Appendix C

Settling Tank Calculations

Ravenswood Process Tank QED 070810 P a g e | C1

Appendix C SFPUC Bay Tunnel Water Treatment System – Ravenswood Site

Process Tank Calculations

Settling tank performance is highly dependent on influent water quality, tank construction parameters, and flow conditions. Shown below are the theoretical calculations for estimating the Bay Tunnel – Ravenswood Portal Site settling tank system performance based on ideal Type I (discrete, non-interfering and non-flocculating particles) settling. The following operating conditions, assumptions, constants and conversion factors were used:

Tank Total Working Volume = 4,813 cf (36,000 gallons) Peak Flow Rate, 2,000 gpm = 2,000 gpm x 0.1337 ft3/gal

= 267.4 ft3/min Tank Dimensions = 40 ft x 8.5 ft x 8.5 ft.; two tanks in series.

The two tanks in series will be treated as one long tank for the purpose of determining retention time. The scour velocity calculation will evaluate scour velocity at peak flow within one compartment of one tank, thereby estimating a worst-case scour velocity.

Assume Water Temperature = 55oF (12.8oC) Kinematic Viscosity of water (at 12.8C), v = 1.22x10-6 m2/s

(ref. Brater, Handbook of Hydraulics, 7th ed. 1996) Specific gravity of water, SGw = 1.0 Assume fine sand of uniform density and shape Specific gravity of sand, SGp = 2.65 (density = 2650kg/m3) Diameter of sand particle, D = 0.075 mm (7.5x10-5m) Gravitational constant, g = 9.81 m/s2

The theoretical settling velocity, Vs, of a particle is described by Stokes’ law for Reynolds numbers < 1:

Vs = g(SGp – SGw)D2/18v = [(9.81m/s2)(2.65 – 1.0))(7.5x10-5m)2]/18(1.22x10-6 m2/s) = 4.15x10-3m/s or (4.15x10-3m/s)(3.28ft/m)(60s/min)

Ravenswood Process Tank QED 070810 P a g e | C2

= 0.82 ft/min

The Reynolds number can be determined by the product of the sand diameter and settling velocity divided by the water viscosity:

Re = DVs/v = (7.5x10-5m)(4.15x10-3m/s)/(1.22x10-6 m2/s) = 0.25

Since Re < 1, the simplifications from which Stokes’ law is derived are applicable and the settling velocity calculated as shown above is valid. Detention Time, (Dwell) = total volume/flow rate

Dwell (at 2,000 gpm or 267.4 cfpm) = 4,813cf/267.4cfpm = 18 min. Sinkrate = Rise (working depth, vertical inclination)/Dwell

Rise = 7.0 ft Sinkrate at 2,000 gpm = 0.38 ft/min = 0.12 m/min Particles with a settling velocity greater than the sinkrate would, in theory, be able to reach the bottom of a clean pond (Type I conditions). By rearranging Stokes’ law, an estimate of the smallest sand size which would settle can be calculated using the sinkrate values obtained above: D = [Sinkrate/((g/18v)(SGp – SGw))]1/2 = [(0.12 m/60s)(18)(1.22x10-6 m2/s)/(9.81m/s2)(2.65 – 1.0)]1/2 = 5.2x10-5 m (0.05 mm) This particle size is less than 0.0625 mm and is therefore smaller than the geological definition for sand. By using the minimum size for a sand particle (0.0625 mm), a higher estimate for scoured particle constant (B=0.04), and a higher value for Darcy-Weisbach friction factor (f=0.03), a conservative estimate for scouring velocity can be calculated as follows: Scour Velocity = [8B(SGp – SGw)gD/f]1/2

Ravenswood Process Tank QED 070810 P a g e | C3

= [8(0.04)(1.65)(9.81m/s2)(6.25x10-5m)/0.03]1/2 = (0.104 m/s)(3.28ft/m)(60s/min)= 20.44 ft/min

Based on a peak flow rate of 2,000 gpm (267.4cfpm) and a tank cross-section of 60ft2 (7ft x 8.5ft, 1.5ft freeboard), the horizontal velocity within the tank would be:

Horizontal Velocity = Flowrate/Tank Cross-section

=(267.4ft3/min)/(60 ft2) = 4.5 ft/min

Since the horizontal velocity is less than the scouring velocity, scour of settled particles is not expected to occur within the tank compartments. An assessment of settling performance can be obtained by subtracting the overflow rate (flowrate/tank plan area) from the theoretical (0.075 mm diameter) particle settling velocity to obtain an observed settling velocity. The observed settling velocity would be how quickly the particle is moving downwards taking into account the upward movement of the water as it flows out of the tank. The observed settling velocity multiplied by the dwell would provide an indication as to whether or not the particle has enough time to reach the bottom given the upward flow regime within the tank. Overflow Rate (2,000 gpm) = Flowrate/Plan Area

=(267.4 ft3/min)/(80 ft x 8.5 ft) =0.39 ft/min

Observed settling velocity =

Theoretical particle settling velocity – Overflow Rate =0.82 ft/min – 0.39 ft/min =0.43 ft/min

Time Required for Settling = 6.0 ft/(0.43 ft/min) = 13.9 min

Ravenswood Process Tank QED 070810 P a g e | C4

Time Available for Settling = 4,813 ft3/(267.4 ft3/min) = 18 min

These calculations demonstrate that the proposed tank system would be sufficient to achieve theoretical settling under the assumptions as stated above and that removal of sand particles would occur. For influent flows lower than the peak flow, greater settling time and reduced turbulence could be available but would not likely result in significant clarification of the water since most of the particles would have already settled to the bottom.