Open channel hydraulics for engineers. Chapter 4 non uniform flow

Linking up with Chapter 2, dealing with uniform flow in open channels, it may be noted that any change in the flow phenomenon (i.e. flow rate, velocity, flow depth, flow area, bed slope do not remain constant) causes the flow to be non-uniform. This chapter willdiscuss the effect of change in any one of the above quantities, including specific energy, critical depth and slope, and flow types. How to draw water surface profiles will also be introduced.
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Open channel hydraulics for engineers. Chapter 4 non uniform flow OPEN CHANNEL HYDRAULICS FOR ENGINEERS-----------------------------------------------------------------------------------------------------------------------------------Chapter NON-UNIFORM FLOW_________________________________________________________________________ 4.1. Introduction 4.2. Gradually-varied steady flow 4.3. Types of water surface profiles 4.4. Drawing water surface profiles_________________________________________________________________________SummaryLinking up with Chapter 2, dealing with uniform flow in open channels, it may be notedthat any change in the flow phenomenon (i.e. flow rate, velocity, flow depth, flow area,bed slope do not remain constant) causes the flow to be non-uniform. This chapter willdiscuss the effect of change in any one of the above quantities, including specific energy,critical depth and slope, and flow types. How to draw water surface profiles will also beintroduced.Key wordsNon-uniform; specific energy; critical; gradually-varied steady flow; water surface profiles_________________________________________________________________________4.1. INTRODUCTION4.1.1. General In the previous Chapter 2, the flow was uniform under all circumstances underconsideration. In many situations the flow in an open channel is not of uniform depth alongthe channel. In this chapter the flow conditions studied relate to steady, but non-uniform,flow. This type of flow is created by, among other things, the following major causes:  Changes in the channel cross-section.  Changes in the channel slope.  Certain obstructions, such as dams or gates, in the stream’s path.  Changes in the discharge – such as in a river, where tributaries enter the main stream.A non-uniform flow is characterized by a varied depth and a varied mean flow velocity: V h  0 or 0 (4-1) s sIf the bottom slope and the energy line slope are not equal, the flow depth will vary alongthe channel, either increasing or decreasing in the flow direction. Physically, the differencebetween the component of weight and the shear forces in the direction of flow produces achange in the fluid momentum which requires a change in velocity and, from continuityconsiderations, a change in depth. Whether the depth increases or decreases depends onvarious parameters of the flow, with many types of surface profile configurations possible.Fig. 4.1. illustrates some typical longitudinal free-surface profiles. Upstream anddownstream controls can induce various flow patterns. In some cases, a hydraulic jumpmight take place. A jump is a rapid-varied flow phenomenon; calculations were developedin Chapter 3. However, it is also a control section and it affects the free surface profilesupstream and downstream.-----------------------------------------------------------------------------------------------------------------------------------Chapter 4: NON-UNIFORM FLOW 70OPEN CHANNEL HYDRAULICS FOR ENGINEERS----------------------------------------------------------------------------------------------------------------------------------- upstream control downstream control control sluice gate sharp-crested hydraulic jump weirrapid gradually rapid gradually rapidvaried varied varied varied variedflow flow flow flow flow upstream control critical depth hc supercritical flow subcritical control downstream flow hydraulic control jump overflow (critical depth) rapid hc varied gradually flow varied flow rapid gradually rapid varied varied varied flow flow flow Fig. 4.1. Examples of non-uniform flow4.1.2. Accelerated and Retarded flow ...