Name_____________________________
ENGRI 113 Prelim 1
February 23, 2006
The total number of points in the exam is 100. Read each problem carefully before beginning to
work on the answer! Don't forget to check the information on the last sheet!
May the time you spent preparing for this exam pay off.
Short Answer (6 point each)
1) What are the two broad tasks of environmental engineers?
Protect the environment from humans
Protect humans from the environment
2) The industrialized world likes to criticize slash and burn subsistence agriculture in the tropics
because it contributes to the destruction of tropical forests. What is an analogous example of
“slash and burn” that is practiced by the industrialized world?
Consumption of non renewable resources (coal, oil)
3) Where is population growth occurring on the planet? Name two characteristics that are shared
by these locations.
Population growth is occurring almost exclusively in less developed countries.
Characteristics shared are poverty, inadequate access to contraception, high birth rates, and
many other characteristics that go along with poverty.
4) The global rural population is stabilizing around 3 billion. Is the rural population contributing
to global population growth? Explain why or why not.
The rural population IS contributing to the global population growth because the birth rate
in poor rural areas is high. The rural population is holding steady because of migration to
urban areas.
5) Why is swimming in the ocean near a Latin American coastal city a potential pubic health
risk?
Most Latin American cities do not treat their wastewater. In coastal cities the wastewater is
discharged directly into the ocean.
6) In 1799 the NYC Common Council submitted to the New York state legislature a bill to grant
the city of New York with “pure and wholesome water” and a special clause that allowed the
formation of a new company. The Manhattan Company was incorporated with the purported
goal of providing this wholesome water. What was Aaron Burr’s real motive for creating the
Manhattan Company?
He wanted to form a bank. This is the origin of the Manhattan bank.
1
7) Explain how a rapid sand filter can be thought of as a
series of very tiny sedimentation tanks. Explain and draw
picture to illustrate this concept that clearly shows the
path of a particle.
The particle is diverted from the streamline when the
streamline has a horizontal component. The particle has
an extra vertical velocity due to gravity.
a
8) Explain how a peristaltic pump works, explain why the flow rate is related to the diameter of
the peristaltic pump tubing, and chose the correct exponent for this equation ( Q  d n ) where
Q is the flow rate and d is the tube diameter.
A peristaltic pump squeezes a tube and moves the point of the squeeze forward to force fluid
forward in the tube. The correct exponent is 2 since the flow is proportional to the cross
sectional area of the tubing.
9) As part of the filtration avoidance criteria imposed by the Environmental Protection Agency
on NYC, NYC has implemented a Waterfowl Management Program. What is the objective
of this program?
The objective is to reduce fecal coliform contamination in NYC reservoirs from waterfowl
excrement.
10) List 3 transport mechanisms that could cause a particle to collide with a sand grain in a rapid
sand filter.
Brownian motion, gravity, interception or straining, and electrostatic.
2
Problem solving
1) (20 points) A conventional sedimentation tank is 3 m deep and has a residence time of 4
hours. You know that the important design parameter for a sedimentation tank and you are
going to create a small sedimentation tank for your water treatment plant with a design flow
of 100 mL/min. You know that greater depth means the particles have to travel even further
to be removed and so you are going to use a shallow tank that is only 10 cm deep.
What is the critical velocity for the conventional sedimentation tank?
If your tank has the same critical velocity as a conventional tank and if your tank is circular,
what is the diameter?
(The conversions aren’t meant to be difficult, so here they are: 1 mL = 1 cm3, 100 cm = 1 m)
First calculate the critical velocity for the conventional design
H 3m
Vc 

 0.75 m / hr
 4 hr
Now we need to find an equation that relates the surface area of the sedimentation tank to the
critical velocity and the flow rate.
Q
Q
4Q
Vc 
therefore As 
and d 
As
Vc
 Vc

cm3 
4 100

min 

=10 cm
d
cm 

  75

 60 min 
3
2) (20 points) In experiments conducted in the Environmental Engineering laboratory last
weekend we observed that the size of floc formed in a tube flocculator decreases when the
flow rate reaches 500 mL/min (meaning that the floc couldn’t grow larger because the shear
was too high). The tube inner diameter was 9.5 mm. What was the maximum velocity
gradient in the tube at this flow rate?
32Q
Gmax 
 d3

cm3 
32  500

60 s 

Gmax 
=99/s
3
  0.95cm 
Equations
4Q 
 D
4 gd   p   w 
3 CD
w
100
10
1
Reynolds Number
10
00
00
0
10
00
00
00
10
00
00
10
00
0
10
00
4
10
0
0.1
10
24
CD 
Re
1000
1


0.
1
Vt 
Vd 
Drag Coefficient
Re 
Vt 
d 2 g   p  w 
18
gd   p   w 
0.3
w
Vt 
Vc 
H

 
G
HQ
Q
Q



LW As
du
dy
tcollision 
Gmax 

 particles
G  C particles
32Q
 d3
64Q
3 d 3
5