December 2, 2020

Problems and Solutions for Chapter 2

Problem 2-1

Using the data provided in Example 2-1, determine the a) mean, and

variance, b) frequency as a function of the response, c) number affected as a

function of the of the response, and d) show graphs for the frequency and

number affected.

Solution 2-1

Note to instructor: A few of these problems are easy, but they give

you an opportunity to have the students use the correct tools for making

calculations. In this case we are using MathCad, but you can use

whatever tool that you prefer.

a) Determine the mean and variance. N is the nuimber with the

specific response

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b) determine the frequency as a function of the response

c) determine the number affected as a function of the of the response

d) show graphs for the frequency and number affected as a function of response.

x

End of Problem 2-1.

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Problem 2-2

Using the data provided in Example 2-1, and a) determine the accumulated

frequency between minus infinity and infinity (using Equation 2-1), b) between the

mean and infinity (using Equation 2-10, c) between the mean plus the two

standard deviations and infinity (Equation 2-1), and d) state your conclusions.

Solution 2-2

a) Determine the accumulated frequency between minus inﬁnity and inﬁnity

d) State your conclusions. Answer - the results are perfect, indicating the

End of Problem 2-2.

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Problem 2-3

Using Equation 2-6 determine the probability for probits of 4.39, 5.25, and 6.23.

Solution 2-3

____________

Looking at the details as shown below:

_________

If your computing program does not have an error function, then go

down the following path:

Results

Probit P P1 P2 Table 2-4 Prob.

End of Problem 2-3

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Problem 2-4. A blast produces a peak overpressure of 47,000 N/m2. What

fraction of structures will be damaged by exposure to this overpressure? What

fraction of people exposed will die as a result of lung hemorrhage? What fraction

will have eardrums ruptured? What conclusions about the effects of this blast can

be drawn? Repeat this problem with 30,000, 80,000, and 100,000 N/m2.

Solution.

End of Problem 2-4

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Problem 2-5. A volatile substance evaporates from an open container into a room

of volume 28.3 m3. The evaporation rate is 100 mg/min. If the air in the room is

assumed to be well mixed, how many m3/min of fresh air must be supplied to ensure

that the concentration of the volatile is maintained below its TLV is 100 ppm? The

temperature is 25 deg. C, and the pressure is 1 atm. The volatile molecular weight of

100. Under most circumstances the air in a room cannot be assumed to be well

mixed. How would poor mixing affect the quantity of air required?

Solution for 2-5.

End of Problem 2-5.

Problem 2-6.

If 500 workers in a plant are exposed to the following concentrations of ammonia

for the given number of hours, how many deaths will be expected?

a to d) 1000 ppm for 1 hr., 2000 ppm for 2 hr., 300 ppm for 3 hr., and 150 ppm

for 2 hr.

Repeat this problem with the concentrations given in a., but assume the

times are 2, 4, 6, and 2 hours.

Solution 2-6.

Use the data given in Table 2-5:

End of Problem 2-6.

Problem 2-7. Use OSHA data for TLVs and convert TLV in ppm to mg/ m3 for benzene,

chlorine, cyclohexanol, and ethylene oxide. Assume a temp of 25 deg. C and pressure of 1 atm.

Solution 2-7.

C 1.801mg/cu m End of Problem 2-7.

Problem 2-8. Estimate four exposure concentrations in ppm that will result in

fatalities for 80% of the exposed individuals if they are exposed to chlorine for 2, 4,

6, 8 min.

Solution 2-8.

End of Problem 2-8.

Problem 2-9. Determine the deaths resulting from the following exposures

to chlorine: a) 200 ppm for 150 min, b) 100 ppm for 50 min, and c) 50 ppm for

20 min.

Solution 2-9.

End of Problem 2-9.

Problem 2-10. The peak overpressure expected as a result of the

explosion of a tank in a plant facility is approximated by the equation

log 7.1094 1.8log ,Pr

Where P is the overpressure in N/m

2

and r is the distance from

the blast in meters. The plant employs 500 people who work in

an area from 3 to 150 m from the potential blast site. Estimate

the number of fatalities due to lung hemorrhage as a result of

this blast. Assume there are 5 shells around the center and the

people are evenly distributed through the area.

Solution.

Note: The negative Probits correspond to a Probability of ZERO.

Note to Professor: You should ask the students to repeat the calculation

with more shells; at some point the answer should stabalize.

End of Problem 2-10

Problem 2-11. Use this book's appendix to determine the hazardous

properties of ammonia; i.e. TLV-TWA, TLV-STEL, TLV-C, PEL, and the

NFPA daimond ratings.

Solution.

End of Problem 2-11

Problem 2-12. At what overpressure (Pa and psi) would 50% of

structures be damaged?

Solution.

End of Problem 2-12

Problem 2-13. For methane in air at 1 atm and 298 K, how many ppm

is 100 mg/m3?

Solution.

End of Problem 2-13

Problem 2-14. Humans breathe about 500 ml of air per breath and take

about 12 breaths per minute during normal activities. If a person is

exposed to an atmosphere containing benzene at a concentration of 10

ppm (by volume), how many grams of benzene will be deposited in the

lungs during an 8-hour shift if all the benzene that enters remains in the

lungs? How many drops of liquid is this? A drop of liquid contains about

0.05 cm3. The specific gravity of benzene is 0.879. If you were the

worker, would this be acceptable?

Solution.

End of Problem 2-14