Basic Math Operations - Mathematics and Statistics for the Environment - page 58

Solution:

200 200 mL

50 mL

TON == =

V T

4

2.11 GEOMETRICAL MEASUREMENTS
Wastewater treatment plants consist of a series of tanks and channels. Proper design and operational
control requires the engineer and operator to perform several process control calculations. Many
of these calculations include parameters such as the circumference or perimeter, area, or volume
of the tank or channel as part of the information necessary to determine the result. Many process
calculations require computation of surface areas. To aid in performing these calculations, the fol-
lowing definitions and relevant equations used to calculate areas and volumes for several geometric
shapes are provided.
Environmental practitioners involved in fisheries, water/wastewater treatment plants, and other
operations dealing with tanks, basins, and ponds operations must know the area and volume of
all tanks, basins, and ponds they deal with. For example, in water and wastewater treatment plant
operations, the plant configuration usually consists of a series of tanks and channels. Proper design
and operational control require the environmental practitioner and plant operator to perform several
process control calculations. Many of these calculations require parameters such as circumference
or perimeter, surface area, or volume of a tank or channel. Moreover, in fisheries operations, exact
measurements of area and volume are essential to calculate stocking rates and chemical applica-
tions. Stocking fish in a pond of uncertain area can result in poor production, disease, and possibly
death. Chemical treatments can be ineffective if the volume or area is underestimated and can be
potentially lethal if they are overestimated (Masser and Jensen, 1991). To aid in performing these
calculations, the following definitions and relevant equations used to calculate areas and volumes
for several geometric shapes are provided.

2.11.1 d eFinitions
Area —The area of an object, measured in square units.
Base —The term used to identity the bottom leg of a triangle, measured in linear units.
Circumference —The distance around an object, measured in linear units. When determined
for other than circles, it may be called the perimeter of the figure, object, or landscape.
Cubic units —Measurements used to express volume, cubic feet, cubic meters, etc.
Depth —The vertical distance from the bottom the tank to the top. It is normally measured
in terms of liquid depth and given in terms of sidewall depth (SWD), measured in linear
units.
Diameter —The distance, measured in linear units, from one edge of a circle to the opposite
edge passing through the center.
Height —The vertical distance, measured in linear units, from one end of an object to the
other.
Length —The distance, measured in linear units, from one end of an object to the other.
Linear units —Measurements used to express distance (e.g., feet, inches, meters, yards).
Pi (π)—A number in the calculations involving circles, spheres, or cones (π = 3.14).
Radius— The distance, measured in linear units, from the center of a circle to the edge.
Sphere— A container shaped like a ball.
Square units— Measurements used to express area (e.g., square feet, square meters, acres).
Volume— The capacity of a unit (how much it will hold), measured in cubic units (e.g., cubic
feet, cubic meters) or in liquid volume units (e.g., gallons, liters, million gallons).
Width— The distance from one side of the tank to the other, measured in linear units.