Delta Cross Channel Gates

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Delta Cross Channel Gates
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A gate formulation Q g A3 v 2gDh
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Matthai,H.F. 1967. Measurement of peak discharge
at width contractions by indirect methods.
Chapter A4 in Techniques of water-resources
investigations of the United States Geological
Survey.
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Photo courtesy of Lloyd Peterson, USBR.
Figure III.2.i-1. Delta Cross Channel and gates,
circa 1950s. Sacramento River is in the
foreground.
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Figure III.2.i-3. USGS Monitoring locations in
the vicinity of Delta Cross Channel, Sep 2003 to
Nov 2004.
Sacramento River above DCC
Delta Cross Channel
Sacramento River below GS
Snodgrass Slough
Mokelumne River
Georgiana Slough
Dead Horse Cut
North Fork
South Fork
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Figure III.2.i-4. Comparison of field
measurements (blue rhombuses) in Delta Cross
Channel and simulated flow (solid lines) based on
gate equation for two gate coefficients. Flow
estimates at maximum and minimum water depth are
also shown as dashed lines.
USGS flow measurements are 15-minute averages.
Stage measurements are instantaneous values. The
stage difference in this plot is the average of
two time-steps.
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Alternative Formulation
Mass balance (continuity) and energy balance
(Bernoulli equation) give vd 1 f (Ad /
Au)2)-½ 2 g (hu - hd)½ where the friction
loss term is assumed to take the form hf ½ f
vd2 Binomial expansion about mean water level
(and dropping h.o.t.s) give Qd Ad 2 g (hu -
hd)½ 1 f bo2 (1 ad dhd - au dhu)-½
where the ratio of cross-sections b is assumed
to take the form b Ad / Au bo 1 ad dhd
- au dhu higher order terms (h.o.t.s) and ad
wd / Ado and au wu / Auo
Semi-empirical coefficients to be calibrated
f, bo2, au, ad, Ado
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Figure III.2.i-5. Simulated flows in the Delta
Cross Channel using open channel hydraulic
formulation. Values of coefficients in Equation
III.2.i-6 are given in Table III.2.i-2. Field
data at 15-minute intervals span over 50 M2 tide
cycles, from July 24 to August 18, 2004.
1 f bo2 au ad Ado
1.400 0.200 0.030 0.075 2732 sq.ft.
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Figure III.2.i-6. Comparison of simulated flows
in the Delta Cross Channel using gate-type
formulation and open channel hydraulics
formulation shown in Fig.III.2.i-4. Field data
at 15-minute intervals span over 50 M2 tide
cycles, from July 24 to August 18, 2004.
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Figure III.2.i-7. Range of simulated flows in
the Delta Cross Channel for a stage difference of
¼ that estimated. Simulated flow are computed
using the open channel hydraulics formulation
(equation III.2.i-3). Only a small fraction of
the data shown in Figs.III.2.i-4,5 are shown in
this plot for better clarity. (b) At high flow
rates
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Figure III.2.i-7. Range of simulated flows in
the Delta Cross Channel for a stage difference of
¼ that estimated. Simulated flow are computed
using the open channel hydraulics formulation
(equation III.2.i-3). Only a small fraction of
the data shown in Figs.III.2.i-4,5 are shown in
this plot for better clarity. (a) At low flow
rates
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Observations DCC gates formulation

• Current formulation is inappropriate
• An alternate formulation appears to simulate
  measured flow more closely
• Uncertainty in stage difference leads to large
  scatter at low flows