Calculation of the Ratio of Sequent Depths:

The Froude Number (Fr) is a dimensionless number that represents the ratio of inertial forces to gravitational forces in a fluid flow. It is defined as the ratio of the flow velocity to the velocity at which gravity would cause the fluid to flow.

The pre-jump Froude Number (Fr1) is given as 10. This means that the flow velocity is 10 times larger than the velocity at which gravity would cause the fluid to flow.

The ratio of sequent depths (H2/H1) can be determined using the Froude Number and the energy equation.

The energy equation for an open channel flow is given as:

H + (V^2/2g) = constant

where H is the depth of flow, V is the velocity of flow, and g is the acceleration due to gravity.

Steps to Calculate the Ratio of Sequent Depths:

1. Let the pre-jump depth be H1 and the post-jump depth be H2.

2. Using the energy equation, we can write the equation for the pre-jump depth as:

H1 + (V1^2/2g) = constant

3. The Froude Number (Fr1) is given as 10, which means:

V1 = 10 * (g * H1)^0.5

4. Similarly, for the post-jump depth, we can write the equation as:

H2 + (V2^2/2g) = constant

5. The Froude Number (Fr2) for the post-jump depth is given by:

Fr2 = V2 / (g * H2)^0.5

6. Since the flow is subcritical before and after the jump, the Froude Numbers are related as:

Fr2 = 1 / Fr1

7. Substituting the values of Fr1 and Fr2, we get:

1 / 10 = V2 / (g * H2)^0.5

8. Rearranging the equation, we can solve for H2:

H2 = (V2^2 * 100 / g)

9. Substituting the value of V2 from the equation in step 5, we get:

H2 = ((10 * (g * H1)^0.5)^2 * 100 / g)

10. Simplifying the equation, we get:

H2 = 1000 * H1

11. Therefore, the ratio of sequent depths (H2/H1) is:

H2/H1 = 1000

Final Answer:

The ratio of sequent depths is 1000.