**Explanation of the Hydraulic Jump in a Rectangular Channel**

Hydraulic jump is a phenomenon that occurs when there is a sudden change in the flow regime of water in an open channel. It is characterized by a rapid increase in water depth and a significant energy loss. Hydraulic jumps are commonly observed in channels, spillways, and other hydraulic structures. In this explanation, we will discuss the intensity and initial depth of a hydraulic jump in a rectangular channel given the energy loss and Froude number.

**1. Understanding the Froude Number:**
The Froude number (Fr) is a dimensionless parameter that describes the flow conditions in an open channel. It is defined as the ratio of the flow velocity to the wave velocity. The Froude number can be calculated using the formula:

Fr = V / √(gD)

Where:
- Fr is the Froude number
- V is the velocity of the flow
- g is the acceleration due to gravity
- D is the flow depth

**2. Relationship between Energy Loss and Froude Number:**
The energy loss (ΔE) across a hydraulic jump can be determined using the following equation:

ΔE = (1 - Fr2 / Fr1) * (V1^2 / 2g)

Where:
- ΔE is the energy loss
- Fr1 is the Froude number before the jump
- Fr2 is the Froude number after the jump
- V1 is the velocity before the jump
- g is the acceleration due to gravity

**3. Calculation of Initial Depth:**
To calculate the initial depth (D1) of the hydraulic jump, we can rearrange the Froude number equation to solve for D1:

D1 = (V1^2) / (g * Fr1^2)

**4. Calculation of Intensity:**
The intensity (I) of the hydraulic jump is the ratio of the energy loss to the initial depth:

I = ΔE / D1

**5. Example Calculation:**
Let's assume that the energy loss after the jump is 9 m and the Froude number after the jump is 0.12. We need to determine the intensity and initial depth.

Using the energy loss equation, we can rearrange it to solve for V1:

V1 = √((2g * ΔE) / (1 - Fr2 / Fr1))

Substituting the given values, we get:

V1 = √((2 * 9.81 * 9) / (1 - 0.12 / Fr1))

Next, we can calculate the initial depth using the Froude number equation:

D1 = (V1^2) / (9.81 * Fr1^2)

Finally, the intensity can be calculated as:

I = 9 / D1

By solving these equations, we can determine the intensity and initial depth of the hydraulic jump in a rectangular channel given the energy loss and Froude number.