HEC-RASVersion 4 0Version 4.0

Basic Principles of WaterBasic Principles of Water Surface Profile Computations

O Ch l FlSmooth Bo ndar

Open Channel Flow•Smooth Boundary•Rough Boundary

Conservation of MassContinuity Equation

Q (discharge)=VA = constantQ (discharge) VA constant

• Q is flow• V is velocityy• A is cross section area

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

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

Normal Depth Applies to Diff t T f SlDifferent Types of Slopes

YnYc

YcYn

Flow = f( Slope, Boundary Friction)

Newton's second law

Antoine Chezy (18th century)

oRSCV =

RASQ =49.1 3

22

1

cfsflowQ

RASn

Q

=

=

)(

32

Acoeffn

cfsflowQ=

)(

slopeSareaA

==

AR

perimeterwettedP =

PAR =

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)

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.

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)

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.

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

(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

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

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.

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

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

++=

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

QQ

KSSARn

Q ff ==

221

)(, KQSK

QS ff ==

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 +

Flow oClassification

St l lSteep slope: normal depth below critical

Mild slope: normal depth above critical

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.

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.

HEC-RAS

The default method of conveyance subdivision is by breaks in Manning’s ‘n’ valuesbreaks in Manning s n values.

HEC-2

• Contraction losses• Expansion losses

VVCSLh2

12

2 ααg

Vg

VCSLh fe 2212 αα

−+=

C = contraction or expansion coefficient

Contraction and Expansion Energy L C ffi i t

VV 22

Loss Coefficients

gV

gVCSLh fe 22

21

22 αα−+=

gg 22

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

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

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

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

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

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)

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

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

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.

In HEC-RAS, we have a choice ,for the calculations

Still need to examine transitions closely

GENERAL SHAPE OF PROFILE

Sluice gatedc dn

Mdn

S

M

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

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 ∆⋅⋅=−+−

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.

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

Classifications of Open Steady versus Unsteady

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...