uniform flow will be discussed.  The thirteen possible types of gradually varied non-uniform flow surface profiles will be presented and discussed.  Also, the procedure and equations for step-wise calculation of gradually varied non-uniform surface profiles will be presented and illustrated with examples.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

At the conclusion of this course, the student will:

• Be able to determine the critical depth for a specified volumetric flow rate through a rectangular channel of specified bottom width;
• Be able to determine the critical slope for a specified volumetric flow rate through an open channel of specified shape, size, & Manning roughness coefficient, with known critical depth;
• Be able to determine whether a specified volumetric flow rate through an open channel of given shape & size, with known depth of flow will be critical, subcritical or supercritical flow;
• Be able to calculate the depth of flow after a hydraulic jump if given the depth before the hydraulic jump, the volumetric flow rate and the shape and dimensions of the open channel;
• Be able to identify which type of surface profile (e.g. M1, M2, M3, S1, S2,  S3, etc.) is present in a specified gradually varied flow situation; and
• Be able to carry out a stepwise calculation of the surface profile for a specified, gradually varied, non-uniform open channel flow.

Intended Audience

This course is intended for hydrologists, civil engineers, hydraulic engineers, highway engineers and environmental engineers.  This course is intended to be taken after the course, H138, “Open Channel Hydraulics I – Uniform Flow.”  It will be assumed that anyone taking this course is familiar with the major classifications used for open channel flow (steady or unsteady state, laminar or turbulent flow, uniform or non-uniform flow, and critical, subcritical or supercritical flow) and with the use of the Manning equation and the parameters in that equation (e.g. hydraulic radius) for uniform open channel flow.

Benefits to Attendee

An attendee of this course will gain knowledge about the meaning of critical, subcritical, and supercritical flow, about basic calculations related to those three types of flow, about the hydraulic jump and basic calculations concerning it, about the classification scheme for types of gradually varied non-uniform flow, and about how to carry out a stepwise calculation of a gradually varied, non-uniform flow surface profile.  Upon completing this course, the student will be prepared to take additional open channel hydraulics courses.

Course Introduction

In this course, the parameter called specific energy will be used to introduce the concepts of critical, subcritical, and supercritical flow.  Various calculations related to critical, subcritical and supercritical flow conditions will be presented.  The hydraulic jump as an example of rapidly varied non-uniform flow will be discussed.  The thirteen possible types of gradually varied non-uniform flow surface profiles will be presented and discussed.  Also, the procedure and equations for step-wise calculation of gradually varied non-uniform surface profiles will be presented and illustrated with examples.

Course Content

The course content is in the following PDF file:

Open Channel Hydraulics II – Critical & Non-uniform Flow

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Course Summary

Through the use of the Froude number, it is possible to determine whether a specified example of open channel flow is subcritical or supercritical flow.  When supercritical flow occurs on a mild slope, which cannot maintain the supercritical velocity, there will be an abrupt transition to subcritical flow in the form of a hydraulic jump.  Non-uniform flow, which occurs as a smooth transition from one flow condition to another, is often called gradually varied flow.  Any gradually varied flow example will be one of 13 possible classifications, based on the slope of the channel and the relationships among  y,  yc, &  yo.  A specified gradually varied flow profile can be calculated as depth versus distance along the channel using a step-wise calculation, which was discussed in this course.

References:

1.  Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

2.  Chow, V. T., Open Channel Hydraulics, New York: McGraw-Hill, 1959.

Websites:

1.  Indiana Department of Transportation Design Manual, available on the internet at: http://www.in.gov/dot/div/contracts/standards/dm/index.html

2.  Illinois Department of Transportation Drainage Manual, available on the internet at:  http://dot.state.il.us/bridges/brmanuals.html

Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.