Froude Number Formula - Definition, Applications

The Froude number formula , often denoted as Fr, is a dimensionless number used in fluid dynamics to characterize the behavior of fluids in various flow situations. It is named after the British engineer William Froude, who made significant contributions to the study of ship resistance and propulsion in the 19th century. The Froude number plays a crucial role in the analysis of open-channel flows, such as rivers and canals, as well as in the study of various other fluid flow scenarios, including naval architecture, hydraulics, and aerodynamics.

Definition of Froude Number

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Significance of Froude Number

1. Subcritical Flow (Fr < 1) : In subcritical flow, the Froude number is less than 1. This indicates that the gravitational forces dominate, and the flow behaves in a relatively calm and stable manner. In open-channel flows, subcritical flow typically occurs in tranquil conditions, with smooth water surfaces.
2. Critical Flow (Fr = 1): When the Froude number is exactly 1, it represents critical flow. Critical flow is a transitional state between subcritical and supercritical flow. In open channels, critical flow often occurs at specific points such as weirs and hydraulic jumps.
3. Supercritical Flow (Fr > 1): In supercritical flow, the Froude number is greater than 1, indicating that inertial forces are dominant. Supercritical flow is associated with rapid and often turbulent flow conditions. It is more likely to occur in steep, fast-flowing rivers or when a fluid is rapidly accelerated.

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Formula Details Of Froude number

1. Velocity (V): This is the speed at which the fluid is flowing. It can be measured in various units, such as meters per second (m/s) for liquids or meters per second squared (m²/s) for gases.
2. Acceleration due to Gravity (g): This constant represents the acceleration experienced by objects due to Earth's gravitational pull. It is typically taken as 9.81 m/s², although it can vary slightly with location.
3. Characteristic Length (L): The choice of characteristic length depends on the specific flow scenario being analyzed. In open-channel flows, it is often one of the following:

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Applications of Froude Number

1. Hydraulics and Civil Engineering:

2. Naval Architecture:

3. Aerodynamics:

4. Environmental Science:

5. Coastal Engineering:

6. Fluid Mechanics Research:

7. Geology:

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Interpretation of Froude Number

1. Subcritical Flow (Fr < 1): When Fr is less than 1, the flow is subcritical. In this regime, the flow is relatively calm and steady. Water surfaces tend to be smooth, and the flow velocity is generally moderate. For open-channel flows, subcritical conditions are often associated with tranquil river sections.
2. Critical Flow (Fr = 1): At Fr equal to 1, the flow is critical. This represents a transitional state, and it often occurs at specific hydraulic structures such as weirs and critical depths in open channels. Critical flow is characterized by changes in flow depth and velocity.
3. Supercritical Flow (Fr > 1): When Fr exceeds 1, the flow is supercritical. In supercritical flow, the flow is more energetic and can be turbulent. Rapid changes in water surface elevation and increased flow velocity are typical features. Steep mountain streams and fast rivers often exhibit supercritical flow.