Sample Problems

 

1. What is q, the volume flow rate of vapor formed, if 0.5 gallons of toluene are evaporated uniformly over a 7-hr shift? What volume flow rate Qd is required for dilution to 10ppm, if Kmixing = 2? (Assume STP; d=1.0)

What is the average face velocity of air in a room 10 * 8 * 40 for these conditions?

 

Solution:

 

SG=0.866, MW=92.1

Q = 387 * lbs evaporated/MW * minutes * d

Note: lbs evaporated = gal * 8.31 * SG

Q = 387 * 0.5gal * 8.31lbs/gal * 0.866/9.21 * 480 minutes * 1.0 = 0.0315 scfm

Qd = q * 106 * Kmixing/Ca (ppm)

Qd = 0.0315 * 106 * 2/10 = 6,300 scfm

Vface = Qd/A = 6300/80 = about 80 fpm

 

2.     What is q, the volume flow rate of vapor formed, if 500 grams of xylene are evaporated uniformly over a 4-hr shift? What volume flow rate Qd is required for dilution to 25 ppm, if Kmixing = 1.5? (Assume STP; d=1.0)

 

Solution:

 

q = 0.0241 * grams evaporated/MW * seconds * d

q = 0.0241 * 500/106.2 * 4 * 60 * 60 * 1.0 = 7.88 * 10-6 acms at STP (i.e. scms)

Qd = q * 106 * Kmixing/Ca (ppm)

Qd = 7.88 * 10-6 * 106 * 1.5/25 = 0.47 acms at STP

 

3.     Calculate N (number of air changes per hour)

 

Solution:

 

(i) Q = 6,300 scfm, Volume, V = 10 * 8 * 40 = 3,200 cubic feet [3,200 * 0.0283 = 90.5 cubic meters)

N = Q * 60/Vol = 6,300 * 60/3200 = 120 ac/hr

(i) Q = 0.47 acms, Volume, V = 10 * 8 * 40 = 3,200 cubic feet [3,200 * 0.0283 = 90.5 cubic meters)

N =Q * 3600/Vol = 0.47 * 3600/90.5 = 19 ac/hr

 

4. What is the estimated time required for the buildup in an acetone concentration to 750 ppm, given the following conditions?

STP Kmix = 2

Co=0, start of shift Ct=750 ppm (after time t has elapsed)

US Units SI units

Volume 100,000 cubic feet 2832 cubic meters

q 2.25 scfm 0.00106 scms

Qd 2,000 scfm 0.9440 scms

 

Solution:

 

In US units

t = -2 * (10000/2000) * Ln [((2.25 * 106/2000) - 750)/((2.25 * 106/2000) - 0)]

= -2 * 50 * Ln (375/1125) = 110 minutes

In SI units

t = -2 * (2832/0.944) * Ln[((0.00106 * 106/0.944) - 750)/( (0.00106 * 106/0.944) - 0)]

=-2 * 3000 * Ln (373/1123) = 6600 seconds = 110 minutes.

 

5. An automobile garage was contaminated with carbon monoxide. If dilution air is provided for 30 minutes, what will the CO concentration be? Assume STP, q=0; Co=500 ppm; Kmix=2.0

US Units SI Units

Volume 10,000 cubic feet 283.2 cubic meters

Qd 200 scfm 0.0944 scms

t 30 min 1800 seconds

 

Solution:

 

US units:

Ct=500 * EXP [-200/(2 * 10000) * 30 minutes]

Ct=500 * EXP [-0.30] = 500 * 0.74 = 370 ppm

In SI units:

Ct=500 * EXP [-0.0944/(2 * 283.2) * 1800 seconds] = 370 ppm

 

6. Methyl chloroform is lost by evaporation from a tank at a rate of 1.5 pints per 60 minutes. What is the effective ventilation rate

Q and the actual ventilation rate (Q) required to maintain the vapor concentration at the TLV?

 

Solution:

 

TLV = 350 ppm, SG = 1.32, MW = 133.4, Assume K = 5

Assuming perfect dilution, the effective ventilation rate (Q) is given by

Q = 403 * 106 * 1.32 * (1.5/60)/(133.4 * 350) = 285 cfm

Due to incomplete mixing the actual ventilation rate (Q) is

Q = 403 * 106 * 1.32 * (1.5/60) * 5/(133.4 * 350) = 1425 cfm

 

7.     A cleaning and gluing operation is being performed; methyl ethyl ketone (MEK) and toluene are both being released. Both have narcotic properties and the effects are considered additive. Air samples disclose concentrations of 150 ppm MEK and 50 ppm toluene. The volumetric flow rate at standard conditions required for dilution of the mixture to the TLV would be as follows.

 

Solution:

 

Assume 2 pints of each is being released each 60 min. Select a K value for MEK and a K value of 5 for toluene; Sp gr for MEK=0.805, for toluene = 0.866; MW for MEK = 72.1, for toluene = 92.13

Q for MEK =403 * 0.805 * 106 * 4 * (2/60)/(72.1 * 200) = 3000 cfm

Q for toluene = 403 * 0.866 * 106 * 5 * (2/60)/(92.13 * 100) = 6313 cfm

Q for mixture = 3000 + 6313 = 9313 cfm

 

8.     A batch of enamel-dipped shelves is baked in a recirculating oven at 350 F for 60 minutes. Volatiles in the enamel applied to the shelves consist of two pints of xylene. What oven ventilation rate, in cfm, is required to dilute the xylene vapor concentration within the oven to a safe limit at all times?

 

Solution:

 

For xylene, the LEL = 1.0%; sp g = 0.88; MW = 106; Sf = 10; B = 0.7

Q = 403 * 0.88* (2/60) * 100 * 10/(106 * 1.0 * 0.7) = 159 cfm

Since the above equation is at standard conditions, the airflow rate must be converted from 70 F to 350 F.

QA = (cfmSTP) (Ratio of Absolute Temperature)

=( cfmSTP) (460 F + 350 F)/(460 F + 70 F)

QA = 159(810/530) = 243 cfm

 

9.     Air contains 400 ppm of acetone (TLV = 750 ppm), 150 ppm of ethyl acetate (TLV = 200 ppm) and 100 ppm of methyl ethyl ketone (TLV = 200 ppm). What is the TLV of the mixture?

 

Solution:

 

C1/ T1 + C2/ T2 + C3/ T3 + ------------------+ Cn/ Tn = 1

Hence 400/750 + 150/200 + 100/200 = 0.53 + 0.75 + 0.5 >1

Hence threshold limit is exceeded.