Critical Flow Analysis in Rectangular Channel

The problem involves a rectangular open channel where the flow is critical, and the flow depth ($y$) is given as $2$ m. We need to determine the correct statements regarding the specific energy ($E$) and the Froude number ($Fr$).

Understanding Critical Flow Conditions

Critical flow in an open channel occurs when the Froude number is exactly $1.0$. This condition signifies a unique state where, for a given discharge, the specific energy is at its minimum value.

• Froude Number ($Fr$): For a rectangular channel, $Fr = \frac{V}{\sqrt{gy}}$, where $V$ is the flow velocity and $g$ is the acceleration due to gravity. At critical flow, $Fr = 1$.
• Specific Energy ($E$): For a rectangular channel, $E = y + \frac{V^2}{2g}$.

Calculating Froude Number

The definition of critical flow directly implies the value of the Froude number.

• Given that the flow is critical, by definition: $Fr = 1.0$

Therefore, the statement "Froude number is $1.0$" is correct.

Calculating Specific Energy at Critical Flow

At critical flow ($Fr = 1$), the relationship $V^2 = gy$ holds true. We can substitute this into the specific energy equation.

1. The specific energy equation is $E = y + \frac{V^2}{2g}$.
2. Substitute $V^2 = gy$ (for critical flow): $E_{crit} = y + \frac{gy}{2g}$
3. Simplify the expression: $E_{crit} = y + \frac{y}{2} = \frac{3}{2} y$
4. Given the flow depth $y = 2$ m: $E_{crit} = \frac{3}{2} \times (2 \text{ m})$
5. Calculate the specific energy: $E_{crit} = 3 \text{ m}$

Therefore, the statement "Specific energy for the flow is $3.0 \text{ m}$" is correct.

Conclusion

Based on the analysis, the correct statements are:

• Specific energy for the flow is $3.0 \text{ m}$.
• Froude number is $1.0$.

These correspond to options A and C.