Contents preface (VII) introduction 1—37

9.2. HYDRAULIC JUMP
Hydraulic jump occurs when, in the same reach of a channel, the upstream control causes supercritical flow while the downstream control dictates subcritical flow. Hydraulic jump is always accompanied by considerable turbulence and energy dissipation. The following are the useful applications of hydraulic jump:

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318 IRRIGATION AND WATER RESOURCES ENGINEERING
(i) The dissipation of energy of flow downstream of hydraulic structures such as dams, spillways, weirs, etc.
(ii) The reduction of net uplift pressures under hydraulic structures by raising the wa-ter depth on the apron of the structure.
(iii) The maintenance of high water levels in channels for water distribution purposes.
(iv) The mixing of chemicals for water purification or other purposes (in chemical indus-tries).
On applying Newton’s second law of motion to the control volume, shown in Fig. 9.1, one obtains,

P1 – P2 + W sin θ – Ff = ρQ(β2 u2 – β1 u1)

(9.1)

where P₁ (= ρ g z₁A₁) and P₂ (= ρ g z₂ A₂) are the pressure forces at sections 1 and 2, W the

weight of liquid between sections 1 and 2, F_f the component of unknown forces (along the direction of flow) acting between sections 1 and 2, θ the longitudinal slope of the channel, β₁ and β₂ the momentum correction coefficients at sections 1 and 2, u₁ and u₂ are the average

velocities at sections 1 and 2 and z₁ and z₂ are the distances to centroids of respective flow areas A₁ and A₂ from the free surface.

Section 1

Q

u
Control volume boundary

Section 2

W sin

h1	1
	P1

z1
W

z2
u₂

F_f

P₂

h2
Q