For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is 2. The Froude number of supercritical stream is

The correct option is √3.

Understanding the concepts:
A hydraulic jump occurs when a supercritical flow (high velocity, shallow depth) encounters a subcritical flow (low velocity, deep depth), resulting in an abrupt rise in the water surface. The depth before the jump is called the initial depth ($y_1$) and the depth after the jump is called the sequent depth ($y_2$). The ratio of these depths is the sequent depth ratio, $\frac{y_2}{y_1}$.

For a horizontal, rectangular channel, the relation between the sequent depth ratio and the Froude number of the incoming supercritical stream ($F_1$) is given by the Belanger equation:

$$\frac{y_2}{y_1}=\frac{1}{2}\left(-1+\sqrt{1+8F_1^2}\right)$$

Step-by-step Derivation:
We are given that the sequent depth ratio is 2:

$$\frac{y_2}{y_1}=2$$

Substitute this value into the Belanger equation:

$$2=\frac{1}{2}\left(-1+\sqrt{1+8F_{\mathrm{1<!--\; <mn-->2}}^{}}\right)$$

Multiply both sides by 2 to clear the fraction:

Add 1 to both sides of the equation:

$$5=\sqrt{1+8F_1^2}$$

Square both sides of the equation to eliminate the square root:

$$25=1+8F_1^2$$

Subtract 1 from both sides:

$$24=8{\mathrm{F<!--\; <mn-->1\; <mn>2</mn>}}_{}^{}$$

Divide both sides by 8: