6.1: Areas
Circle
Area of a circle = \(0.785 \times D^2\)
Typically, you will know the diameter of a circle, for example the diameter of a pipe or a storage tank. You may have learned the following formula (\(\pi \times r^{2}\)) for calculating the area of a circle. However, in this text we will only use the previous formula. Both formulas work, but in the water industry diameters are most commonly used.
Much of the time you will be asked to calculate the area of the opening of a pipe. However, the unit given to you will typically be given in inches. There are two ways to go about solving this type of problem.
Example \(\PageIndex{1}\)
What is the area of a 12” diameter pipe?
Solution
If you were to plug 12” into the formula (0.785 \times D^2\) you would end up with square inches and then you would most likely need to then convert to square feet.
So, the easiest way to solve all area problems where “feet” are not given is to convert to feet first and then plug the numbers into the formula.
A 12” diameter pipe equals a 1 foot diameter pipe.
\[\dfrac{12 \not{\text { inches }}}{1} \times \dfrac{1 \text { foot }}{12 \not{\text { inches }}}=1 \text { foot } \nonumber \]
By converting to feet before starting the problem you will avoid getting into units you are not familiar with.
Rectangles
Area of a rectangle = \(L \times W\)
Rectangles are common shapes of storage reservoirs, sedimentation basins, and even room in an office. Calculating the area for these types of structures is simple if you know how the length and width of the structure. Remember, the area of a square is calculated the same way. These types of dimensions are typically given in feet.
Trapezoid
Area of a trapezoid = \(\dfrac{b1+b2}{2} \times H\)
Trapezoids are not as common as circles, rectangles, and squares, but they are still found in the waterworks industry. Typically open channels and aqueducts are shaped like a trapezoid. In calculating the area of a trapezoid, you need to know the width across the aqueduct and the height of the water level. Now the width changes from the bottom of the trapezoid to the top. For example, the distance across the bottom of the trapezoid is a shorter distance then it is at the top of the trapezoid. The other point that needs to be addressed is the distance across the top of the trapezoid that is needed is the distance across the top of the water level. See the diagram below for an example of the base 1.
Once you know the distance across the trapezoid at the water level, then add it to the distance across the bottom of the trapezoid and divide that number by 2. Doing this finds the average distance across the trapezoid. Multiply this number by the height of the water level and you know have the area of the trapezoid.
Exercise 6.1
Calculate the following areas.
- What is the area of a circle with a 2 foot diameter?
- What is the area of a 36” diameter pipe?
- What is the area of a sedimentation basin that is 30 feet wide and 10 feet deep?
- What is the area of an aqueduct that is 5 feet across the bottom, 10 feet across the top and 7 feet deep?
- The roof on an above ground storage tank has a 130 foot diameter. What is the area?
- A filter is 25 feet long and 20 feet wide. What is the area?
- A water aqueduct is 10 feet wide at the bottom and 20 feet wide at the top. If it is 20 feet deep what is the area?