Examples
Review for first exam
Learning Objectives for
st
1
Exam
Be able to define accident and loss
statistics (OSHA Incident rate, FAR,
Fatality rate) and be able to calculate
FAR and Fatality rates
 List the various responses of humans to
toxic exposure and whether they are
reversible.

Learning Objectives for
st
1
Exam
Be able to explain the difference
between ED, TD and LD.
 Be able to determine the predicted
response to various exposures using
probit analysis.
 Be able to calculate Threshold Limit
Values (TLV) and time weighted TLV’s.

Learning Objectives for
st
1
Exam
Be able to estimate the vaporization
rate of a liquid and the expected
ambient concentration.
 Be able to calculate the flow rate of
liquids through a) a hole with constant
back pressure; b) a hole in a tank; and
c) through a broken pipe.

Learning Objectives for
st
1
Exam
Be able to calculate the flow rate of
vapors/gases through a hole, adiabatic
flow through a pipe and isothermal flow
through a pipe.
 Be able to calculate the rate of release
for a flashing and boiling liquid

In Class Homework Team Problem

A gasoline filling station has an underground gasoline
storage tank with a volume of 5000 gallons. The tank
has a 1.0 inch diameter vent. The tank must be filled
every week with 4000 gallons of gasoline through an
8 inch diameter opening from a tank truck. The tank
is never emptied completely. It takes one hour to fill
the tank from the truck.

Vapor Pressure @77°F=4.6 psia, Approximate
molecular weight=94

What is the gasoline concentration in ppm assuming
an effective ventilation rate for outside exposures of
3000 ft3/min during the filling operation?
In Class Homework Team Problem
Solution to Part A

Cppm during filling (modified 3.24)
C ppm 
 PsatT
kQv ,out PTL
Q
L
 KA  10
6
3
3


4000
gal
hr
ft



ft
QL  

8.913



min
 hr  60 min   7.48gal 
In Class Homework Team Problem
Solution to Part A

Eq. 3.18
1/ 3
 M0 
K  K0 

M 


 18 
cm
K  0.83
s  94 
1
3
 in.   ft   60sec 
cm
K  0.478
s  2.54cm   12in.   min 
K  0.942 ft
min
In Class Homework Team Problem
Solution to Part A
Avent 
  ft 
2
   0.00545 ft
4  12 
Afill 
  8 ft 
2
2

  0.349 ft
4  12 
2
Assume ½ of fill pipe “open” for
evaporation Afill~0.175ft2
In Class Homework Team Problem
Solution to Part A

Assume worst case conditions
– Φ=1 Splash Filling
– k=0.1 Poor Mixing
– Vapors escape through ½ of 8” hole during
filling
– Qv =3000 ft3/min
– P=atmospheric=14.7 psia
– Psat=4.6 psia
In Class Homework Team Problem
Solution to Part A
C ppm 


(4.6 psia ) 1.0
8.913 ft 3
ft
2
2 

0.942
0.175
ft

0.00545
ft
 106


3


min
min

 0.1  3000 ft min  14.7 psia  


Cppm=9474 ppm
 If no evaporation through fill pipe 9302
ppm
 If neglect evaporation entirely 9297ppm

In Class Homework Team Problem

A gasoline filling station has an underground gasoline
storage tank with a volume of 5000 gallons. The tank
has a 1.0 inch diameter vent. The tank must be filled
every week with 4000 gallons of gasoline through an
8 inch diameter opening from a tank truck. The tank
is never emptied completely. It takes one hour to fill
the tank from the truck.

Vapor Pressure @77°F=4.6 psia, Approximate
molecular weight=94

What is the gasoline concentration in ppm assuming
that the tank is vented with an effective ventilation
rate of 3000 ft3/min when the tank is not being filled?
In Class Homework Team Problem
Solution for Part B

Modified Eq 3.14
Cmax
 Tin   Pout 
MKAP sat
 T   P  CinQv ,out  RT
out   in 
L


kQv ,out
Assume no gasoline in venting air and
ideal gas
In Class Homework Team Problem
Solution for Part B

Eq. simplifies for evaporation through 1” vent
C ppm
P sat

KA  106
kQv P
C ppm 

 4.6 psia 1.0
3

ft
 0.1  3000 min  (14.7 psia )


Cppm = 5.4 ppm

0.942 ft
0.00545 ft   10
min  
2
6
In Class Homework Team Problem

A gasoline filling station has an underground gasoline
storage tank with a volume of 5000 gallons. The tank
has a 1.0 inch diameter vent. The tank must be filled
every week with 4000 gallons of gasoline through an
8 inch diameter opening from a tank truck. The tank
is never emptied completely. It takes one hour to fill
the tank from the truck.

TLV for gasoline is 300 ppm

What is the time weighted average exposure for a
worker on a 10 hour shift during which the tank is
filled?
What is the time weighted average exposure for a
worker on a 10 hour shift during which the tank is not
filled?

In Class Homework Team Problem
Solution for Part C & D
TLVTWA
1hr  9474 ppm   (9hr )  5.4 ppm 


8hr
TLVTWA  1190 ppm  300 ppm
TLVTWA
10hr  5.4 ppm 


8hr
TLVTWA  6.8 ppm  300 ppm
In Class Homework Team Problem
Determine the average time-weighted
concentration, CTWA, of hydrogen sulfide
in ppm that would be estimated to
cause 10% fatalities if exposed for 15
minutes.
 How many times greater is this
compared to the TLVTWA, i.e., what is
the Safety Factor?

In Class Homework Team Problem
Solution for Problem 2

TLVTWA = 10 ppm (Table 2.8)
 From Handout in class
Y  a  b ln V
V  C nt

C in ppm, t in min
 For H2S
– a=-11.5
– b=1.0
– n=1.9
In Class Homework Team Problem
Solution for Problem 2
From Table 2.4
10% corresponds to Y=3.72
Some algebra

Y a
 ln(V )
b
V e
Y a 


 b 
In Class Homework Team Problem
Solution for Problem 2

More Algebra
V  C nt
V
 Cn
t
V 
ln    n ln C
t
V 
ln  
t

ln C 
n
In Class Homework Team Problem
Solution for Problem 2
 

More algebra
Ce
 ln V 

t 


n


  Y a   
 b 
 e

ln
  t 
 
 

C  exp 

n








In Class Homework Team Problem
Solution for Problem 2
C ppm
C ppm
 
 3.72  11.15   
 /15 
 ln exp 
1.0
 

 
 exp 

1.9




 602 ppm
In Class Homework Team Problem
Solution for Problem 2
CTWA 
 602 ppm 15min   hr 60 min 
8hr
CTWA  18.8 ppm
CTWA
18.8

 1.9
TLVTWA
10
The concentration that would kill 10% of the people is
nearly twice the threshold limit value