Channel Flow Routing

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Channel Flow Routing
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Steady vs. Unsteady Flow

• Steady
• Unsteady

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Unsteady flow through channels and reservoirs

• Affect of channel or reservoir storage on flow
  hydrographs
• Reduce peak flows
• Prolong hydrograph base times

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Routing Example

• Affected by
• Slope
• Shape
• Roughness
• Storage

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Flow Routing
Channel reach or
Reservoir
Inflow Hydrograph
Outflow Hydrograph
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Flow Routing Used To

• Determine impacts of
• Channel modifications
• Reservoir spillway modifications
• Design structures to
• Control storm water
• Mitigate flood flows
• Trap sediment

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Storage Routing Methods

• Based on the continuity equation
• Also known as hydrologic routing
• Methods include
• Basic storage routing
• Muskingum routing
• Convex Routing
• Kinematic Routing

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Hydraulic Flow Routing

• Based on momentum and continuity equations
• Usually done by a numerical solution of the
  governing equations or by the method of
  characteristics.

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Continuity and Momentum Equations A Review
I O DS
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Continuity Equation
Volume of the control element
Inflow
Outflow
Continuity equation
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Momentum Equation
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Storage Routing
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Storage Routing

• Storage based on
• Channel geometry
• Depth of flow
• Flow rate
• can be related to depth of flow through Mannings
  equation assuming steady, uniform flow
• Storage can be based on the average
  cross-sectional area of the reach for a given
  flow rate

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Storage

• Storage can be based on the average
  cross-sectional area of the reach for a given
  flow rate.
• Length of the channel section multiplied by the
  average cross-sectional area of the channel at a
  given flow rate would give the storage in the
  reach at that flow rate.

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Other inflows (or outflows)

• Tributary inflows
• Overland flows
• Ground water contributions

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Channel routing

• Channel usually divided into several reaches
  where outflow from one become inflow to the next.
• Reaches should have fairly uniform hydraulic
  properties.
• Routing interval should not exceed 1/5 to 1/3 of
  the time to peak of the hydrograph being routed.
• Routing interval should not exceed travel time
  through the reach.
• Common method to solve is to plot characteristic
  curves (SODt/2 and S-ODt/2 versus discharge or
  depth.

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Example

• A channel is 2500 ft long, has a slope of 0.09
  and is clean with straight banks and no rifts or
  deep pools. The appropriate Mannings n is
  0.030. A typical cross section is shown in the
  figure on the next page. Along the length of the
  channel there is no lateral inflow. The inflow
  hydrograph to the reach is triangular in shape
  with a base time of 3 hr, a time to peak of 1
  hour and a peak flow rate of 360 cfs. Route the
  hydrograph through the channel reach using the
  storage routing procedure.

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Muskingum Method
Storage Routing
Muskingum Routing
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Muskingum Routing

• Storage in reach is a linear function of both the
  inflow and outflow rate.
• x and k must be determined from channel
  characteristics (For best results based on
  observed hydrographs).
• x of zero corresponds to reservoir storage
  routing x of ½ makes the storage a function of
  the average flow rate in the reach.

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Muskingum Routing (no streamflow records)

• In the absence of streamflow records, k may be
  estimated as the flow travel time in the reach
  and x may be taken as about 0.25.

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Muskingum-Cunge Method

• Procedure to get better estimates for k and x.
• c represents a flood wave celerity
• m comes from the uniform flow equation and may be
  taken as 5/3.
• v is the velocity at bankful discharge

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Muskingum-Cunge

• qo is the flow per unit width generally
  calculated at the peak flow rate.
• So is the slope of the channel.

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Example Muskingum-Cunge Method

• Repeat storage routing example using the
  Muskingum-Cunge method.

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Convex Routing

• Involves only inflow-outflow hydrograph
  relationships i.e. continuity equation is not
  directly involved.
• C is a parameter between 0 and 1.0 and can be
  estimated from

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Convex Routing

• Travel time is calculated by DtCK where K can be
  approximated by the travel time through the
  reach.
• May result in an inconvenient time interval.
• The C value of C for a more convenient time
  interval can be calculated from
• where Dt is from the equation above and the
  ratio of Dt/Dt is kept close to unity.

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Example Convex Routing

• Repeat the previous example problem using Convex
  Routing.