The sequent depth ratio in a hydraulic jump termed in a horizontal rec...
To explain the answer to this question, let's break it down into the following sections:
1. Introduction to hydraulic jump:
- A hydraulic jump occurs when a high-velocity, supercritical flow transitions into a low-velocity, subcritical flow.
- It typically occurs in open channels with a sudden change in water velocity, such as when water flows over a weir or a spillway.
2. Sequent Depth Ratio:
- The sequent depth ratio (y2/y1) is the ratio of the downstream depth (y2) to the upstream depth (y1) in a hydraulic jump.
- It is a measure of the energy dissipation that occurs during the jump.
- The larger the sequent depth ratio, the greater the energy dissipation.
3. Froude Number:
- The Froude number (Fr) is a dimensionless parameter that describes the flow regime.
- It is defined as the ratio of the flow velocity (V) to the square root of the product of gravity (g) and the flow depth (y).
- Mathematically, Fr = V / √(g * y).
- A Froude number less than 1 indicates subcritical flow, while a Froude number greater than 1 indicates supercritical flow.
4. Relationship between sequent depth ratio and Froude number:
- There is a relationship between the sequent depth ratio and the Froude number for a hydraulic jump.
- The relationship is given by the equation: Fr2 = (5/4) * (Fr1^2 - 1), where Fr2 is the Froude number downstream of the jump and Fr1 is the Froude number upstream of the jump.
- In this case, the sequent depth ratio is given as 5, so we can rewrite the equation as: 5 = (5/4) * (Fr1^2 - 1).
- Solving this equation, we find that Fr1 is approximately 3.87.
5. Determining the Froude number of the supercritical stream:
- The question asks for the Froude number of the supercritical stream, which is Fr1.
- From the previous calculation, we found that Fr1 is approximately 3.87.
- Therefore, the correct answer is option 'B', which states that the Froude number of the supercritical stream is 3.87.
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