1.3.4. Classification Based on Froude Number

Now, there is another classification that depends on Froude number. This Froude number we have seen in the last week’s lecture, where we were dealing with a topic called dimensional analysis. This Froude number normally is given by V under root g h, where h is the depth of the water, in this case.

The Froude number is a dimensionless value used to compare the inertia of a flow to the gravitational forces acting on it. Specifically, it is defined as the ratio of the flow velocity (V) to the square root of the product of gravitational acceleration (g) and a characteristic length (typically the water depth h). This helps in understanding the nature of flow in open channels, whether it is calm or turbulent.

Imagine a playground slide. When you slide down fast (high velocity), you might briefly catch air and feel as if you're flying (analogous to supercritical flow), but if you are sliding down slowly (low velocity), you stay firmly on the slide (analogous to subcritical flow). The Froude number helps categorize these different experiences.

This Froude number based classification has 3 regimes: one is subcritical flow, the other is critical flow, the third one is supercritical flow.

The classification of flow based on the Froude number falls into three distinct regimes. Subcritical flow occurs when the Froude number is less than 1, indicating that gravitational forces dominate, and the flow is generally tranquil. Critical flow occurs when the Froude number equals 1, signifying the balance between gravitational and inertial forces. Supercritical flow occurs when the Froude number exceeds 1, indicating that inertial forces dominate over gravitational forces, leading to rapid flow.

Think of a river flowing under a bridge. If the water level is low and flows slowly, it represents subcritical flow. If the water just meets the bridge height, that’s critical flow. If there’s a rapid rush of water over and under the bridge during a storm, that’s supercritical flow, showcasing high-speed water rushing downstream.

So, a Froude number is given by V / √(g * l), where V is the average velocity of the fluid that you already know, g is acceleration due to gravity, and l is the characteristic length of the flow.

The Froude number is calculated by dividing the average velocity of the flow (V) by the square root of the product of gravitational acceleration (g, about 9.81 m/s² on the surface of the earth) and a characteristic length (l), which is usually the water depth. This ratio provides insight into whether the flow is dominated by gravity or inertia, and helps engineers evaluate various design elements in hydraulic structures.

If you're swimming in a pool, moving fast and splashing around represents a high Froude number because your inertia (speed) is greater than the gravitational pull trying to keep you in the water. However, if you're floating and moving slowly, your motions are dominated by gravity, therefore exhibiting a lower Froude number.

If Froude number is less than 1, this means, the flow is going to be subcritical. If the Froude number is equal to 1, this flow will be called critical open channel flow. And very obviously, if the Froude number is more than 1, this is called supercritical flow.

The relationship between the Froude number values and the corresponding flow conditions is straightforward: a Froude number below 1 indicates calm, slower flow (subcritical), equal to 1 indicates a balance between gravitational and inertial forces (critical), and above 1 implies high, fast-moving flow that overcomes gravitational forces (supercritical). Each state indicates different behaviors and flow characteristics in open channels.

Picture water flowing through a garden hose. If you gently twist the hose to maintain a steady trickle, that's akin to subcritical flow. If you suddenly open the nozzle fully and water shoots out rapidly, that's similar to supercritical flow, with the Froude number shooting upwards, emphasizing how fast and forceful the discharge is.

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