6. Non-Uniform Flow and Hydraulic Jump

Welcome students. This is the 7th lecture for this broad topic, that is, open channel flow and as we were going to start this gradually varied flow as promised in the last lecture. Until now, we have studied that in open channel flow with the classification based on space, the dimensions, I mean, there are 3 type of flows; one is uniform flow and other is non-uniform flow. So, non uniform have 2 different categories; the first is gradually varied flow and the second is rapidly varied flow.

This introductory chunk discusses the overall topic of the lecture series, focusing specifically on non-uniform flow categorized into two distinct types: gradually varied flow and rapidly varied flow. Understanding these categories of flow is essential to grasp the complexities of open channel flow behavior, which varies depending on factors like channel shape, slope, and discharge.

Think of a river flowing downhill. If the slope is gentle and the river flows smoothly and steadily, this represents gradually varied flow. Conversely, if the river suddenly steepens with rocks and waterfalls causing abrupt changes in flow speed or water depth, this would illustrate rapidly varied flow.

To get started, we should understand what exactly a gradually varied flow is. The flow in a channel is termed as gradually varied if the flow depth changes gradually over a large length of the channel.

Gradually varied flow refers to a situation where the depth of the stream changes slowly over a significant distance, indicating a smooth gradual transition as opposed to abrupt changes. This can be understood as a softening in velocity and energy gradients along the channel, which is crucial for designing stable channels that efficiently handle the flow.

Imagine water flowing down a slide that gradually slants downwards. The water maintains a smooth flow as it descends without any sudden drops. This represents gradually varied flow, where the water depth (or slide steepness) shifts gently over distance.

First, that the channel is prismatic, this means. What does it mean by the channel is prismatic? That the cross sectional shape, size and the bed slope are constant, so this is what it means, being prismatic. Second assumption is that the flow in the channel is steady and non-uniform. Non-uniform means that dy by dx, a steady means, dy by dt is 0 but dy by dx is not equal to 0.

For analyzing gradually varied flow, there are several key assumptions made. Firstly, the channel is assumed to have a uniform shape (prismatic), meaning its cross-section does not change along its length. Secondly, the flow must be steady, implying that the velocity of the flow at a point does not change with time, though it may change with respect to the position along the channel. Thirdly, the gradients should be defined clearly, where dy/dx expresses the slope of the water surface and must be less than 1.

Consider a long, straight garden hose. If the hose maintains the same diameter and shape throughout its length, and the water flow remains constant (but can be deeper at one end), it exemplifies the idea of gradually varied flow: consistent form and steady changes in water depth.

The total energy H of a gradually varied flow can be expressed as; ... In principle, we must have this equation; z + y + alpha V square by 2g.

The total energy in a gradually varied flow is a combination of three components: the elevation head (z), the flow depth (y), and the velocity head (αV²/2g). In basic terms, this total energy determines how much work the water can do as it flows, which is critical for calculating characteristics like pressure and velocity along different points in the channel. The parameter α helps adjust calculations based on flow conditions.

Think of a rollercoaster. Just as the total energy of the coaster at any point depends on its altitude, its speed, and the effects of gravity, similarly, the energy in water flow combines height, depth, and speed, dictating how that water interacts with the channel.

Now, what the going to the differential equation of the gradually varied flow. ... dy/dx is going to be S - S divided by 1Q square T by gA cube.

To understand gradually varied flow numerically, the flow can be described using a differential equation that relates the change in energy to the slope of the energy line and channel bed. The terms in this equation reflect how the flow behaves in response to changes in the channel shape and flow conditions, allowing engineers to predict water behavior effectively.

Imagine tracking a ball rolling down a hill, where the slope influences how quickly it accelerates. Similarly, this equation helps predict how quickly the flow adjusts in response to channel shape changes, maintaining control over hydraulic systems.

What are the flow profiles in gradually varied flow? ... the channels are classified into 5 categories, the channels itself.

The flow profiles in gradually varied flow can be classified based on the relationship between normal depth and critical depth. This results in five distinctive categories of channels: mild slope (where normal depth is greater than critical depth), steep slope (normal depth less than critical depth), critical slope (normal depth equals critical depth), horizontal bed (no normal depth), and adverse slope (also no normal depth). These classifications are important for understanding how water behaves in different channel conditions.

This classification resembles the way roads are categorized: flat, hilly, steep, or winding. Just as different road types require unique driving strategies, varying channel profiles help engineers determine the best approaches to manage water flow and prevent flooding.

So, this 2; the horizontal bed and adverse slope cannot sustain uniform flow. ... So, these are the 3 regions depending upon where the CDL and NDL is.

In understanding the flow dynamics, regions are defined based on where the normal and critical depths are situated relative to the flow. The critical depth line divides the channel into distinct regions which affect flow behavior; these include areas of supercritical flow, subcritical flow, and critical flow. Recognizing these boundaries helps assess how water will behave during different conditions, which is vital for effective channel management.

Think of a swimming pool with a shallow end and a deep end. Swimmers will behave differently depending on whether they're in shallow or deep waters. Similarly, in our channels, these flow regions can dictate how water interacts with its surroundings, impacting flow, sediment transport, and overall river health.

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