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Module 1: Basic Concepts - Review Exercises

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Instructions:
Work these problems on a sheet of paper and check your answers against those provided below.

Important:
This Page has several links back to lesson material covered in Module 1. To return to this page, please use your browser's "Back" button.

Helpful Calculators:
The following calculators may be useful in solving these problems. You can access them either from the "Calculators" link in the Features box or from the links below.

Mole Calculator I
Mole Calculator II
Pressure Converter
Temperature Converter

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Q icon #1
What is the mass of water in a pipe having an inside diameter of 3 in. and a length of 20 ft? Use a water density of 62.4 lbm/ft3.

  1. 244.92 lbm
  2. 61.15 lbm
  3. 8817.12 lbm
  4. 2939.04 lbm
A icon
Answer: b. 61.15 lbm

Solution:
  1. Calculate the volume of water.

    equation 1(1)

  2. Calculate the mass of water.


    To review material, see lessons on Systems of Units and Plane Geometry.

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Q icon #2
There are three, small ventilation ducts that combine into a single large air handling duct. Data concerning each of the smaller ducts is provided in Figure 1. Using this data and the following equation, calculate the total air flow (in ft3/sec) entering the large air handling duct.

practice equation 2(a)

Figure 1 rev

To refresh your memory on geometric calculations, see Table 1, Geometric Formulas Useful in Air Pollution.

  1. 9.38 actual ft3/sec
  2. 1846.32 actual ft3/sec
  3. 21.82 actual ft3/sec
  4. 38.46 actual ft3/sec
A icon
Answer: c. 12.82 actual ft3/sec

Solution:

practice equation 2(b)

To review material, see lessons on Exponents and Plane Geometry.

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Q icon #3
The Antoine Equation is often used to express the vapor pressure as a function of temperature. A common form of this equation has a set of three constants and a temperature term as shown below:

practice equation 3(a)

Given that the vapor pressure of ethyl acetate in air over the range of -20°C to more than 150°C can be estimated by using the following constants (A = 7.098, B = 1238.71, C = 217) in the Antoine Equation, calculate the vapor pressure (in mm Hg) of ethyl acetate at the following temperatures.

  1. What is the vapor pressure (in mm Hg) at -20°C?
    1. 0.81
    2. 20.3
    3. 74.37
    4. 6.46

  1. What is the vapor pressure (in mm Hg) at 0°C?
    1. 64.5
    2. 1.39
    3. 24.5
    4. 49.1

  1. What is the vapor pressure (in mm Hg) at 50°C?
    1. 287.5
    2. 631.3
    3. 156.2
    4. 2.46

  1. What is the vapor pressure (in mm Hg) at 100°C?
    1. 837.6
    2. 1,550.2
    3. 3.19
    4. 1,863.5
A icon
For ethyl acetate over the range of -20°C to 150°C, the following equation can be used to estimate the vapor pressure:

practice equation 3(b)

Answer: i. d. 6.46

Solution:
Calculate the vapor pressure of ethyl acetate at -20°C.

practice equation 3(1)

Answer: ii. c. 24.5

Solution:
Calculate the vapor pressure of ethyl acetate at 0°C.

practice equation 3(2)

Answer: iii. a. 287.5

Solution:
Calculate the vapor pressure of ethyl acetate at 50°C.

practice equation 3(3)

Answer: iv. b. 1,550.2

Solution:
Calculate the vapor pressure of ethyl acetate at 100°C.

practice equation 3(4)

This data is graphed in Figure 1 of the Logarithms lesson.

To review material, see lesson on Logarithms.

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Q icon #4
The Deutsch-Anderson equation is sometimes used as an approximate estimate of the particulate removal efficiency of an electrostatic precipitator. What is the particulate removal efficiency (%) of an electrostatic precipitator based on the equation and data shown below?

practice equation 4(a)

  1. 2.19%
  2. 92.72%
  3. 95.83%
  4. 99.78%
A icon
Answer: d. 99.78%

Solution:

practice equation 4(b)

To review material, see lessons on Exponents and Logarithms.

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Q icon #5
A carbon bed adsorber has a total gas flow rate of 12,000 actual ft3/min. There are three adsorber beds operating in parallel and the gas stream is split equally among the three. What is the average velocity through the bed if the depth of each bed is 2 ft, the density of the carbon is 40 lbm/ft3, and there are 6,000 lbm of carbon per bed? Use the following equation:

Gas velocity = Gas flow rate/Area

Figure 2 rev

  1. 160.41 ft/min
  2. 53.33 ft/min
  3. 26.67 ft/min
  4. 13.33 ft/min
A icon
Answer: b. 53.33 ft/min

Solution:
  1. Calculate the volume of an adsorber bed.

    Equation 5(1)

  2. Calculate the cross-sectional area of an adsorber bed.

    Equation 5(2)

  3. Calculate the gas flow per adsorber bed.

    Equation 5(3)

  4. Calculate the average gas velocity through the adsorber bed.

    Equation 5(4)

    To review material, see lessons on Exponents and Plane Geometry.

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Q icon #6
Calculate the amount of water vapor in a gas stream leaving an evaporative cooler (in lbm/min). The inlet gas stream carries 9.34 lb mole/min of water vapor. The water spray rate is 50 gpm and 80% of the spray evaporates. The remainder of the spray water is removed from the drain of the evaporative cooler.

Hint: See Conversion Factors (under Quick Reference) for density of water.


  1. 501.74 lbm/min
  2. 342.94 lbm/min
  3. 585.14 lbm/min
  4. 251.54 lbm/min
A icon
Answer: a. 501.74 lbm/min

Solution:
  1. Construct a water balance around the evaporative cooler. Pertinent equations are given below.


  2. Calculate the amount of water vapor in the inlet gas stream (in lbm/min).


  3. Calculate the amount of water evaporated (in lbm/min).


  4. Calculate the amount of water vapor in the outlet gas stream (in lbm/min).


    To review material, see lesson on Material Balance.

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Q icon #7
The gas temperature entering a fabric filter is 310°F. The gas temperature leaving the fabric filter is 120°C. What is the temperature drop across the fabric filter expressed in degrees Rankine?

  1. 22.6°R
  2. 62.6°R
  3. 121.3°R
  4. 159.8°R
A icon
Answer: b. 62.6°R

Solution:
  1. Convert the inlet and outlet temperatures to degrees Rankine.


  2. Calculate the temperature drop in degrees Rankine.


    To review material, see lesson on Temperature.

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Q icon #8
A baghouse door (6 ft by 3 ft) is subject to a pressure of 1 in. water column (W.C.). If this door opens accidentally, how hard (with what force) would it hit you? Calculate your answer in pounds force. You may want to refer to "Conversion Factors" or Table 1 (Units of Pressure). Use the following equation:

Force = Pressure Area

  1. 0.6 lbf
  2. 7.8 lbf
  3. 69.1 lbf
  4. 93.6 lbf
A icon
Answer: d. 93.6 lbf

Solution:
Force = Pressure Area

  1. Calculate the area of the door.

    Area = Length Width = 6 ft 3 ft = 18 ft2

  2. Calculate the pressure on the door in psia (pounds per square inch, absolute)


  3. Convert pressure from psia to pounds per square foot, absolute.


  4. Calculate the force on the door.


    To review material, see lessons on Systems of Units, Plane Geometry, and Pressure.

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Q icon #9
Urea and nitric oxide are needed to evaluate an SNCR (Selective Non-Catalytic Reduction System) for NOx control. How much urea (expressed in lbm/min) is needed to react with nitric oxide (NO) being emitted at a rate of 120 lbm/min? Use the following reaction to calculate the urea requirement.


  1. 60 lbm
  2. 120 lbm
  3. 240 lbm
  4. 360 lbm
Answer: b. 120 lbm urea/min

Solution:
  1. Calculate the molecular weights of both reactants.

  2. Calculate the emission rate of nitric acid in lb moles per minute.


  3. Calculate the amount of urea needed in pounds mass per minute. Based on the reaction, 0.5 lb mole urea are needed per lb mole of NO.


    To review material, see lessons on Dimensional Calculations and Moles.

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