Hydraulic Jump Sequent Depth

\frac{y _{2}}{y _{1}} = \frac{1}{2} (- 1 + 1 + 8 Fr_{1}^{2})

A jump dissipates energy from supercritical (Fr1 > 1) to subcritical (Fr2 < 1) flow. Sequent (conjugate) depths are related by the momentum equation. Head loss E1 − E2 grows with Fr1. Used below sluice gates and at steep-to-mild breaks.

$y_{1}$ (m): Upstream depth
$y_{2}$ (m): Sequent depth
$Fr_{1}$: Upstream Froude number

Step-by-step solved example

y1 = 0.30 m, V1 = 6.0 m/s. Find Fr1 and y2 (g = 9.81).

Sequent depth y2/y1 = ½(−1+√(1+8 Fr1²)).

1. Fr1
Fr1 = 6/√(9.81×0.30) = 6/1.716 = 3.50.
$Fr_{1} = 3.50$
2. y2
y2/y1 = 0.5(−1+√(1+8×12.25)) = 0.5(−1+√99) = 0.5(−1+9.95) = 4.47. y2 = 1.34 m.
$y_{2} = 1.34 m$

Answer: Fr1 = 3.50, y2 = 1.34 m

10 practice questions

0/10 correct

1.A jump requires upstream flow that is

2.If Fr1 = 1, y2/y1 =

3.Energy is

4.Downstream Fr2 is

5.The sequent-depth formula comes from

6.Larger Fr1 makes y2/y1

7.Jump length is on the order of

8.A drowned jump means

9.y1 = 0.2 m, Fr1 = 5. y2 ≈

10.Stilling basins use jumps to