Chapter 2 FE EXAM FORMATTED PROBLEMS
2-1.
The decay of chlorine in a distribution system follows a first order decay with a rate
constant of 0.360 d-1. If the concentration of chlorine in a well mixed water storage tank
is 1.00 mg/L at time zero, what will the concentration be one day later. Assume no water
flows out of the tank.
From Eq. 2-13
ln
c
 kt
co
ln
c
 0.360 d 1 (1d )
1.00 mg / L
c  (1.0mg / L)e 0.360d
c  0.698 mg / L
2-2.
1
(1d )
A 350m3 retention pond that holds rain water from a shopping mall is empty at the
beginning of a rain storm. The flow rate out of the retention pond must be restricted to
320L/min to prevent downstream flooding from a 6 hour storm. What is the maximum
flow rate (in L/min) into the pond from a 6 hour storm that will not flood it?
From Eq. 2-3
Mass rate of accumulation = mass rate of input – mass rate of output
350 m 3 (1000 L / m 3 )  ( x)(6hours)(60 min/ hour)  (320 L / min)( 6hours)(60 min/ hour)
3.5 10 3 L  4.65 10 3 L  x(360 min)
x  1290 L / min
2-3
A pipeline carrying 0.50 MGD of a 35,000 mg/L brine solution (NaCl) across a creek
ruptures. The flow rate of the creek is 2.80 MGD. If the salt concentration in the creek is
175 mg/L, what is the concentration of salt in the creek after the pipeline discharge mixes
completely with the creek water?
Using a modified Eq. 2-4
C R b 
C R QR  Cb Qb (175 mg / L)(2.80 MGD)  (35000 mg / L)(0.5MGD)

 5,450 mg / L
QR  Qb
(2.80 MGD)  (0.5MGD)
Or 5.45x103mg/L
2-4
A wastewater treatment plant has experienced a power outage due to a winter storm, A
treatment facility (anaerobic digester) contains 2,120m3 of wastewater at 37°C. If the
wastewater temperature falls below 30°C, the digester will fail. The digester is made of
concrete with a thermal conductivity of 2 W/m∙K. The surface area of the digester is
989.6m2. The concrete walls and ceiling are 30 cm thick. If the outside temperature is
0°C and there is no wind or sunshine, how long will the operator have to get the heating
system back into operation before the digester fails? Assume the specific heat capacity of
the wastewater is the same as that of water and ignore the lack of mixing.
From Eq. 2-52
dH
dT
 37  0 
 htc A
 (2W / m  K )(989 .6m 2 )
  244,101 .33W  244,101 .33 J / s
dt
dx
 0.30 m 
From Eq. 2 - 47 ΔH for 7K drop
H  Mcv T  (2120 m 3 )(1000 kg / m 3 )(4.186  10 3 J / kg  K )(7 K )  6.21  1010 J
t
6.21  1010 J
1hr
1day 
 1min
 254,485 .8s


  2.95days or 3days
244,101 .33 J / s
60
s
60
min
24 hr 
