What is the Froude number and how is it related to gradually varied now?
The Froude number is a dimensionless number used to characterize the flow regime in open channel flow situations. It is defined as the ratio of inertial forces to gravity forces and is given by the equation:
Fr = V / (gD)^0.5
where:
- Fr is the Froude number
- V is the flow velocity
- D is the flow depth
- g is the acceleration due to gravity
The Froude number is related to gradually varied flow by indicating the type of flow regime present in a channel. For example:
- Fr < 1 indicates subcritical flow, where the flow velocity is less than the wave celerity, meaning that water surface elevation changes are gradual and continuous.
- Fr > 1 indicates supercritical flow, where the flow velocity is greater than the wave celerity, leading to rapid changes in water surface elevation.
- Fr = 1 indicates critical flow, where the flow velocity is equal to wave celerity, producing hydraulic jumps and abrupt changes in the flow profile.
In gradually varied flow analysis, the Froude number is used to determine the critical or normal depth in open channel flow calculations. By considering the Froude number, engineers can predict and analyze flow behavior and profile changes in different channel configurations.