Delta Cross Channel Gates

A “gate” formulation ——— Q =  A 3 √ 2g  h Matthai,H.F Measurement of peak discharge at width contractions by indirect methods. Chapter A4 in Techniques of water-resources investigations of the United States Geological Survey.

Figure III.2.i-1. Delta Cross Channel and gates, circa 1950’s. Sacramento River is in the foreground. Photo courtesy of Lloyd Peterson, USBR.

Figure III.2.i-3. USGS Monitoring locations in the vicinity of Delta Cross Channel, Sep 2003 to Nov Sacramento River above DCC Sacramento River below GS Georgiana Slough Delta Cross Channel Snodgrass Slough Mokelumne River North Fork South Fork Dead Horse Cut

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.

Mass balance (continuity) and energy balance (Bernoulli equation) give v d = [1 + f – (A d / A u ) 2 )] -½ [2 g (h u - h d )] ½ where the friction loss term is assumed to take the form h f = ½ f v d 2 Binomial expansion about mean water level (and dropping h.o.t.s) give Q d = A d [2 g (h u - h d )] ½ [1 + f –  o 2 (1 +  d  h d -  u  h u )] -½ where the ratio of cross-sections  is assumed to take the form  = A d / A u =  o [1 +  d  h d -  u  h u + higher order terms (h.o.t.s)] and  d ≈ w d / A do and  u ≈ w u / A uo Semi-empirical coefficients to be calibrated: f,  o 2,  u,  d, A do Alternative Formulation

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, f 22 auau adad A do sq.ft.

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.

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

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

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