Rapidly Varied Flow and culvert hydraulics
AbbiyTeshome
11 views
43 slides
Nov 01, 2025
Slide 1 of 43
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
About This Presentation
This presentation provides a comprehensive overview of open channel flow and hydraulic structure design, focusing on discharge measurement over spillways, weirs, and critical depth flumes. It covers the origin and profile design of the ogee spillway, and explains the use of the momentum equation in ...
Slide Content
Rapidly Varied Flow-1: Hydraulic
Jump
By Getacher Teshome(M.Sc.)
MekelleUniversity
Jump
By Getacher Teshome(M.Sc.)
MekelleUniversity
•Iftheflowattheupstreamofacrosssectionissupercritical(Y1<Yc)butsub
critical(Y2>Yc)atthedownstreamofthatcrosssection.
•Thetransitionfromsubcriticalflowtothesupercriticalflowwillbeabruptwith
ajumpcalledHydraulicJump.
Hydraulic Jump
Toincreasethewaterlevelonthed/softhehydraulicstructures.
Toreducethenetupliftforcebyincreasingthedownwardforceduetothe
increaseddepthofwater.
Toincreasethedischargefromasluicegatebyincreasingtheeffectivehead
causingflow,
Foraerationofdrinkingwater.
Forremovingairpocketsinapipeline
Reducedownstreamerosion.
Purposes of hydraulic jump:-
critical(Y2>Yc)atthedownstreamofthatcrosssection.
•Thetransitionfromsubcriticalflowtothesupercriticalflowwillbeabruptwith
ajumpcalledHydraulicJump.
Hydraulic Jump
Toincreasethewaterlevelonthed/softhehydraulicstructures.
Toreducethenetupliftforcebyincreasingthedownwardforceduetothe
increaseddepthofwater.
Toincreasethedischargefromasluicegatebyincreasingtheeffectivehead
causingflow,
Foraerationofdrinkingwater.
Forremovingairpocketsinapipeline
Reducedownstreamerosion.
Purposes of hydraulic jump:-
•HydraulicjumpsareclassifiedaccordingtotheupstreamFroudenumberanddepth
ratio.
Types of Hydraulic Jump
F
r1
y
2
y
1
Classification
<1 1 Jump impossible
1-1.7 1-2 Undular jump(Standing wave)
1.7-2.5 2-3.1 Weak Jump
2.5-4.5 3.1-5.9Oscillating jump
4.5-9 5.9-12 Steady jump(45-70% energy loss)
>9 >12 Strong or chopping jump(=85%energy loss
ratio.
Types of Hydraulic Jump
F
r1
y
2
y
1
Classification
<1 1 Jump impossible
1-1.7 1-2 Undular jump(Standing wave)
1.7-2.5 2-3.1 Weak Jump
2.5-4.5 3.1-5.9Oscillating jump
4.5-9 5.9-12 Steady jump(45-70% energy loss)
>9 >12 Strong or chopping jump(=85%energy loss
Hydraulic Jump
Contd.
Contd.
Basic Characteristics of :the Jump
Several basic characteristics of the hydraulic jump are:
EnergyLoss,Thelossofenergyinthejumpisequaltothedifferencein
specificenergiesbeforeandafterthejump.Itcanbeshownthatthe
lossis
∆E=E
1
−E
2
The ratio of ∆E/E1
Efficiency:
??????
2
??????
1
Relative loss.
Height of jump:
ℎ
�=??????
2−??????
1
Relative Height:
ℎ
�
??????
1
Roller
??????
2
??????
1
�
2�
1
??????
�
ℎ
�
∆??????
??????
1
??????
2
Energy Line
Several basic characteristics of the hydraulic jump are:
EnergyLoss,Thelossofenergyinthejumpisequaltothedifferencein
specificenergiesbeforeandafterthejump.Itcanbeshownthatthe
lossis
∆E=E
1
−E
2
The ratio of ∆E/E1
Efficiency:
??????
2
??????
1
Relative loss.
Height of jump:
ℎ
�=??????
2−??????
1
Relative Height:
ℎ
�
??????
1
Roller
??????
2
??????
1
�
2�
1
??????
�
ℎ
�
∆??????
??????
1
??????
2
Energy Line
•Thelengthofthehydraulicjumpissmall;consequently,thelossofhead
duetofrictionisnegligible,
•Thechannelishorizontalasithasaverysmalllongitudinalslope.The
weightcomponentinthedirectionofflowisnegligible.
•Theportionofchannelinwhichthehydraulicjumpoccursistakenasa
controlvolume&itisassumedthejustbefore&afterthecontrolvolume
•theflowisuniform&pressuredistributionishydrostatic.
In the mathematical derivation of hydraulic jump, the following
assumptions are made:
duetofrictionisnegligible,
•Thechannelishorizontalasithasaverysmalllongitudinalslope.The
weightcomponentinthedirectionofflowisnegligible.
•Theportionofchannelinwhichthehydraulicjumpoccursistakenasa
controlvolume&itisassumedthejustbefore&afterthecontrolvolume
•theflowisuniform&pressuredistributionishydrostatic.
In the mathematical derivation of hydraulic jump, the following
assumptions are made:
•Momentumequationwillbeappliedtothecontrolvolumetakenatthehydraulic
jumpsectionforaunitwidthperpendiculartothecontrolvolume.
•Themomentumofwaterpassingthroughsection(1)perunittimeisgivenas:
ρQV
1
•Momentumatsection(2)perunittimeis:
ρQV
2
•Rateofchangeofmomentumb/nsection1&2:
∆P
t
=ρQ(V
2
−V
1
)
•Thenetforceinthedirectionofflow=F1-F2:
F
1
=γA
1
Y
1
F
2
=γA
2
Y
2
•Where,
Y
1
&
Y
2
arethecentreofpressureatsection1&2.
jumpsectionforaunitwidthperpendiculartothecontrolvolume.
•Themomentumofwaterpassingthroughsection(1)perunittimeisgivenas:
ρQV
1
•Momentumatsection(2)perunittimeis:
ρQV
2
•Rateofchangeofmomentumb/nsection1&2:
∆P
t
=ρQ(V
2
−V
1
)
•Thenetforceinthedirectionofflow=F1-F2:
F
1
=γA
1
Y
1
F
2
=γA
2
Y
2
•Where,
Y
1
&
Y
2
arethecentreofpressureatsection1&2.
•Therefore
F1-F2 =
∆M
t
=ρQ (V2-V1)=γA
1
Y
1
-γA
2
Y
2
=
γ
g
Q(V
2
−V
1
)
HydraulicJumpinaHorizontalRectangularChannel
Q=A
1
V
1
=A
2
V
2
=Y
1
BV
1
=Y
2
BV
2
Y
1
=
Y
1
2
,
Y
2
=
Y
2
2
V
1
=
q
Y
1
andV
2
=
q
Y
2
•Forunitwidthperpendiculartothecontrolvolume.
γy
1
2
2
−
γy
2
2
2
=ρqV
2
−ρqV
1
,where,γ=ρg
This is for Hydraulic Jumps in Horizontal non-Rectangular and rectangular
Channel
F1-F2 =
∆M
t
=ρQ (V2-V1)=γA
1
Y
1
-γA
2
Y
2
=
γ
g
Q(V
2
−V
1
)
HydraulicJumpinaHorizontalRectangularChannel
Q=A
1
V
1
=A
2
V
2
=Y
1
BV
1
=Y
2
BV
2
Y
1
=
Y
1
2
,
Y
2
=
Y
2
2
V
1
=
q
Y
1
andV
2
=
q
Y
2
•Forunitwidthperpendiculartothecontrolvolume.
γy
1
2
2
−
γy
2
2
2
=ρqV
2
−ρqV
1
,where,γ=ρg
This is for Hydraulic Jumps in Horizontal non-Rectangular and rectangular
Channel
ρg
2
y
1
2
−y
2
2
=ρ(
q
2
y
2
2
y
2
−
q
2
y
1
2
y
1
)
g
2
y
1
−y
2
(y
1
+y
2
)=q
2
(
1
y
2
−
1
y
1
)
2q
2
g
=y
1
y
2
(
y
2
2
−y
1
2
y
2
−y
1
)
2q
2
g
=y
1
y
2
(y
2
+y
1
)
??????
2??????
1
2
+??????
1??????
2
2
−
2�
2
�
=0
2
y
1
2
−y
2
2
=ρ(
q
2
y
2
2
y
2
−
q
2
y
1
2
y
1
)
g
2
y
1
−y
2
(y
1
+y
2
)=q
2
(
1
y
2
−
1
y
1
)
2q
2
g
=y
1
y
2
(
y
2
2
−y
1
2
y
2
−y
1
)
2q
2
g
=y
1
y
2
(y
2
+y
1
)
??????
2??????
1
2
+??????
1??????
2
2
−
2�
2
�
=0
Rearranging,tosolveusingquadraticequationbydividingtheaboveexpression
byy
1
3
:
y
2
y
1
2
y
1
3
+
y
1
y
2
2
y
1
3
−
2q
2
gy
1
3
=0⟹
y
2
y
1
+
y
2
2
y
1
2
−
2q
2
gy
1
3
=0
•Nowusingquadraticequation,solvingfor
y
2
y
1
fora=1,b=1andc=−
2q
2
gy
1
3
:
•But,Fr=
V
gy
⟹
2q
2
gy
1
3
=2Fr
1
2
•Solving quadratic equation results:
y
2
y
1
=
1
2
1+8F
r1
2
−1
byy
1
3
:
y
2
y
1
2
y
1
3
+
y
1
y
2
2
y
1
3
−
2q
2
gy
1
3
=0⟹
y
2
y
1
+
y
2
2
y
1
2
−
2q
2
gy
1
3
=0
•Nowusingquadraticequation,solvingfor
y
2
y
1
fora=1,b=1andc=−
2q
2
gy
1
3
:
•But,Fr=
V
gy
⟹
2q
2
gy
1
3
=2Fr
1
2
•Solving quadratic equation results:
y
2
y
1
=
1
2
1+8F
r1
2
−1
Jumps In Horizontal Non-rectangular Channels
Basic Equations: consider a horizontal frictionless channel of any
arbitrary shape. The general momentum equation with the assumption
of �
1=�
2=1redusced to:
F1-F2 =
∆M
t
=ρQ (V2-V1)=γA
1
Y
1
-γA
2
Y
2
=
γ
g
(Q
2
V
2
−Q
1
V
1
)
=(
γ
g
Q
2
2
A
2
−
γ
g
Q
1
2
A
1
)
where A = area of cross-section any
Y
1
=
depth of the center of gravity of the area
from the water surface.
Basic Equations: consider a horizontal frictionless channel of any
arbitrary shape. The general momentum equation with the assumption
of �
1=�
2=1redusced to:
F1-F2 =
∆M
t
=ρQ (V2-V1)=γA
1
Y
1
-γA
2
Y
2
=
γ
g
(Q
2
V
2
−Q
1
V
1
)
=(
γ
g
Q
2
2
A
2
−
γ
g
Q
1
2
A
1
)
where A = area of cross-section any
Y
1
=
depth of the center of gravity of the area
from the water surface.
γA
1
Y
1
+
γ
g
Q
1
2
A
1
=γA
2
Y
2
+
γ
g
Q
2
2
A
2
=constant
Specificforce(Ps)=
P+M
γ
=A
Y+
Q
2
gA
=Constant
The specific-force
diagram provides a
convenient means of finding
sequent depths for a given
discharge in a given
horizontal channel.
For Steady Flow , Q is constant.
??????
�=A
Y+
Q
2
gA
1
Y
1
+
γ
g
Q
1
2
A
1
=γA
2
Y
2
+
γ
g
Q
2
2
A
2
=constant
Specificforce(Ps)=
P+M
γ
=A
Y+
Q
2
gA
=Constant
The specific-force
diagram provides a
convenient means of finding
sequent depths for a given
discharge in a given
horizontal channel.
For Steady Flow , Q is constant.
??????
�=A
Y+
Q
2
gA
The energy loss ELdue to a jump in a non-rectanglarhorizontal
channel is
Sequent-depth Ratios
channel is
Sequent-depth Ratios
Hydraulic Jump As An Energy Dissipater
•If we write the difference of the specific energies before
after the hydraulic jump:
∆E=
(y
2
−y
1
)
3
4y
1
y
2
•The power lost by hydraulic jump can be calculated by,
N=γ
w
Q∆E
Frompracticalviewpoint,Hydraulicjumpisausefulmeansofdissipating
excessenergyinsupercriticalflow.
Itsmeritisinpreventingpossibleerosionbelowoverflowspillway,chutes,
andforitquicklyreducesthevelocityoftheflowona·pavedaprontoa·
point.wheretheflowbecomesincapableofscouringthedownstream
channelbed,
•If we write the difference of the specific energies before
after the hydraulic jump:
∆E=
(y
2
−y
1
)
3
4y
1
y
2
•The power lost by hydraulic jump can be calculated by,
N=γ
w
Q∆E
Frompracticalviewpoint,Hydraulicjumpisausefulmeansofdissipating
excessenergyinsupercriticalflow.
Itsmeritisinpreventingpossibleerosionbelowoverflowspillway,chutes,
andforitquicklyreducesthevelocityoftheflowona·pavedaprontoa·
point.wheretheflowbecomesincapableofscouringthedownstream
channelbed,
•IftheFroudenumberatthedropofahydraulicjumppoolis6andthewater
depthis0.50m,findoutthelengthofthehydraulicjump.Calculatethepower
dissipatedwiththehydraulicjumpifthedischargeonthespillwayis1600
m3/sec.
Hydraulic Jump
=0.5�
?
Spillway
depthis0.50m,findoutthelengthofthehydraulicjump.Calculatethepower
dissipatedwiththehydraulicjumpifthedischargeonthespillwayis1600
m3/sec.
Hydraulic Jump
=0.5�
?
Spillway
•Itispreferredtobeonthesafesidewiththehydraulicstructures.Therefore,
thelongestresultwillbechosen.Thelengthofthehydraulicjumpwillbetaken
asL=22.4mfordesignpurposes.Energydissipatedashead.
thelongestresultwillbechosen.Thelengthofthehydraulicjumpwillbetaken
asL=22.4mfordesignpurposes.Energydissipatedashead.
Rapidly Varied Flow-2: Flow over Spillway and weir
Rapidly varied flow is a type of flow in which the flow depth,
velocity etc., change very significantly over a short distance
caused by obstructions.
Rapidly varied flow is a type of flow in which the flow depth,
velocity etc., change very significantly over a short distance
caused by obstructions.
Characteristics of the RVF
•Pronounced curvatureleads to non-
hydrostatic pressure distribution.
•Friction plays a minor role since RVF is a local
phenomena.
•Physicalcharacteristicsofthefloware
basicallyfixedbytheboundarygeometryof
thestructureandbythestateofflow.
•Separation zones, eddies and rollerstend
to complicate the flow and distort the
velocity distribution.
Roller
Eddy
Separation
Zones
•Pronounced curvatureleads to non-
hydrostatic pressure distribution.
•Friction plays a minor role since RVF is a local
phenomena.
•Physicalcharacteristicsofthefloware
basicallyfixedbytheboundarygeometryof
thestructureandbythestateofflow.
•Separation zones, eddies and rollerstend
to complicate the flow and distort the
velocity distribution.
Roller
Eddy
Separation
Zones
Hydraulic jump
Flow over
spillway
Flow under
sluice
Sharp crested
weir
Broad crested
weir
Common Rapidly varied flows
Flow over
spillway
Flow under
sluice
Sharp crested
weir
Broad crested
weir
Common Rapidly varied flows
Sharp-crested Weirs
Sharp-crestedweirsare
extensivelyusedasafairly
preciseflow-measuringdevice
inlaboratories.
When Air completely evacuated( Incase of water
completely spanned the full width of the channel).
To maintain standardized
conditions for flow
measurement,the air pocket
below the lower nappe
should be kept at a constant
pressure.
The atmospheric pressure
in this pocket is achieved
through the provision of air
vents.
Contd.
Sharp-crestedweirsare
extensivelyusedasafairly
preciseflow-measuringdevice
inlaboratories.
When Air completely evacuated( Incase of water
completely spanned the full width of the channel).
To maintain standardized
conditions for flow
measurement,the air pocket
below the lower nappe
should be kept at a constant
pressure.
The atmospheric pressure
in this pocket is achieved
through the provision of air
vents.
Contd.
Discharge Equation
Weir as a flow-measuring device
•By considering an ideal undeflectedjet
•And rectangular weir of length L spanning the
full width of the rectangular channel (L=B)
�
1�
�
�
�=�
1+
�
�
2
2�
��
�=??????2�ℎ�ℎ
�
�=??????2�
????????????
2
2??????
??????1+
????????????
2
2??????
ℎ�ℎ
Q=
2
3
�
�2�??????�
1
3/2
Ideal discharge Assumptions
No effect of approach velocity and
Weir height
No effect of Head of water above
the weir crest
Un deflected jet
No effect of viscosity
No effect of surface tension
Where �
�is coefficient of
discharge. Q is actual
discharge
�
�=0.611+0.08
�
1
�
���
�
1
�
≤5…��ℎ�����������
�
�=�
�
�
1
�
,�
�,�
??????
���
1����
�����??????�??????����??????ℎ??????�ℎeffect of surface
tension and Reynolds number is negligible. thus
Contd.
Weir as a flow-measuring device
•By considering an ideal undeflectedjet
•And rectangular weir of length L spanning the
full width of the rectangular channel (L=B)
�
1�
�
�
�=�
1+
�
�
2
2�
��
�=??????2�ℎ�ℎ
�
�=??????2�
????????????
2
2??????
??????1+
????????????
2
2??????
ℎ�ℎ
Q=
2
3
�
�2�??????�
1
3/2
Ideal discharge Assumptions
No effect of approach velocity and
Weir height
No effect of Head of water above
the weir crest
Un deflected jet
No effect of viscosity
No effect of surface tension
Where �
�is coefficient of
discharge. Q is actual
discharge
�
�=0.611+0.08
�
1
�
���
�
1
�
≤5…��ℎ�����������
�
�=�
�
�
1
�
,�
�,�
??????
���
1����
�����??????�??????����??????ℎ??????�ℎeffect of surface
tension and Reynolds number is negligible. thus
Contd.
For H1/P > 20,the weir acts as a sill and
the discharge is controlled by a critical
section immediately u/s from the sill.
??????
�
�
1+�=??????
�=(
�
2
��
2
)
1/3
�=��(�
1+�)
3
2=
2
3
�
�2�??????�
1
3/2
�
�=1.06(1+
�
�
1
)
3
2..���H1/P>20
�
�
1
Sill
Discharge Equation
Weir as a flow-measuring device
4�
1
��>
??????
�
??????
>??????
Generally the effect of fluid properties
on Cd is insignificant if�
1≥2��
the discharge is controlled by a critical
section immediately u/s from the sill.
??????
�
�
1+�=??????
�=(
�
2
��
2
)
1/3
�=��(�
1+�)
3
2=
2
3
�
�2�??????�
1
3/2
�
�=1.06(1+
�
�
1
)
3
2..���H1/P>20
�
�
1
Sill
Discharge Equation
Weir as a flow-measuring device
4�
1
��>
??????
�
??????
>??????
Generally the effect of fluid properties
on Cd is insignificant if�
1≥2��
Submerged sharp crested weir
�
??????=�
11−
�
2
�
1
�0.385
If the tail water(H2) level is above
the weir crest, the flow pattern
would be much different from the
free-flow case.
where Q1 = free-flow discharge under head
Thus to ensure free-flow it is usual to specify the
tail water surface to be at least 8 cm below the
weir crest for small weirs.
In sharp-crested rectangular weirs the
submergence effect is felt even before the tail
water reaches the crest elevation
Theminimumvalueof
H
2
H
1
iscalledmodular
limit.
�
1=
2
3
�
�2�??????�
1
3/2
When,Q
1
−Qs=10%Q
1
the
associated
H
2
H
1
is the minimum to
sustain submergence.
Contd.
�
??????=�
11−
�
2
�
1
�0.385
If the tail water(H2) level is above
the weir crest, the flow pattern
would be much different from the
free-flow case.
where Q1 = free-flow discharge under head
Thus to ensure free-flow it is usual to specify the
tail water surface to be at least 8 cm below the
weir crest for small weirs.
In sharp-crested rectangular weirs the
submergence effect is felt even before the tail
water reaches the crest elevation
Theminimumvalueof
H
2
H
1
iscalledmodular
limit.
�
1=
2
3
�
�2�??????�
1
3/2
When,Q
1
−Qs=10%Q
1
the
associated
H
2
H
1
is the minimum to
sustain submergence.
Contd.
Contracted Weir
•If the length of the weir L is smaller
than the width of the channel, such
weir are known as contracted weir.
•Theflowissuingoutoftheweiropening
willundergocontractionatthesidesin
additiontothecontractioncausedby
upperandlowernappes.
Discharge Equation
??????
�=??????−0.1��
1
wheren=numberofendcontractions.For
theweirshown,n=2,andifmnumberof
piersareintroducedonaweircrest,
n=2m+2
The actual Discharge
•If the length of the weir L is smaller
than the width of the channel, such
weir are known as contracted weir.
•Theflowissuingoutoftheweiropening
willundergocontractionatthesidesin
additiontothecontractioncausedby
upperandlowernappes.
Discharge Equation
??????
�=??????−0.1��
1
wheren=numberofendcontractions.For
theweirshown,n=2,andifmnumberof
piersareintroducedonaweircrest,
n=2m+2
The actual Discharge
Kindsvaterand Carterhave
given a modified version from
extensive experimental
investigation covering a wide
range of variables
Where;
Cdc= coefficient of
discharge for
contracted weir,
Le= effective length
and
Hle= effective head.
Cdcaccountsforcontraction
causedbyupperandlower
nappes.��
??????
??????
,
??????1
??????
Contracted Weir
This equation is subject to
the limitations of
H1/ P < 2.0, H1 > 0.03 m,
L > 0.15 m and
P > 0.10 m.
given a modified version from
extensive experimental
investigation covering a wide
range of variables
Where;
Cdc= coefficient of
discharge for
contracted weir,
Le= effective length
and
Hle= effective head.
Cdcaccountsforcontraction
causedbyupperandlower
nappes.��
??????
??????
,
??????1
??????
Contracted Weir
This equation is subject to
the limitations of
H1/ P < 2.0, H1 > 0.03 m,
L > 0.15 m and
P > 0.10 m.
Broad-crested Weir
Weirs with a finite crest width in the
direction of flow are called broad-crested
weirs.
Possible Flow separation
over the Sharpe edge
Subcritical
flow
Super critical
flow
critical
flow
Weirs with a finite crest width in the
direction of flow are called broad-crested
weirs.
Possible Flow separation
over the Sharpe edge
Subcritical
flow
Super critical
flow
critical
flow
Let as consider a simple,
rectangular, horizontal broad-crested
weir
Broad-crested Weir
������??????��ℎ����,�
�=�
�??????
�=
2
3
2
3
��
3/2
������??????��ℎ����,�
�=1.705�
3/2
Ideal Discharge in terms of energy head
�������??????��ℎ����,�=1.705�
�1�
3/2
Q=
2
3
�
�2�??????�
1
3/2
The most convenient intermsof water
head sufficiently upstream fothe weir
face
long-crested weir
true broad-crested weir.
Sharp crested weir. Narrow crested weir.
??????
??????
??????
??????
??????
??????
Has Insignificant effect
rectangular, horizontal broad-crested
weir
Broad-crested Weir
������??????��ℎ����,�
�=�
�??????
�=
2
3
2
3
��
3/2
������??????��ℎ����,�
�=1.705�
3/2
Ideal Discharge in terms of energy head
�������??????��ℎ����,�=1.705�
�1�
3/2
Q=
2
3
�
�2�??????�
1
3/2
The most convenient intermsof water
head sufficiently upstream fothe weir
face
long-crested weir
true broad-crested weir.
Sharp crested weir. Narrow crested weir.
??????
??????
??????
??????
??????
??????
Has Insignificant effect
Ogee (Overflow) Spillway
is a control weir having an ogee (S-shaped) overflow
profile.
It is probably the most extensively used spillway to
safely pass the flood flow out of a reservoir.
a well-ventilated
sharp-crested
rectangular weir
This profile Assures for the design head
a high discharge coefficient with out cavitation.
Atmospheric pressure on the weir
���
�
1
�
≈0,ℎ
�=0.98�
�1
Emanation of Ogee (Overflow) Spillway profile
is a control weir having an ogee (S-shaped) overflow
profile.
It is probably the most extensively used spillway to
safely pass the flood flow out of a reservoir.
a well-ventilated
sharp-crested
rectangular weir
This profile Assures for the design head
a high discharge coefficient with out cavitation.
Atmospheric pressure on the weir
���
�
1
�
≈0,ℎ
�=0.98�
�1
Emanation of Ogee (Overflow) Spillway profile
Uncontrolled Ogee Crest
•No crest gate over them
Elements of a spillway crest according to USBR Profile
Crest profile
upstream of the apex
crest
downstream of
the apex
Where Hdis design head
K, n –constants depending on the
inclination of u/s face and approach
velocity
Contd.
•No crest gate over them
Elements of a spillway crest according to USBR Profile
Crest profile
upstream of the apex
crest
downstream of
the apex
Where Hdis design head
K, n –constants depending on the
inclination of u/s face and approach
velocity
Contd.
The expression for the design discharge Qd
Ogee (Overflow) Spillway
Where �
��= coefficient of discharge at the design
head Hd.�
��=fn(
??????
????????????
, �����������)
If �
�= any energy head over the ogee spillway
�
�=
2
3
�
��2�??????
��
�
3/2
�=
2
3
�
�2�??????
��
�
3/2
�
�
�
�
�
�
The use of �
�and �
�, the
energy heady is not very
convenient fro discharge
estimation so,
For
ℎ??????
??????
<0.5, The velocity of approach is very
small and ℎ
�≈�
�andℎ
�≈�
�.
�
�=
2
3
�
��2�??????
�ℎ
�
3/2
Cavitation &
Separation
Ogee (Overflow) Spillway
Where �
��= coefficient of discharge at the design
head Hd.�
��=fn(
??????
????????????
, �����������)
If �
�= any energy head over the ogee spillway
�
�=
2
3
�
��2�??????
��
�
3/2
�=
2
3
�
�2�??????
��
�
3/2
�
�
�
�
�
�
The use of �
�and �
�, the
energy heady is not very
convenient fro discharge
estimation so,
For
ℎ??????
??????
<0.5, The velocity of approach is very
small and ℎ
�≈�
�andℎ
�≈�
�.
�
�=
2
3
�
��2�??????
�ℎ
�
3/2
Cavitation &
Separation
Contd.
The overflow spillway, when working at 1 < Ho/Hd
< 3.0, has the desirable feature of higher values of
Co. The inception of cavitation is the only problem
to be guaranteed against.
The increased discharge coefficient at (H0 / Hd) > 1.0 is due to the
occurrence of negative pressures on the crest.
Positive pressure over the
crest
Negative pressure over
the crest
flow
Separation
Cavitation may
occur
IfPm=Vaporpressure,
Cavitationwilloccur.
Contd.
�
�
��
�
=−1.17
�
�
�
�
−1
�
�
��
�
=−1.17
�
�
�
�
−1
< 3.0, has the desirable feature of higher values of
Co. The inception of cavitation is the only problem
to be guaranteed against.
The increased discharge coefficient at (H0 / Hd) > 1.0 is due to the
occurrence of negative pressures on the crest.
Positive pressure over the
crest
Negative pressure over
the crest
flow
Separation
Cavitation may
occur
IfPm=Vaporpressure,
Cavitationwilloccur.
Contd.
�
�
��
�
=−1.17
�
�
�
�
−1
�
�
��
�
=−1.17
�
�
�
�
−1
•Imposed by the presence of
abutments and piers
•The effective length of the
spillway is estimated by
Contraction on the spillway
Where
•L = actual length of the spillway
•n = number of piers
•Kp= pier contraction coefficient
•Ko= abutment contraction
coefficient
For preliminary study the following values are usually adopted
Piers
Abutment
Sharp Corner
abutments and piers
•The effective length of the
spillway is estimated by
Contraction on the spillway
Where
•L = actual length of the spillway
•n = number of piers
•Kp= pier contraction coefficient
•Ko= abutment contraction
coefficient
For preliminary study the following values are usually adopted
Piers
Abutment
Sharp Corner
Spillway with Crest Gates
When spillways are provided with crest gates, they have to
operate as uncontrolled spillway under high flood conditions
and with partial gate openings at lower flows
At partial gate
openings, the water
issues out of the
gate opening as an
orifice flow and the
trajectory is a
parabola.
orifice flow cause negative pressure
during partial gate opening.
At full gate openings Cg<Cdo
These negative
pressures can
be minimized if
the gate sill is
placed
downstream of
the apex of the
crest
When spillways are provided with crest gates, they have to
operate as uncontrolled spillway under high flood conditions
and with partial gate openings at lower flows
At partial gate
openings, the water
issues out of the
gate opening as an
orifice flow and the
trajectory is a
parabola.
orifice flow cause negative pressure
during partial gate opening.
At full gate openings Cg<Cdo
These negative
pressures can
be minimized if
the gate sill is
placed
downstream of
the apex of the
crest
Critical-depth Flumes
Critical-depthflumesare flow-measuringdevices in which a control
section is achieved through the creation of a critical-flow sectionby a
predominant width constriction.
Sub-critical flow Sub-critical flowcritical flow
Super-critical
flow
Where Cf= overall
discharge coefficient of the
flume = f (H1/L)
In practice, these are like
broad-crested weirs but
with a major change that
these are essentially flow-
measuring devices and
cannot be used for flow-
regulation purposes.
Critical-depthflumesare flow-measuringdevices in which a control
section is achieved through the creation of a critical-flow sectionby a
predominant width constriction.
Sub-critical flow Sub-critical flowcritical flow
Super-critical
flow
Where Cf= overall
discharge coefficient of the
flume = f (H1/L)
In practice, these are like
broad-crested weirs but
with a major change that
these are essentially flow-
measuring devices and
cannot be used for flow-
regulation purposes.
Culvert Hydraulics
A culvert is a conduit provided to transmit the
flow of a stream past an obstacle.such as:
a roadway,
railway or
any kind of embankment
The flow through a culvert
•can be subcritical or supercritical
•closed conduit or open channel flow
•may have an inlet or an outlet control
•May be GVF, RVF or uniform flow or any
combination of these
•Both Inlet and outlet may or may not
submerged
Box culvert
Pipe culvert
A culvert is a conduit provided to transmit the
flow of a stream past an obstacle.such as:
a roadway,
railway or
any kind of embankment
The flow through a culvert
•can be subcritical or supercritical
•closed conduit or open channel flow
•may have an inlet or an outlet control
•May be GVF, RVF or uniform flow or any
combination of these
•Both Inlet and outlet may or may not
submerged
Box culvert
Pipe culvert
Control Section—thelocation where there is a unique(fixed)
relationship between the flow rate and the upstream water
surface elevation.
An inlet or an outlet control
water can flow through and out of the culvert faster than it
can enter.
Is governed by the inlet geometry
usually occurs if the culvert is operating on a steep slope.
only the headwater and the inlet configuration affect the
culvert performance.
the control section is at the upstream end of the barrel (the
inlet)
flow passes through critical depth
shallow, high velocity
supercritical flow in the culvert barrel.
Depending on the tail water, a hydraulic jump may occur
downstream of the inlet.
Inlet control
Contd.
relationship between the flow rate and the upstream water
surface elevation.
An inlet or an outlet control
water can flow through and out of the culvert faster than it
can enter.
Is governed by the inlet geometry
usually occurs if the culvert is operating on a steep slope.
only the headwater and the inlet configuration affect the
culvert performance.
the control section is at the upstream end of the barrel (the
inlet)
flow passes through critical depth
shallow, high velocity
supercritical flow in the culvert barrel.
Depending on the tail water, a hydraulic jump may occur
downstream of the inlet.
Inlet control
Contd.
Flow types under inlet control.
Type A
Inlet/Outlet Unsubmerged
??????
�
supercritical
??????�??????�????????????�,??????
�
Subcritical
supercritical
Type B
Outlet Submerged, Inlet Unsubmerged
Hydraulic
jump
Subcritical
??????
�
??????�??????�????????????�,??????
�
Type C
Inlet Submerged
supercritical
Subcritical
??????�??????�????????????�,??????
�
Normal depth
??????
�
??????
�
Type D
Inlet and Outlet Submerged
Hydraulic
jump Subcritical
supercritical
??????
�
??????�??????�????????????�,??????
�
Contd.
Type A
Inlet/Outlet Unsubmerged
??????
�
supercritical
??????�??????�????????????�,??????
�
Subcritical
supercritical
Type B
Outlet Submerged, Inlet Unsubmerged
Hydraulic
jump
Subcritical
??????
�
??????�??????�????????????�,??????
�
Type C
Inlet Submerged
supercritical
Subcritical
??????�??????�????????????�,??????
�
Normal depth
??????
�
??????
�
Type D
Inlet and Outlet Submerged
Hydraulic
jump Subcritical
supercritical
??????
�
??????�??????�????????????�,??????
�
Contd.
Outlet control
water can flow into the culvert faster than it can flow
through and out.
can flow either partially full or full.
water is relatively deep and slower.
depths and velocity that are subcritical.
flow is controlled downstream
(roughness, area, shape, length, and slope) and the tail
water elevation affect culvert performance in outlet
control.
Flow types under outlet control.
Type A: Inlet & Outlet Submerged
pressure flow
Contd.
water can flow into the culvert faster than it can flow
through and out.
can flow either partially full or full.
water is relatively deep and slower.
depths and velocity that are subcritical.
flow is controlled downstream
(roughness, area, shape, length, and slope) and the tail
water elevation affect culvert performance in outlet
control.
Flow types under outlet control.
Type A: Inlet & Outlet Submerged
pressure flow
Contd.
Type B: Outlet Submerged, Inlet Unsubmerged
pressure flow
Type C: inlet Submerged, Outlet Unsubmerged
Type D: Inlet Submerged, Outlet Partially Submerged
Type E: Inlet Unsubmerged, Outlet Unsubmerged
more typical.
rare condition
typical
Subcritical Flow
Mild Slope
Mild Slope
??????
�
M2
Contd.
pressure flow
Type C: inlet Submerged, Outlet Unsubmerged
Type D: Inlet Submerged, Outlet Partially Submerged
Type E: Inlet Unsubmerged, Outlet Unsubmerged
more typical.
rare condition
typical
Subcritical Flow
Mild Slope
Mild Slope
??????
�
M2
Contd.
Proper culvert design and analysis requires
checking for inlet and outlet control to
determine which will govern particular culvert
designs.
Designs for low headwater
•depths reduce pipe diameter and fill material,
•but risk overtopping and often result in undersized
culverts when exposed to natural conditions.
designs for higher headwater depths are more
conservative and generally govern design.
Allowable Headwater
•not higher than 300 mm below the
edge of the shoulder.
•HW/D not greater than 1.5
•no higher than the low point in the
road grade,
•equal to the elevation where flow
can be diverted around the culvert
Review
(Check)
Headwater
Contd.
does not exceed 500
mm increase over the
existing 100-year
flood
has a level of
inundation that is
tolerable to upstream
property
checking for inlet and outlet control to
determine which will govern particular culvert
designs.
Designs for low headwater
•depths reduce pipe diameter and fill material,
•but risk overtopping and often result in undersized
culverts when exposed to natural conditions.
designs for higher headwater depths are more
conservative and generally govern design.
Allowable Headwater
•not higher than 300 mm below the
edge of the shoulder.
•HW/D not greater than 1.5
•no higher than the low point in the
road grade,
•equal to the elevation where flow
can be diverted around the culvert
Review
(Check)
Headwater
Contd.
does not exceed 500
mm increase over the
existing 100-year
flood
has a level of
inundation that is
tolerable to upstream
property
Tags
hydraulic jump
ogee spillway
sharp crested weir
broad crested weir
culvert hydraulics
critical depth flume
specific force
rapidly varied flow
discharge coeficient
pressure over spillway crest
inlet control
outlet control
spillway with crest gate
contracted spillway
submerged weir
critical depth
sequient depths
mild slope
steep slope
Categories
ScienceDownload
Download Slideshow Get the original presentation fileQuick Actions
Statistics
- Views 11
- Slides 43
- Age 6 days
Related Slideshows
23
Earthquakes_Type of Faults_Science G8.pptx
0 views
15
Quiz #1 Science 10 in the first quarter for jhs
0 views
9
Astronomy history from long ago till doday
0 views
9
Great history of astronomy from long ago till today
0 views
20
EARTHQUAKE-DRILL.powerpoint.............
0 views
9
History of astronomy from old times to the present times
0 views