4.9 How much water must be continually added to the wet scrubber shown in Figure 4.26 in
order to keep the unit running? Each of the streams is identified by a number located in a
diamond symbol. Stream 1 is the recirculation liquid flow stream back to the scrubber and it is
20 gallons per minute (gpm). The liquid being withdrawn for treatment and disposal (stream 4) is
2 gpm. Assume that inlet gas stream (number 2) is completely dry and that the outlet stream
(number 6) has 10 lbm/min of moisture evaporated in the scrubber. The water being added to the
scrubber is stream number 5. 1 gallon of water weighs 8.34 lbs. (problem from EPA Air
Pollution Training Institute, http://www.epa.gov/apti/bces/)
Solution:
4.10 In the winter, a stream flows at 10 m3/s and receives discharge from a pipe that contains
road runoff. The pipe has a flow of 5 m3/s. The stream’s chloride concentration just upstream of
the pipe’s discharge is 12 mg/L, and the runoff pipe’s discharge has a chloride concentration of
40 mg/L. Chloride is a conservative substance. (a) Does wintertime salt usage on the road elevate
the downstream chloride concentration above 20 mg/L? (b) What is the maximum daily mass of
chloride (metric tons/day) that can be discharged through the road runoff pipe without exceeding
the water quality standard?
Solution:
4.11 A wet scrubbing system has three separate inlet streams (Figure 4.27). The mass flow rates
in these inlet streams are 100 lbm/min, 58 lbm/min, and 74 lbm/min. The water spray into the
scrubber is 60 lbm/min and some of this spray evaporates and leaves with the gas stream. The
water stream leaving the scrubber is 49 lbm/min. What is the mass of the gas stream leaving the
scrubber? (problem from EPA Air Pollution Training Institute, http://www.epa.gov/apti/bces/)
Solution:
4.12 Calculate the hydraulic residence times (the retention time) for Lake Superior and for Lake
Erie using data in Table 4.3.
Solution:
4.13 The total flow at a wastewater–treatment plant is 600 m3/day. Two biological aeration basins
are used to remove BOD from the wastewater and are operated in parallel. They each have a
volume of 25,000 L. In hours, what is the aeration period of each tank?
Solution:
4.14 You are designing a reactor that uses chlorine in a PFR or CMFR to destroy pathogens in
water. A minimum contact time of 30 min is required to reduce the pathogen concentration from
100 pathogens/L to below 1 pathogen/L through a first-order decay process. You plan on treating
water at a rate of 1,000 gal/min. (a) What is the first-order decay rate constant? (b) What is the
minimum size (in gallons) of the reactor required for a plug flow reactor? (c) What size (in
gallons) of CMFR would be required to reach the same outlet concentration? (d) Which type of
reactor would you select if your treatment objective stated that “no discharge can ever be greater
than 1 pathogen/L”? Explain your reasoning. (e) If the desired chlorine residual in the treated
water after it leaves the reactor is 0.20 mg/L and the chlorine demand used during treatment is
0.15 mg/L, what must be the daily mass of chlorine added to the reactor (in grams)?
Solution:
4.15 The concentration of BOD in a river just downstream of a wastewater treatment plant’s
effluent pipe is 75 mg/L. If the BOD is destroyed through a first-order reaction with a rate
constant equal to 0.05/day, what is the BOD concentration 50 km downstream? The velocity of
the river is 15 km/day.
Solution:
distance 50 3.3
velocity 15
kt
to
CCe
V km
t days
km
Q
d
−
= ×
= = = =
4.16 A
6
1.0 10×
gallon reactor is used in a water reclamation plant. The influent concentration is
100 mg/L, the effluent concentration is 25 mg/L, and the flow rate through the reactor is 500
gal/min. (a) What is the first–order rate constant for decay of BOD in the reactor? Assume the
reactor can be modeled as a CMFR. Report your answer in units per hour. (b) Assume the reactor
should be modeled as a PFR with first-order decay, not as a CMFR. In that case, what must be
the first-order decay rate constant within the PFR reactor? (c) It has been determined that the
outlet concentration is too high, so the residence time in the reactor must be doubled. Assuming
all other variables remain constant, what must be the volume of the new CMFR?
Solution:
4.17 You are to design a reactor for removal of reduced iron (Fe2+) from water. The influent
water has an iron concentration of 10 mg/L and this must be reduced to 0.1 mg/L. The water has
a pH of 6.5 and the plan is to oxidize the iron to Fe3+ using pure oxygen gas, then remove the
resulting particulate matter in a sedimentation basin. It has been found that the reduction in Fe2+
concentration over time equals Kapparent × [Fe 2+] where Kapparent equals: 8 ×1013×[partial pressure
of 02] × Kw2/[H+]2. The units of Kapparent determined from this expression are min-1 and the
partial pressure of oxygen is 0.21 atm and the dissociation constant for water, Kw, equals 10–14.
Determine the volume (m3) of a plug flow reactor to treat 1 MGD of water.
Solution:
4.18 How many watts of power would it take to heat 1 L of water (weighing 1.0 kg) by 10°C in
1.0 h? Assume that no heat losses occur, so all of the energy expended goes into heating the
water.
Solution:
4.19 Your house has a 40 gal. electric water heater that heats water to a temperature of 110°F.
Several friends are visiting you over the weekend and they are taking consecutive showers.
Assume that at the maximum heating level, the heater uses 5 kW of electricity. The water use
rate is a continuous 2 gpm with the new water saving showerhead you recently installed. Your
very old showerhead had used 5 gpm! You replaced the showerhead because you learned that
heating water was the second highest energy use in your home. What is the temperature of the
water exiting the heater (a) using the old showerhead and (b) the new efficient showerhead?
Assume the system is at steady state so all of the energy used heats the water.
Solution:
4.20 (a) Determine the heat loss (in
Btu / F-day°
and Btu/degree-day) through a 120 sq. ft.
insulated wall described in the following table. (b) Determine the heat loss through the same wall
when a 3 ft. by 7 ft. door
( )
R factor 4.4=
is inserted into the wall.
Component of Wall
R Factor
2 in. Styrofoam board insulation on outside of
wall under siding
10
Old cedar log wall
20
Fiberglass insulation on inside of wall
11
½
in. drywall on inside of wall
0.45
Inside air film along inside of wall
0.68
Outside air film along outside of wall
0.17
Solution:
