Open Channel Hydraulics

Chapter 2: Energy and Momentum Principles

2.1 CRITICAL FLOW

Critical flow, a special type of open-channel flow, occurs under certain conditions. It is a cross-sectional flow type. In other words, critical flow is not maintained along a length of a channel. It may occur at the entrance of a steep channel, at the exit of a mild channel, and at sections where channel characteristics change.

Various concepts to be discussed in the subsequent sections will help in understanding the significance of critical flow. While deferring the definitions of certain terms to later sections, here we will provide a list of conditions associated with critical flow. Reference will be made to these conditions later where appropriate. At the critical sate of flow:

  • the Froude number is equal to unity

  • the specific energy is minimum for a given discharge

  • the discharge is maximum for a given specific energy

  • the specific momentum is minimum for a given discharge, and

  • the discharge is maximum for a given specific momentum.

2.1.1 FROUDE NUMBER

The Froude number, a dimensionless number, is a cross-sectional flow characteristic defined as


where F r = Froude number, V = velocity, Q = discharge, g = gravitational acceleration, D = hydraulic depth, A = flow area, and T = top width. The denominator, , represents the speed with which gravity waves propagate in open channels. Sometimes we refer to this as wave celerity.

The flow is said to be subcritical if F r

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