Hydraulic jump in a rectangular channel — find Froude number from sequent depth ratio Given the sequent depth ratio y2 / y1 = 10.30 in a horizontal, rectangular channel, determine the upstream Froude number F1.

Introduction / Context:
A hydraulic jump links supercritical and subcritical flow states. In a rectangular channel, y2 / y1 (the sequent depth ratio) is related to the upstream Froude number F1 by a standard momentum-based formula. This question evaluates your ability to invert that relation and compute F1 from a known depth ratio.

Given Data / Assumptions:

• Rectangular, horizontal channel.
• Sequent depth ratio r = y2 / y1 = 10.30.
• Hydrostatic pressure distribution and negligible losses outside the jump control section.

Concept / Approach:
The sequent-depth relation for a rectangular channel is:
r = (1/2) * (-1 + sqrt(1 + 8 F1^2))Given r, solve for F1:
2r + 1 = sqrt(1 + 8 F1^2) → (2r + 1)^2 = 1 + 8 F1^2F1 = sqrt( ((2r + 1)^2 - 1) / 8 )

Step-by-Step Solution:
1) Compute 2r + 1 = 2 * 10.30 + 1 = 21.60.2) Square: 21.60^2 = 466.56.3) Subtract 1: 466.56 − 1 = 465.56.4) Divide by 8: 465.56 / 8 = 58.195.5) Take square root: F1 = sqrt(58.195) ≈ 7.63.

Verification / Alternative check:
Back-calculate r using F1 = 7.63 to ensure r ≈ 10.30. The numbers reconfirm the correct option.

Why Other Options Are Wrong:
5.64, 8.05, and 13.61 do not satisfy the exact sequent-depth relation for r = 10.30; they correspond to different depth ratios.

Common Pitfalls:
Using the energy-based conjugate relation (incorrect here); algebraic slip in squaring 2r + 1; rounding too early.

Final Answer:
7.63