CWR4101: Flow Routing Chapter 8

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CWR4101 Flow Routing Chapter 8
Dr. Marty Wanielista 407.823.4144 wanielis_at_mail.uc
f.edu www.stormwater.ucf.edu http//classes.cecs.u
cf.edu/CWR4101/wanielista
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Outline Classifications for Routing

• Hydraulic - Based on momentum and continuity
  equations, also called the St. Venant equations.
• 1. Can be solved using finite difference
  equations for known channel geometries.
• 2. The basic form of the kinematic wave
  equations are 8.8 and 8.10. (section 8.2)
• Hydrologic - Based primarily on a mass balance.
• 1. Inventory Equations (section 8.3)
• 2. Muskingum Method (section 8.4)
• Computer Programs, SMADA, ICPR, HEC1 and others.

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Why? Pond Design and Flow Predictions or
Hydrograph Shapes after Storage
Influent Hydrograph
Discharge or Effluent Hydrographs
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Applications to Systems of flow

• Watersheds have different characteristics, such
  as, slopes, impervious cover, soils, flow paths,
  etc, thus separate ID is necessary
• Many river or estuary sections require an
  estimate of flows downstream
• Many decision points for peak discharges, volume,
  and low flows (MFLs)
• See handout from HEC 1 Users Manual

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How to keep track of the system? Use A Watershed
Schematic

• Hydrograph Generation
• Analysis Point
• Detention Pond, River Segment, or Reservoir

See handout for discussion
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Hydraulic Routing

• Momentum Equation
• Continuity Equation QAV

Equation 8.1
Equation 8.2
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Kinematic Wave

• Using Continuity
• Q a Am
• where aand m are kinematic wave constants.
• To solve use differential form of equation 8.2
• dA/dt amA(m-1)dA/dx q (unit flow) (8.5)
• Let dA/dx DA/Dx (Ai,j-1 Ai-1,j-1)/Dx
• Or solve by finite differences. (8.8,8.9,8.10)
• And average velocity (celerity) am(Aavg)m-1
  (8.13)
• Which must be less than Dx/Dt and L/2 ltDxgtL/50

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Kinematic Wave Overland Flowfor unit width flow
qo

• qo (1.486/N)So1/2yo5/3 o is overland flow
• Also qo aoyomo
• So ao (1.486 So1/2 /N) and mo 5/3
• See page 309 for other sections and
• Example problem 8.1, pages 310-313.

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Hydrologic Modeling

• Mass Balanced Based
• Must have relationships between storage and
  discharge or among storage stage and discharge.
• Widely applied
• Found in most computer algorithms

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Mass Balanced Based

• Given an input to a watershed, stream or pond,
  what is the output

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Inventory Equations (volume)

• Storage Change Inflow Outflow
• S0 Inflow1 Outflow1 S1
• S1 Inflow2 Outflow2 S2
• S2 S1 I2 O2 and Si Si-1 Ii Oi
• Si - Si-1 (Ii Ii-1)/2 (Oi Oi-1)/2
• However, two unknows, Si Oi
• Thus we need another equation, a
• Stage storage discharge relationship O vs S

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Working Equations - flow rate time

• Mass Balance per time step Equation
• Known Equations (all known numbers on one side
  of the equation)
• Let Iavg (Ii Ii-1)/2 and Ni is a state
  variable
• Ni Si Oi/2Dt Si-1 Oi-1/2Dt
  Iavg Dt
• NOTE Still two unknows Si and Oi

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Stage Storage Discharge Relationship

• S- O relationship
• O (S S_at_O0)/slope and Sslope(O) S_at_O0
• Known Equations substituting with the S-O
  equation

O cfs
N slope(O) S_at_O0 O/2Dt and N slope
Dt/2 O S_at_O0 Do Example Problem 8.2 Page
315-317
1
slope
S CF
S_at_O0
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Muskingum Method

• Application to river systems
• Postulate
• S cSI (1-c)SO where c is a weighting factor
  lt 0.5
• and SO is outflow and SI is inflow
• Must also have relationships between Discharge
  and stage and between Storage and stage (depth),
  given as
• O ayn and S bym
• where a,b,n, and m are specific for a river
  reach.
• See pages 322-329

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End Flow Routing, Chapter 8
Dr. Marty Wanielista 407.823.4144 wanielis_at_mail.
ucf.edu www.stormwater.ucf.edu http//classes.cec
s.ucf.edu/CWR4101/wanielista