1. Module 1: Basic Concepts - Plane Geometry
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Contents:
Lesson Material
Animation:
Animations of Area and Volume Calculations
Summary Table
Practice Problems
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Objective
Calculate the surface areas and volumes of common geometric shapes important in air pollution control.
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2. Lesson Material
Geometry is needed in many types of air pollution control problems involving the sizing of equipment, the
emissions from sources, and the design of control system components. For example, plane geometry is
used to evaluate the velocities through ductwork and stacks, the minimum and maximum sizes of control
systems, and the areas available for heat transfer in condensers. Solid geometry is used to evaluate the
capacity of hoppers and the residence time of combustion gases in incinerators.
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Q icon #1
What 3-dimensional geometric shapes do you see in this fabric filter?
equation 1
Answer to Question
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Animations of Area and Volume Calculations
Provided below are four animations that show how to calculate the area and volume of geometric shapes
commonly found in the field of air pollution control. Note the many different shapes associated with the
parallel large-diameter cyclone (see Figure below). This type of cyclone is used for removing relatively
large-sized particles.
cyclonespace
Four Animations Break Line To see animations,
either click on the four pieces of equipment
(shown in Figure)

3. or select text below.
(No audio)
Duct
Particles
Cyclone Tube
Hopper
geomety1
Note: Animations require a Netscape 4.7 or Internet Explorer 4.01 or higher browser and a Shockwave
Flash plug-in (Netscape browsers) or Shockwave Flash ActiveX Control (Internet Explorer browsers).
Shockwave Flash plug-in/ActiveX Control (version 3.0 minimum) can be obtained at the Macromedia Exit
EPA Disclaimer web site. Before downloading or installing any software or plug-ins, please refer to your
organization's network/computer policies or check with your system administrator.
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Summary Table
The following Table summarizes the formulas commonly encountered in air pollution work.
Table 1
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Example Problem 1 illustrates how solid geometry formulas might be used to calculate emission rates.
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Example Problem 1.

4. Calculate Droplet Emission Rate
What is the total emission rate of droplets in terms of pounds mass per hour, if an emission testing
instrument indicates that the droplet concentration in the gas stream is 1 106 drops/cm3 and the gas flow
rate is 10,000 actual ft3/min? Assume that all of the droplets are 1 micrometer in diameter and that the
density of the droplet is 1.0 gm/cm3.
Solution:
Calculate the volume of a 1 micrometer droplet.
equation 1-1
Calculate the mass of a droplet.
equation 1-2
Calculate the total emission rate of droplets in grams per minute.
equation 1-3
Convert the emission rate of droplets from grams per minute to pounds mass per hour.
equation 1-4
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Practice Problems
Plane Geometry

5. Instructions:
Complete the Practice Problems before proceeding to the next lesson. Click on the button below.
Practice Problems
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Last updated on Saturday, January 30, 2010