The abrupt increase in depth of rapidly flowing water is called hydraulic depth.Flow at the jump changes from a supercritical to a subcritical stage with an accompanying loss of kinetic energy. The change in depth occurs over a finite distance, known as the length of jump. The upstream surface of the jump, known as the roller, is a turbulent mass of water.
The depth before a jump is the initial depth, and the depth after a jump is the sequent depth. The specific energy for the sequent depth is less than that for the initial depth because of the energy dissipation within the jump.

F=[ d₂²- d₁²]w/2

where d₁ =depth before jump, ft (m)

d₂ =depth after jump, ft (m)

w=unit weight of water, lb/ft³ (kg/m³)

One of the more popular of the numerous equations developed for determination of flow in an open channel is Manning’s variation of the Chezy formula:

V=C ?RS

where
R= hydraulic radius, ft (m)

V =mean velocity of flow, ft/s (m/s)

S= slope of energy grade line or loss of head due to friction, ft/linear ft (m/m), of channel

C =Chezy roughness coefficient

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For a given value of specific energy, the critical depth gives the greatest discharge, or conversely, for a given discharge, the specific energy is a minimum for the critical depth.

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The flow in the pipe is said to be open channel if the pipe is only half full eg Free surface flow, or open-channel flow, includes all cases of flow in which the liquid surface is open to the atmosphere.

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The momentum change and the unbalanced internal pressure of the water leads to forces on the pipes
The force diagram in figure is a convenient method for finding the resultant force on a bend. The forces can be resolved into X and Y components to find the magnitude and direction of the resultant force on the pipe.
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