Lafayette College
Department of Civil and Environmental Engineering
CE 425: Water Supply and Pollution Control
Fall 2007
Homework #1
Due: Wednesday, 9/17/07 by 4 pm
1. Five million gallons per day (MGD) of a conservative substance, with concentration 10.0
mg/L, is released into a stream having an upstream flow of 10 MGD and substance
concentration of 3.0 mg/L. Assume complete mixing.
a. What is the concentration in ppm just downstream?
b. How many pounds of substance per day pass a given spot downstream?
2. A completely mixed reactor has an influent flow rate of 100 gal/min (380 l/min). The BOD
concentration (nonconservative pollutant) of the wastewater entering the reactor is 150 mg/L.
The detention time of the reactor is 2 hours. The reaction is first order, therefore the rate
dC
  kC and the rate constant is 0.40 hr-1.
equation is
dt
a. What is the volume of the reactor? Report your answer in gallons.
b. Assuming the initial concentration of the reactor is 0 mg/L and a BOD of concentration
150 mg/L added at time 0, what is the concentration of the reactor after 2 hours?
c. What is the concentration of the BOD leaving the reactor after 2 hours?
d. What is the concentration of the BOD within the reactor assuming it reaches steady state?
e. Assume that there was no flow in or out of the reactor and the BOD was initially 150
mg/L. What is the concentration of the BOD after 2 hours?
3. The two-pond system shown in the following figure is fed by a stream with a flow rate of 1.0
MGD and a BOD (nonconservative pollutant) concentration of 20 mg/L. The rate of decay is
0.30/day. The volume of the first pond is 5.0 million gallons and the second is 3.0 million
gallons. Solve for C1 and C2 in mg/L.
4. Given the following configuration and a substance that is conservative
a.
b.
c.
d.
What is the mass rate of the substance in lb/day passing downstream of point A
What is the concentration in mg/l at point A?
What is the concentration in mg/l at point B?
What is the concentration in mg/l at point C?
5. Easton wastewater treatment plant treats wastewater at average flow rate and BOD of 11.50
ft3/sec and 150 mg/L respectively. The reactor decay constant is 0.40 day-1.
a. Under the stated conditions the hydraulic detention time is 16 hours. What is the volume
of the treatment reactor? Report your answer in million gallons (Mgal).
b. Assuming completely mixed conditions, what is the steady state concentration of the
BOD in the upper right quadrant of the reactor? Report your answer in mg/L.
c. On September 18th, 2004, topical storm Ivan blows through the Lehigh Valley causing
flooding in low-lying areas, Easton being one of the hardest hit areas. The Easton
wastewater treatment plant (EWWTP) receives wastewater through a combined sewer
system (i.e., both the stormwater and sewage combine and are treated together at the
treatment plant). The added storm flow increases the average flow rate entering the
EWWTP by 4 cfs. Assuming that the storm flow has a BOD of 20 mg/L and degradation
(breakdown) of the combined storm flow and wastewater BOD does not start until the
flow enters the reactor at the EWWTP, what is the new BOD concentration entering the
reactor? Report your answer in mg/L.
d. Because tropical storm Ivan hits the Valley so fast the increased flow conditions affect
the EWWTP almost immediately. Assuming the volume of the tank (reactor) remains the
same what is the new hydraulic retention time? Report your answer in hours.
e. Assuming flow rates and BOD concentrations entering remain constant what would the
BOD in the tank (reactor) be 6 hours after the storm flows hit the EWWTP? Because of
the dilution of the influent wastewater a new decay rate is calculated to be 0.35 day-1.
f. What is the BOD concentration of the outflow from the reactor entering the Delaware
River 6 hours after the storm flow hits? Assuming a river dilution factor of 20, a river k
of 0.20 d-1 and the ability to travel down river 2 days later to collect a sample from this
slug, what would the concentration of BOD in the down river slug sample be? Report
you answer as mg/L.
g. Assuming the high flows remain constant for an extended period what would the new
steady state BOD concentration in the reactor be? Report you answer as mg/L.
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6. Reynolds and Richards Problem # 3.1
7. Reynolds and Richards Problem # 3.4
8. Reynolds and Richards Problem # 3.7
9. A CMFR is used to treat an industrial waste product, using a reaction that destroys the
pollutant according to first-order kinetics, with k=0.216 d-1. The reactor volume is 500 m3,
the volumetric flow rate of the single inlet and exit is 50 m3 day-1, and the inlet pollutant
concentration is 100 mg L-1.
a. Assuming the CMFR has reached steady state, what is the outlet concentration after
treatment? State your answer in units of mg/L.
b. The manufacturing process that generates the waste in Part A has to be shut down, and,
starting at t=0, the concentration of Cin entering the CMFR is set to 0.
i. How many hours does it take the tank concentration to reach 10% of it initial,
steady-state value?
ii. How many hours does it take to reach steady state?
c. A plug-flow reactor (PFR) is used to model the chemical transformation of the waste
product presented in Part A. Assume that the flow rate and the first-order decay rate
constant are unchanged (Q = 50 m3 day-1, k = 0.216 day-1). Based on this information
answer the following.
i. What is the volume required for the PFR to obtain the same degree of pollutant
reduction as the CMFR of Part A? Report your answer in m3.
ii. What is the % reduction in volume as compared to the volume of the CMFR for the
same steady-state conditions?
10. A large holding pond (i.e., an aerated lagoon) is to be designed to treat wastewater from a
small community (population 1,350). The wastewater flow is 0.15 MGD (million gallons per
day). The influent wastewater contaminant concentration is 250 mg/L. The required effluent
concentration is 20 mg/L. It was found that the chemical degraded according to first order
kinetics. The k for the reaction is 0.52 d-1.
a. What is the required volume of the lagoon? You may assume that the lagoon is
completely mixed and that conditions in the system are at steady-state.
b. Just after the lagoon is put into operation and reaches steady state condition it is decided
that a wastewater stream of 0.05 MGD from a cement plant containing no contaminants
(i.e., no BOD) will be diverted to the influent supply at a point just above the entry to the
lagoon.
i. Assuming k and lagoon volume remain the same, what will be the effluent
concentration of the lagoon 2 days after the cement wastewater stream is diverted to
the lagoon?
ii. Plot the effluent profile (i.e., y = concentration; x = time) of the water leaving the
lagoon.
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c. Because of downstream water quality issues the state regulatory agency, Pennsylvania
Department of Environmental Protection (DEP), imposes new regulations on the effluent
concentration of the aeration lagoon. Your new limit is to be 10 mg/L BOD or less in the
effluent leaving the lagoon. Would it be wiser to make a second lagoon or just
enlarge the first lagoon thereby increasing the detention time? Assume land value is
not an issue. Provide an explanation and calculations support your answer.
11. You are working for the Pennsylvania Department of Environmental Protection (DEP) and
must issue a discharge permit to a certain industry. The industry wishes to discharge “green
muck” into the Lehigh River. The flow of wastewater from the industry is 0.15 m3/s. The
flow of water in the Lehigh River (upstream from the waste water outfall) is 0.25 m3/s.
Upstream of the outfall, the concentration of “green muck” in the river is 0.1 mg/L. What is
the maximum concentration the industry can discharge if the concentration of “green muck”
in the river (after mixing) cannot exceed 2.5 mg/L?
12. A river with 400 ppm of salts (a conservative substance) and an up stream flow of 25 m3/s
receives an agricultural discharge of 5.0 m3/s carrying 2000 mg/L of salts (see figure below,
P1.7). The salts quickly become uniformly distributed in the river. A municipality just
downstream withdraws water and mixes it with enough pure water (no salt) from another
source to deliver water having no more than 500 ppm salts to its customers.
What should the mixture ratio (F) of pure water to the river water be?
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