15.3.1. Energy Equations

Good morning all of you as we discussed in the last class introduction to open channel flow. Today I will continue open channel flow going slight bit more in depth about the open channel looking that I have been following now the best books for open channel flow which is the books on Hanif Choudhury books but it is a higher level book but I can suggest you to read either FM White book or the Senral Simbala book.

In this segment, the speaker introduces the topic of open channel flow, mentioning previous discussions and referencing key textbooks for further reading. This establishes a foundation for today’s lecture and highlights the importance of understanding the complexities of fluid mechanics.

Consider a classroom where students are learning about rivers and canals. Just as they would refer to textbooks for guidance, engineers refer to specialized literature to design effective water flow systems.

So we can really the correlated the discussions what we are doing it if you follow Sinzel-Simbala book. Let us discuss today what the contents we will go through for lectures. One very interesting things we will discuss about flow-proud numbers and the wave split which is new concept what we will introduce it.

Here, the lecturer indicates the specific topics to be covered, especially focusing on flow regimes and Froude numbers, which are crucial parameters in fluid mechanics. The Froude number helps classify the flow into subcritical, critical, and supercritical categories, which are vital for predicting behavior in open channel flows.

Imagine different types of water flows: a slow-moving river (subcritical), a rapidly flowing stream over rocks (supercritical), and the point where they meet (critical). Each flow type has distinct characteristics that can dramatically change how water interacts with the environment.

In terms of the flow crowd numbers we define as if a lesser than 1 that means the gravity force is more than the inertia forces with this the case we define as subcritical flow okay. When you have a very rare occurs it that you will have a the inertia force is equal to the gravity forces of the flow systems that we call the critical flow. if a flow crowd numbers is greater than 1 we call supercritical flow.

The lecturer explains the classification of flow based on the Froude number. Subcritical flow has a Froude number less than 1, indicating that gravity forces dominate over inertia forces. Critical flow occurs at a Froude number of 1, and supercritical flow has a Froude number greater than 1, indicating that inertia forces dominate.

Think of a heavy train moving slowly (subcritical), a train reaching its peak speed (critical), and a high-speed train zooming past (supercritical). The dynamics change significantly based on the train's speed, just like the characteristics of water flow vary based on its type.

When you create the disturbance of that then we try to look it how that disturbance is propagated. What is the speed of the propagations of this surface wave let be designated as C0.

This part discusses how disturbances in water, such as throwing a stone, create waves that propagate at a certain speed (C0). Understanding how these waves move is essential for predicting the behavior of the water flow in response to various inputs.

Picture tossing a pebble into a still pond. The ripples that spread outward represent the disturbance and can help you visualize how waves travel through water after any input or action.

So we will talk about at the low velocity the flow crowd number lesser than 1 is the subcritical flow. Here you will have a supercritical flow. then you will have a subcritical flow.

This segment informs that when the flow velocity is low (subcritical flow), disturbances affect downstream conditions, while in supercritical flow, disturbances do not influence upstream conditions. This is crucial for understanding water management in various engineering applications.

When a school bell rings slowly, all students can hear it and gather (subcritical flow). However, if the bell rings too fast, only those closer to it can react, while those further away miss it (supercritical flow), illustrating how information (or disturbances) travels through a medium.

So definitions of the flow crowd numbers the speed of the velocity by the speed of the water wave.

The definition of the Froude number is explained: it relates the speed of the flowing water to the speed of surface waves. This ratio helps to characterize the type of flow (subcritical, critical, supercritical) and provides insight into how disturbances will propagate.

Imagine standing on a crowded subway. If everyone moves quickly (high speed), it becomes chaotic, just like water in a supercritical flow. But if they move slowly and in an organized manner (low speed), it allows for smooth movement, similar to a subcritical flow.

So we can have a two heads one is the pressure head which is we define as y and other is the velocity head.

This segment covers how specific energy is calculated in open channels by combining the pressure head and velocity head. Understanding how to quantify energy in open channels helps to analyze flow behavior effectively.

Think of energy in terms of your energy for climbing a hill. You need a certain amount of energy both to lift your body weight (pressure head) and to move upwards quickly (velocity head). Similarly, water needs both pressure energy and kinetic energy to flow effectively.

The energy loss hL as you define in the pipe flow. We did it the same things.

This part explains energy loss in open channel flows, drawing similarities between canal flows and pipe flows. It emphasizes the need for understanding energy loss to predict flow behavior accurately.

Just like a car uses fuel energy, a canal 'uses' water energy. If the canal is too narrow or rocky, energy is wasted (energy loss), just as a car uses more fuel driving on a bumpy road compared to a smooth highway.

Now if you have to talk about how specific energy components are there and again we are revisiting it I think that is not a big issue that specific energy curve.

The concept of alternate depths arises from specific energy relationships. When operating at constant energy, flows can exist at two different depths (subcritical and supercritical) but still have the same specific energy. Understanding alternate depths is key for effective canal design.

Think of trying to walk on two different types of terrain. You can traverse a hilly path (subcritical) or a flat path (supercritical), but as long as your overall energy is the same, both can lead you to your destination, like water flowing through different depths in a canal.

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