A Ras-induced conformational switch in the Ras activator Son of ...
HEC-RAS Version 4 - · PDF fileHEC-RAS Version 4.0 Basic Principles of WaterBasic Principles...
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HEC-RASVersion 4 0Version 4.0
Basic Principles of WaterBasic Principles of Water Surface Profile Computations
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O Ch l FlSmooth Bo ndar
Open Channel Flow•Smooth Boundary•Rough Boundary
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Conservation of MassContinuity Equation
Q (discharge)=VA = constantQ (discharge) VA constant
• Q is flow• V is velocityy• A is cross section area
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Open Channel Flow - ControlsDefinition: A control is any feature of a channel for which a unique depth - discharge relationship occursoccurs.
Weirs/Spill a sWeirs/Spillways
Abrupt changes in slope or width
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Uniform Flow• Mean velocity is constant from section to section• Depth of flow is constant from section to section• Depth of flow is constant from section to section• Area of flow is constant from section to section• Long prismatic channel• Long prismatic channel
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Normal Depth Applies to Diff t T f SlDifferent Types of Slopes
YnYc
YcYn
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Flow = f( Slope, Boundary Friction)
Newton's second law
Antoine Chezy (18th century)
oRSCV =
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RASQ =49.1 3
22
1
cfsflowQ
RASn
Q
=
=
)(
32
Acoeffn
cfsflowQ=
)(
slopeSareaA
==
AR
perimeterwettedP =
PAR =
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Manning’s n
Manning's n values for small, natural streams (top width <30m)
A bulk term, a function of grain size, roughness, irregularities, etc…Values been suggested since turn of century (King 1918)
Lowland Streams Minimum Normal Maximum(a) Clean, straight, no deep pools 0.025 0.030 0.033(b) Same as (a), but more stones and weeds 0.030 0.035 0.040( c) Clean winding some pools and shoals 0 033 0 040 0 045( c) Clean, winding, some pools and shoals 0.033 0.040 0.045(d) Same as (c ), but some weeds and stones 0.035 0.045 0.050(e) Same as (c ), at lower stages, with less effective 0.040 0.048 0.055
and sections(f) Same as (d) but more stones 0.045 0.050 0.060(g) Sluggish reaches, weedy, deep pools 0.050 0.070 0.080(h) Very weedy reaches, deep pools and 0.075 0.100 0.150
fl d ith h t d f ti b d b hfloodways with heavy stand of timber and brushMountain streams (no vegetation in channel, banks steep, trees and brush submerged at high stages(a) Streambed consists of gravel, cobbles and(a) Streambed consists of gravel, cobbles and
few boulders 0.030 0.040 0.050(b) Bed is cobbles with large boulders 0.040 0.050 0.070(Chow, 1959)
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Gradually Varied Flow (GVF)(GVF)
V l it d d th hVelocity and depth changes from section to section.from section to section. However, the energy and
i dmass is conserved.
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Can use the energy and continuity i f hequations to stepstep from the water
surface elevation at one section tosurface elevation at one section to the water surface at another section that is a given distance upstream (subcritical) orupstream (subcritical) or downstream (supercritical)
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HEC-RAS di i l tione dimensional energy equation +
energy losses due to frictionenergy losses due to friction evaluated (Manning’s equation) to compute water surface profiles. Standard Step MethodStandard Step Method.
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Energy Equation•First law of thermodynamics
Bernoulli ‘s Equation
(V2/2g)2 + P2/w + Z2 = (V2/2g)1 + +P1/w + Z1 he( g)2 2 2 ( g)1 1 e
•Kinetic energy + pressure energy + potential energy is conserved•Kinetic energy + pressure energy + potential energy is conserved
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(V2/2 )
Energy Equation
Y
he(V2/2g)2
Y2 (V2/2g)1
Y1Z2
Z1Datum
(V2/2g)2 + Y2 Z2+ = (V2/2g)1 + + +Y1 Z1 he
VV 22
gV
gVCSLh fe 22
21
22 αα−+=Energy Losses
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Standard Step Methodhe
(V2/2g)2
Y2 (V2/2g)1
Y1Z 1Z2
Z1DatumDatum
hVVWSWS ++ )(1 22 αα•Start at a known point.
ehVVg
WSWS +−+= )(2 221112 αα •How many unknowns?
•Trial and error
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HEC-RAS - Computation ProcedureA t f l ti t t /Assume water surface elevation at upstream/ downstream cross-section.
B d th d t f l tiBased on the assumed water surface elevation, determine the corresponding total conveyance and velocity headvelocity head
With values from step 2, compute and solve equation for h
fSequation for he.
With values from steps 2 and 3, solve energy equation for WS2equation for WS2.
Compare the computed value of WS2 with value assumed in step 1; repeat steps 1 through 5 until theassumed in step 1; repeat steps 1 through 5 until the values agree to within the user-defined tolerance.
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Energy Loss - important stuff• Loss coefficients Used:• Loss coefficients Used:
– Manning’s n values for friction loss• very significant to accuracy of computed profile• very significant to accuracy of computed profile• calibrate whenever data is available
– Contraction and expansion coefficients for X-SectionsCo t act o a d e pa s o coe c e ts o Sect o s• due to losses associated with changes in X-Section
areas and velocities• contraction when velocity increases downstream• expansion when velocity decreases downstream
Bridge and culvert contraction & expansion loss– Bridge and culvert contraction & expansion loss coefficients
• same as for X-Sections but usually larger valuessame as for X Sections but usually larger values
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Friction loss is evaluated as the product of the friction slope and the discharge weightedand the discharge weighted reach length
VVCSLh2
12
2 ααfe gg
CSLh −+=22
12
robrobchchloblob QLQLQLL ++
robchlob
robrobchchloblob
QQQQQQL
++=
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Friction loss is evaluated as the product of the friction slopeand the discharge weightedand the discharge weighted reach length
21
22 VVCSLh −+=
αα
11249122 gg
CSLh fe −+=
1
21
213
249.1
KSSARn
Q ff ==
221
)(, KQSK
QS ff ==
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Friction Slopes in HEC-RAS2Average Conveyance (HEC-
RAS default) - best results for all profile types (M1, M2, etc.)
2
21
21f
KKQQS ⎟⎟
⎠
⎞⎜⎜⎝
⎛++
=21 ⎠⎝
Average Friction Slope - best SSS 21 ff
f+
=results for M1 profiles 2
Sf
21 fff SSS ⋅=Geometric Mean Friction Slope -used in USGS/FHWA WSPRO model
Harmonic Mean Friction Slope -best results for M2 profiles
21
ff
fff
SSS2S
S+
⋅=
best results for M2 profiles 21 ff SS +
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Flow oClassification
St l lSteep slope: normal depth below critical
Mild slope: normal depth above critical
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Friction Slopes in HEC-RASHEC RAS has option to allow the program to select bestHEC-RAS has option to allow the program to select best friction slope equation to use based on profile type.
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Friction Slopes in HEC-RASHEC RAS has option to allow the program to select bestHEC-RAS has option to allow the program to select best friction slope equation to use based on profile type.
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HEC-RAS
The default method of conveyance subdivision is by breaks in Manning’s ‘n’ valuesbreaks in Manning s n values.
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HEC-2
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• Contraction losses• Expansion losses
VVCSLh2
12
2 ααg
Vg
VCSLh fe 2212 αα
−+=
C = contraction or expansion coefficient
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Contraction and Expansion Energy L C ffi i t
VV 22
Loss Coefficients
gV
gVCSLh fe 22
21
22 αα−+=
gg 22
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Expansion and Contraction Coefficients
• Contraction0 0
• Expansion0.0
N t iti l 0.0
0.1 0.3
No transition loss
Gradual transitions
0.3 0.5Typical bridge sections
0.6 0.8 Abrupt transitions
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Specific Energy2VyE +=
Definition: available energy of the flow with respect to the bottom of the channel
2Q
gyE +the bottom of the channel
rather than in respect to a datum.
QV
bQq =
y
qV
byQV =
b
y
2qy
qV =Assumption that total energy is the same across the section. Therefore
e are ass ming 1 D22 gy
qyE +=we are assuming 1-D.
Note: Hydraulic depth (y) is cross section area divided by top width
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Specific Energy
constg
qyyE ==− .2
)(2
2 The Specific Energy equation can be used to produce a curve.
yEconsty
g
−=
.2
2
Q: What use is it?A: It is useful when interpreting certain aspect of open channel flowyE −
Y1
Note: Angle isNote: Angle is 45 degrees for small slopes
Y2
or E
ory
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Specific Energy
constg
qyyE ==− .2
)(2
2 For any pair of E and q, we have two possible depths that have the
yEconsty
g
−=
.2
2
same specific energy. One is supercritical, one is subcritical.The curve has a single depth at a
i i ifiyE − minimum specific energy.
Minimum specificY1 specific energy
Y2
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Specific Energy
Q: What is that minimum?2 2
2
+=qyE
A C i i l
01
22
2
==qdEgy A: Critical
01
2
3 =−=
qgydy
Minimum specific
13 =gyq
specific energy
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Froude Number
qE +2
dEgyqyE +=
2
22
Froudegyq
dydE
−=−= 23
2
11
gyV
gyqFroude ==
3
• Ratio of stream velocity (inertia force)
gygy
Ratio of stream velocity (inertia force) to wave velocity (gravity force)
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Froude Number• Ratio of stream velocity (inertia force)
to wave velocity (gravity force)
inertiaFr =Fr > 1, supercritical flowFr < 1 subcritical flowgravity
Fr Fr < 1, subcritical flow
1: subcritical, deep, slow flow, disturbances only propagate upstream3: supercritical, fast, shallow flow, disturbance can not propagate
Subcriticalp p g
upstreamSupercritical
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Critical Flow• Froude = 1• Minimum specific energy• Transition• Small changes in energy (roughness, shape, etc) cause big
changes in depthchanges in depth• Occurs at overfall/spillway
Subcritical
Supercritical Note: Critical depth is independent of roughness and slope
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Critical Depth Determination
S iti l fl i h b ifi d
HEC-RAS computes critical depth at a x-section under 5 different situations:Supercritical flow regime has been specified.
Ç Calculation of critical depth requested by user.È C i i l d h i d i d ll b d iÈ Critical depth is determined at all boundary x-sections.É Froude number check indicates critical depth needs to
b d t i d t if fl i i t d ithbe determined to verify flow regime associated with balanced elevation.
Ê Program could not balance the energy equation withinÊ Program could not balance the energy equation within the specified tolerance before reaching the maximum number of iterationsnumber of iterations.
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In HEC-RAS, we have a choice ,for the calculations
Still need to examine transitions closely
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GENERAL SHAPE OF PROFILE
Sluice gatedc dn
Mdn
S
M
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A rapidly varying flow situation• Going from subcritical to supercritical flow, or
vice-versa is considered a rapidly varying flow situation.
• Energy equation is for gradually varied flow (would d t tif i t l l )need to quantify internal energy losses)
• Can use empirical equations• Can use momentum equation• Can use momentum equation
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Momentum EquationD i d f N t ’ d l F• Derived from Newton’s second law, F=ma
• Apply F = ma to the body of water enclosed by the upstream and downstream x sectionsupstream and downstream x-sections.
Difference in pressure + weight of water - external friction = mass x acceleration
xfx12 VρQFWPP ∆⋅⋅=−+−
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Momentum Equation2 2
( V / 2g ) + Y + Z = ( V / 2g) + Y + Z + hm2 2 2 1 1 1
The momentum and energy equations may be written similarly.The momentum and energy equations may be written similarly. Note that the loss term in the energy equation represents internal energy losses while the loss in the momentum equation (hm) represents losses due to external forcesequation (hm) represents losses due to external forces.
In uniform flow, the internal and external losses are identical. In gradually varied flow, they are close.
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HEC-RAS can use the MomentumHEC RAS can use the Momentum Equation for
• Hydraulic jumps• Hydraulic dropsHydraulic drops• Low flow hydraulics at bridges
S j i• Stream junctions.
Since the transition is short, the external energy losses (due to friction) are assumed to be zero
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Classifications of Open Steady versus Unsteady
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Unsteady ExamplesUnsteady ExamplesNatural streams are always unsteady - when y ycan the unsteady component not be ignored?
• Dam breachE t i
g
• Estuaries• Bays• Flood wave• others...others...