CEE 370 Spring 2001

# Exam #2

April 19, 2001

Closed Book, two sheets of notes allowed

Please answer any 4 of the following 9 questions.  Each is worth 25 points.  Show all work.  Be neat, and box-in your answer.

## 1. Settling Design (25 points)

### You’ve been asked to design a pair of identical primary clarifiers for treating wastewater in the Town of Springfield.The town engineer wants you to size a circular clarifier that is capable of removing particles with a diameter of 0.1 mm and a density of 1.4 g/mL, even in the mid-winter when wastewater temperatures drop to 5 C.If the town’s wastewater flow averages 17 MGD, and it peaks at 25% over this, what diameter clarifier will you recommend?Keep in mind that the town engineer has asked for some specific performance that might not be assured using just the standard design criteria.

#### Solution:

Use Stoke’s Law:

considering the temperature 5 C, and the density and viscosity data on the front cover of the text book,

For the purpose of clarifier design, we set the overflow rate to the settling velocity of the particles that we wish to just be able to capture:

## 2. Settling Performance (25 points)

### The town of Pleasant Valley has a secondary clarifier that is 30 m long and 15 m wide.If the typical wastewater flow is 3.5 MGD, what is the diameter of the largest bacterial particle (assume a density of 1.02 g/cm3) that will be not be retained and therefore discharged into the Pleasant River at 5°C?

First, calculate the overflow rate

This will then be the critical settling velocity, So taking Stokes law and rearranging:

and then solving for Dp:

## 3. Short Answer (25 points)

### a.Sketch a typical growth curve for a bacterial population in a batch culture, and describe the various phases (5 points)

See figure 5-10 in Mihelcic and related description

### b.Sketch 3 different growth models, list their names and briefly describe how they differ. (5 points)

See book or class overheads.  Models include: linear, exponential, logistic, monod

### c.What are the factors that can limit bacterial growth? Explain. (5 points)

Carrying capacity, which might include such factors as population density, presence of toxins, availability of food (electron donor, and carbon source), temperature, pH, light energy (for phototrophs), disease.

### d.List the 4 “Great Spheres” of living and non-living material, and briefly indicate what each encompasses (5 points)

Atmosphere, Hydrosphere, Lithosphere & Biosphere (see section 5.1 in Mihelcic for descriptions)

### e.What are phytoplankton and zooplankton? (5 points)

These are microscopic plants and animals (respectively) that live in natural surface waters.  They are free floating, and constitute an important food source for higher animals

## 4. Groundwater and contaminant flow (25 points)

### Two groundwater wells are located 75 m apart within the same aquifer.Well #1 has a water level at 1273 ft above mean sea level.The second well’s water level is 1311 ft above mean sea level.The mean hydraulic conductivity in this aquifer is 0.18 m/day, and the porosity is 0.65.How long will it take the water to travel from Well #2 to Well #1?

First determine the Darcy’s velocity between the wells

Then determine the true velocity between the wells

Now determine the time it takes for water to travel between the two wells

## 5.         Microbial Growth (25 points)

### a. What is the specific growth rate assuming simple exponential growth throughout?

From Equation 5-5:

so:

From page 236:

Recall:

so:

## 7. Reactor Kinetics #1 (25 points)

### You’re using a CMFR to treat an industrial waste containing phenol.Aqueous chlorine reacts with phenol according to second order kinetics (first order in phenol and first order in chlorine).The observed second order rate constant for this reaction is 2.23x103 M-1min-1 at the temperature and pH of the wastewater (25 C, and pH 7.0).To accomplish this removal you’ve designed a CMFR reactor with a volume is 50 m3 and you’ve decided to add aqueous chlorine so that the concentration in the reactor is constant at 0.001 moles/L.If the volumetric flow rate at the inlet and outlet is 5000 m3/day and then inlet phenol concentration is 10-4 moles/L, what will the phenol concentration at the outlet be?

This may be viewed as a pseudo-first order reaction:

where: k=k2[Chlorine]=2.23x103M-1min-1(0.001M)=2.23min-1=3,210d-1

and now:

## 8. True/False.Indicate whether the following statements are true (T) or false (F).(25 points total; 2.5 points each)

 1 T PFRs are always more efficient that CMFRs for 1st order processes 2 T The latent heat of condensation is the heat released when a gas condenses to form a liquid 3 F Greenhouse gases reflect light energy 4 F Fick’s first law describes advective flow 5 F Stoke’s law describes molecular diffusion 6 T Darcy’s law describes flow in porous media 7 F The lithosphere is a part of the biotic environment 8 F Rotifers are a form of algae 9 T Protozoa can exist in a cyst form 10 F Most primary producers are bacteria

## 9.Reactor Kinetics #2 (25 points)

Northampton uses the Mountain Street Reservoir in Williamsburg for a portion of its water supply.  The water is travels to Northampton in a 20 inch diameter main that stretches 5,310 ft.  The City typically adds 3x10-5 moles/L (2.13 mg/L) of chlorine to the water as it enters the main.  Assume that this level is not substantially diminished in concentration during the time it travels to Northampton, and assume that the flow approximates a plug flow reactor.  Chlorine reacts with manganese by second-order kinetics (first order in chlorine and first order in manganese).  The rate constant under these conditions (pH 7.0, 20 C) is 9 M-1s-1.  If the flow from Mountain Street Reservoir is 1.5 MGD, and the raw water reduced manganese concentration is 2x10-6 moles/L (0.11 mg/L), what will the reduced manganese concentration be once the water reaches the end of the main?

For a PFR:

First let’s calculate the volume of the pipe:

Next let’s determine the pseudo-first order rate constant, k:

where:

now combining:

This is also equal to 29 ppb.

## Appendix

Selected Chemical Constants

 Element Symbol Atomic # Atomic Wt. Valence Electronegativity Aluminum Al 13 26.98 3 1.47 Boron B 5 10.81 3 2.01 Calcium Ca 20 40.08 2 1.04 Carbon C 6 12.01 2,4 2.50 Cerium Ce 58 140.12 3,4 1.06 Helium He 2 4.00 0 Holmiuum Ho 67 164.93 3 1.10 Hydrogen H 1 1.01 1 2.20 Magnesium Mg 12 24.31 2 1.23 Manganese Mn 25 54.94 2,3,4,6,7 1.60 Osmium Os 76 190.2 2,3,4,8 1.52 Oxygen O 8 16.00 2 3.50 Potassium K 19 39.10 1 0.91 Sodium Na 11 22.99 1 1.01 Sulfur S 16 32.06 2,4,6 2.44

Selected Acidity Constants  (Aqueous Solution, 25°C, I = 0)

 NAME FORMULA pKa Hydrochloric acid HCl = H+ + Cl- -3 Sulfuric acid H2SO4= H+ + HSO4- -3 Nitric acid HNO3 = H+ + NO3- -0 Bisulfate ion HSO4- = H+ + SO4-2 2 Phosphoric acid H3PO4 = H+ + H2PO4- 2.15 Hydrofluoric acid HF = H+  + F- 3.2 Nitrous acid HNO2 = H+  + NO2- 4.5 Acetic acid CH3COOH = H+  + CH3COO- 4.75 Propionic acid C2H5COOH = H+  + C2H5COO- 4.87 Carbonic acid H2CO3 = H+  + HCO3- 6.35 Hydrogen sulfide H2S = H+  + HS- 7.02 Dihydrogen phosphate H2PO4- = H+  + HPO4-2 7.2 Hypochlorous acid HOCl = H+  + OCl- 7.5 Ammonium ion NH4+ = H+  + NH3 9.24 Hydrocyanic acid HCN = H+  + CN- 9.3 Phenol C6H5OH = H+  + C6H5O- 9.9 Bicarbonate ion HCO3- = H+  + CO3-2 10.33 Monohydrogen phosphate HPO4-2  = H+  + PO4-3 12.3 Bisulfide ion HS-  = H+  + S-2 13.9

Conversion factors:

1 gal = 3.7854x10-3 m3

1 ft = 0.3048 m

Other Constants from Mihelcic: