Critical Depth in a Rectangular Channel:

The specific energy in an open channel flow is defined as the sum of the elevation head (z), the pressure head (P), and the velocity head (V) of the flow. The critical depth is the depth at which the specific energy is minimum for a given discharge. In a rectangular channel, the critical depth can be calculated using the specific energy equation.

Specific Energy Equation:

The specific energy (E) in a rectangular channel can be calculated using the specific energy equation:

E = (y + z) + (V^2 / 2g)

Where,
E = Specific energy
y = Depth of flow
z = Elevation head
V = Velocity of flow
g = Acceleration due to gravity

Critical Depth Calculation:

At critical depth, the specific energy is minimum. To find the critical depth, we need to differentiate the specific energy equation with respect to the depth (y) and equate it to zero.

dE/dy = 1 + (V^2 / gy^2) = 0

Solving this equation, we can find the critical depth (yc).

Ratio of Specific Energy at Critical Depth to Critical Depth:

Now, we need to find the ratio of the specific energy at critical depth (Ec) to the critical depth (yc). Let's denote this ratio as R.

R = Ec / y

To find this ratio, we substitute the value of critical depth (yc) into the specific energy equation and calculate the specific energy at critical depth (Ec).

Finally, we divide Ec by yc to obtain the ratio R.

Explanation of the Correct Answer:

According to the given options, the correct answer is option 'C' (1.5).

This means that the specific energy at critical depth is 1.5 times the critical depth itself.

This ratio indicates that the specific energy at critical depth is higher than the critical depth. It implies that the flow at critical depth has a higher energy level compared to other depths.

Hence, option 'C' (1.5) is the correct answer.