1. Two filter beds are in a water treatment plant, with media and dimensions as follows. Water discharges into this filter bed over a weir that is set at 110.00 feet above datum. The water then flows downward through each of these filters, with an approach velocity into each of these filter beds of 0.01 ft/sec. Point A is 90.00 feet above datum, and water pressure in the pipe at A is 3.0 psi.
| Parameter, units | Filter B | Filter C |
| Media type | sand | anthracite |
| Media depth, ft | 3 | 5 |
| Filter surface area, ft x ft | 12 x 12 | 15 x 10 |
| Grain diameter, ft | 0.0025 | 0.007 |
| Grain density, lb sec2/ft4 | 5 | 4 |
| Porosity when treating water, unitless | 0.4 | 0.6 |
| Shape factor | 6 | 7 |
| J | 6 | 6 |
For both beds, g = 32.2 ft/sec2, kinematic viscosity = 1.4 x 10-5 ft2/sec,
absolute viscosity = 2.8 x 10-5 lb-sec/ft2, density of water = 1.937 lb sec2/ft4.
All pipes are 8” in diameter. Each pipe has a control valve, set to a k of 10 (including this valve’s short pipe stub). Moreover, from filter C to point A, there is another 100-foot long 8” diameter pipe, as shown, with f = 0.03. (There is no head loss through the underdrain media).
a. What is the water level above the sand filter media in Filter B?
B. What is the water level above the anthracite filter media in Filter C?
c. Are these two water levels the same? Or different? If different, how can this be so?
2. The atomic weight of various atoms are as follows: Ca = 40, Mg = 24.3, Na = 23, K = 39.1, H = 1, O = 16, N = 14, C = 12, Cl = 35.5, S = 32. A water contains the following anionic and cationic species. You may refer to the attached periodic table. The pH is 9.5
Calcium 100 mg/L
Magnesium 120 mg/L as CaCO3
Sodium 92 mg/L
Bicarbonate 200 mg/L as CaCO3
Carbonate 27 mg/L
Sulfate 100 mg/L
a. Compute charge equivalence for all pertinent species, in meq/L
b. With the species listed, is there a charge balance? If there is only one other species, would it be chloride or potassium? How many mg/L would there be of this species?
c. Determine the total hardness as CaCO3
d. Determine the total alkalinity as CaCO3
3. Batch experiments in the laboratory at 20oC show that when the pH is 6.0 and a chlorine dose is 0.8 mg/L as Cl2, the chlorine concentration x time (Ct) required to achieve a 3-log10 removal of giardia is 39 mg/L-minute. For this reaction, = 1.072.
a. All other things being equal, what would be the Ct required when the temperature is 10oC?
b. If you have a plug flow reactor, with pH 6.0, 10oC, and 1.2 mg/L chlorine as Cl2, what would be the Ct required to achieve a 2-log10 inactivation of giardia?
c. If you have a CSTR reactor, with pH 6.0, 10oC, and 1.2 mg/L chlorine as Cl2, what would be the Ct required to achieve a 2-log removal of giardia.
d. Which would you choose to achieve giardia inactivation, plug flow or CSTR flow?
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