15.1.4. Froude Numbers

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 Froude number (Fr) is a dimensionless parameter used to determine the flow regimes in open channel flow. It is calculated as the ratio of the inertial forces to the gravitational forces. If Fr < 1, the flow is subcritical, which means gravitational forces dominate. When Fr = 1, it signifies critical flow, where inertial forces balance gravitational ones. If Fr > 1, the flow is supercritical, indicating that inertial forces overpower gravitational forces.

Imagine a slide at a water park. When the water flow is gentle (subcritical), you glide smoothly down. At just the right speed (critical), you experience the perfect rush; you're not held back, and you don't splash too much. But if the water flows too fast (supercritical), you shoot down with a thrill, but you have a reduced control over your ride!

As the equations is a part of inertia forces in y gravity forces you can can just rewrite this okay from you can find out the flow Froude numbers is a functions of v by square root of gy.

In the context of fluid mechanics, the Froude number can be expressed mathematically as: Fr = v / √(gy), where 'v' is the flow velocity, 'g' is the acceleration due to gravity, and 'y' is the flow depth. This relationship emphasizes that the characteristics of the flow are governed by both the speed of the flow and the depth of the water, alongside gravitational effects.

Think of it as how fast you can roll down a hill. If the hill is steep (greater 'g') and you have a big ramp (greater 'y'), you might roll down faster. Now, if you have more adrenaline (greater 'v'), you'd zoom down more quickly. The Froude number tells us how these factors interact.

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. In between whenever a convergence of flow happens from the supercritical to subcritical flow there will be a formations of the eddies and there are a lot of energy dissipations will happen it their energy loss will happen it.

The behavior of flow varies based on whether the Froude number is less than, equal to, or greater than 1. In subcritical flows (Fr < 1), disturbances can travel upstream and downstream. In contrast, in supercritical flows (Fr > 1), disturbances travel only downstream, and when flows transition from supercritical to subcritical, they can create turbulence, or eddies, that cause energy dissipation.

Imagine a river where water flows slowly with gentle waves (subcritical). If you drop a stick in, it can float upstream. Now, if the water rushes fast like a white-water rapid (supercritical), a stick will only be pushed downstream. When the fast water hits a slower pool, it creates whirlpools or eddies where energy is lost, similar to stirring a pot of soup.

How do you derive the speed of water wave which is a functions of the flow depth.

The speed of surface water waves can be derived from the principles of fluid mechanics. It can be expressed as C₀ = √(g*y), where 'C₀' represents the speed of surface waves, 'g' is the gravitational acceleration, and 'y' is the flow depth. This relationship helps determine how quickly disturbances in the water surface will propagate.

Consider a kid jumping on a trampoline. The deeper they jump (greater 'y'), the higher they bounce, relating to energy (like gravity 'g'). Similarly, in water, a deeper body will transmit surface waves faster compared to a shallow body.

So if you look at that same thing is a subcritical flow supercritical channel. In between whenever a convergence of flow happens from the supercritical to subcritical flow there will be a formations of the eddies and there are a lot of energy dissipations will happen it their energy loss will happen it.

When fluid transitions between subcritical and supercritical flows through hydraulic jumps, significant turbulence can occur. This turbulence results in energy loss as kinetic energy is converted into potential energy, or heat, due to friction and eddies. Thus, hydraulic jumps serve both to dissipate energy and facilitate mixing.

Think about a water slide where the water quickly slows down at the base. This slowing creates waves and splashes, dissipating energy – much like the energy lost during a hydraulic jump in a river when fast water meets slower water.

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