Unit III Rapidly Varied Flows

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Unit IIIRapidly Varied Flows
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Hydraulic Jump- Define

• The hydraulic jump is the phenomenon that occurs
  where there is an abrupt transition from super
  critical flow to sub critical flow. The most
  important factor that affects the hydraulic jump
  is the Froude number.
• The most typical cases for the location of
  hydraulic jump are
• Jump below a sluice gate.
• Jump at the toe of a spillway.
• Jump at a glacis.
• (glacis is the name given to sloping floors
  provided in hydraulic structures.)

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Example
Jump at a glacis
Jump below a sluice gate
Jump at the toe of a spillway
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Hydraulic Jump- Assumption

• General Expression for Hydraulic Jump
• In the analysis of hydraulic jumps, the following
  assumptions are made
• The length of hydraulic jump is small.
  Consequently, the loss of head due to friction is
  negligible.
• The flow is uniform and pressure distribution is
  due to hydrostatic before and after the jump.
• The slope of the bed of the channel is very
  small, so that the component of the weight of the
  fluid in the direction of the flow is neglected.

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• Comments
• This is the general equation governing the
  hydraulic jump for any shape of channel.
• The sum of two terms is called specific force
  (M). So, the equation can be written as
• M1 M2
• This equation shows that the specific force
  before the hydraulic jump is equal to that after
  the jump.

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Classification of the Jump

• The hydraulic jump can be classified based on
  initial Froude number as
• Undular (F1 1.0 - 1.7)
• Weak (F1 1.7 - 2.5)
• Oscillating (F1 2.5 - 4.5)
• Steady (F1 4.5 - 9.0), and
• Strong (F1 gt 9.0)

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Classification of the Jump
Type of Jump Froude Number Remarks
Undular jump 1 lt F1 lt1.7 Undulations on the surface.
Weak jump 1.7 lt F1 lt 2.5 Uniform Velocity Energy Loss - small Small rollers, No baffles D/S Water Surface - Smooth.
Oscillating Jump 2.5 lt F1 lt 4.5 Water Oscillates back and forth from the bottom to the surface.
Steady Jump 4.5 lt F1 lt 9.0 Position, is sensitive to variation of Tail Water, Efficiency is 45 to 70 .
Strong Jump F1 gt 9.0 Efficiency is 85
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Classification of the Jump
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Applications of the Hydraulic Jump
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Define Surge

• A surge is a moving wave front which results in
  an abrupt change of the depth of flow.
• It is a rapidly varied unsteady flow condition
• Two Types
• Positive which results in an increase depth
  of flow
• Negative Which results in decrease depth of
  flow

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Positive surge

Type B Positive surge (Advancing Upstream)
Ex Tail gate closed suddenly.
Type A Positive surge (Advancing Downstream)
Ex Head Gate is opened suddenly.
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Negative Surge

Type C Negative Surge (Retreating
Downstream) Ex Head Gate is closed suddenly.
Type D Negative Surge (Retreating Upstream)
Ex Tail gate opened suddenly.
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Assumptions

• Channel is horizontal and frictionless
• Pressure distribution is hydrostatic at
  locations away from the front
• Velocity is uniform within the cross section, at
  location away from the front
• Change in the flow depth at the front occurs over
  a very short distance
• Water surfaces behind and ahead of the wave front
  are parallel to the bed.

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Case A Surge due to sudden in crease of flow
For example, consider the movement of a positive
surge wave in x-direction in an open channel
having an irregular cross section. Here, as the
surge moves with an absolute velocity, Vw, flow
depth becomes equal to y2 behind the surge.
Undistributed flow depth ahead of the surge is
y1. The corresponding flow velocities behind and
ahead of the slope front are V2 and V1
respectively. The surge has been created due to a
sudden change of flow rate from Q1 to Q2.
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Surge due to sudden in crease of flow
Absolute Velocity of Surge Wave
To make it to steady flow , apply Vw in opposite
direction to V1 and V2 and the surge.
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(1)
(2)
(3)
(4)
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Applying momentum equation to the control volume
of Fig
(5)
(6)
Sub Eq. 2 in Eq. 6
(7)
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Sub Eq. 3 in Eq. 7 and subsequent simplification
leads to
(8)
(9)
(10)
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Now, substitution of Eq. (4) in Eq. (7) and
subsequent simplification leads to
(11)
Equations (10) and (11) can be used to determine
the surge wave velocity and the surge height, if
we know the values of undisturbed flow depth, y1,
flow rate before the surge, Q1, and the flow rate
after the surge, Q2. Equations (10) and (11)
are non-linear equations. They can be solved by
an appropriate numerical technique. For
rectangular channels, Eqs. (10) and (11) simplify
to the following.
(12)
(13)