Measurement of the Surface Area of a Pond (laboratory condition)
AIM: Measurement of the Surface Area of a Pond (laboratory condition)
Theory:
Surface area is one of the most important pieces of information required to appropriately manage a pond. Many pond management decisions depend upon accurate surface area measurement. These measurements are necessary for activities such as fish species selection, fish stocking rates, fish harvest rates. Stocking fish into a pond of uncertain area can result in poor production, more disease and possibly death. Accuracy is also very important in determining chemical applications since over- or underestimating can cause a treatment to be ineffective or cause unintended lethality to fish or other species. Chemical applications in a pond include - herbicide treatment rates, insecticide application rates, clay flocculation chemical treatment rates, alkalinity adjustment lime application rates and phytoplankton fertilization rates.
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Principle
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Ponds come in all shapes and sizes - circle, square, rectangle, trapezoid or can be irregular in shape. Pond dimensions can be measured and surface area calculated using geometric formulas that fit pond shapes. When a single geometric shape does not fit a pond, the pond can be divided into segments with each segment measured separately and the individual areas added together to determine a pond’s overall surface area. Typically, a measuring tape or measuring wheel is used to determine distances between two points. Alternately, a known length of chain (rope) can be used as well. A final option is to use one’s own pace or footsteps to determine the distance between two points.
Conversion formula
1 acre = 43560 square feet = 4047 meter square
Circular
Pond shape (circumference) can be estimated by measuring the distance around the pond shoreline in feet. Then area can be calculated from the formula
A = Csquare / 4ฯ
Alternatively, an estimate of diameter (or radius) can help to calculate the surface area using the formula:
S.A. of a circular pond when diameter is known = (ฯ/4)×d2 = 0.785 x (diameter)2
S.A. of a circular pond when radius is known = ฯr2 = 3.14 X (radius)2
Triangle
Triangular pond areas are estimated by one of two formulas depending on whether the triangle has a 90° angle for one of its corners.
- If a 90° angle is present, the formula is: Area = ½ x length x width
- If no 90° angle is present and the sides are unequal, the formula is:
where S = ½ (A+B+C) and A, B and C are the lengths of the three sides of the triangle
Rectangular
This shape area is estimated by simply measuring the length and width of the pond sides.
Multiply the length with width to get the surface area:
Surface Area of a rectangular pond = length x width = l x w
Square
This shape has all sides equal. So simply measuring any one side and getting the square of that measurement gives an estimate of the surface area:
Surface Area of a square pond = (side)2 = s2
Rhombuses and Parallelograms
The surface area of a rhombus or a parallelogram is calculated by the formula:
A (rhombus or parallelogram) = base x vertical height = b x h
In a rhombus the lengths of all four sides are equal; none of the angles are right angles; opposite sides run parallel.
In a parallelogram the lengths of the opposite sides are equal; none of the angles are right angles; opposite sides run parallel
Trapezoid
Many ponds may be roughly rectangular in shape, but one side may be significantly shorter than the other. The area of this shape is best estimated using a formula for a trapezoid by taking the average length of the two unequal sides (base1 and base2) and multiplying by the width of the pond.
A (trapezium) = ½ (base1 + base2) x vertical height = ½ (b1 + b2) x h
Irregular Shaped
Many ponds have an irregular shape where the surface area cannot be adequately estimated using the formulas for common geometric shapes. Three methods can be used in this case depending on the degree of accuracy you desire.
1. Average Length and Width Method
Take numerous measurements to determine the average length and average width. Make certain you get both the longest and shortest distances in calculating the average length, and the widest and narrowest distances for determining the average width. The more measurements that you make, the more accurate your result will be. The area is then calculated by multiplying the average width times the average length. Depending on the number of width and length measurements made, the final area will probably be within about ±20% of the actual pond surface are
2. Multiple Trapezoids Method
A more accurate method to determine the area of an odd- shaped pond is to divide the pond into multiple trapezoid shapes. A new trapezoid is defined anywhere the shoreline makes a rapid change in direction. This method requires more measurement and effort, but the final area estimate will probably be within ±5 to 10 percent of the actual pond area.
3. Handheld Global Positioning Systems (GPS)
Handheld GPS systems can be used in outdoor activities involving measurement of the surface area of a pond. A pond surface area could be estimated by walking the perimeter of the pond and stopping at various waypoint locations along the pond shoreline. Various locations or ‘waypoints’ can be stored in the GPS unit for use with a coordinating mapping software. The software can connect the waypoints and calculate the area inside the resulting shape upto 99% accuracy levels. Geographical Information Websites: There are also geographical information programs on the internet, like Google Earth or Bing Maps, which use satellite imagery to display a map of your pond or lake. These website tools can make it very easy to determine the surface area of a water resource.
Do It Yourself:-
Numericals to be done in practical file on white side:
Determination of surface area of pond
Instructions:
a) Write your answers in m2, acres and square feet.
b) Draw diagrams of the pond in each question.
1. Find out the surface area of a pond circular in shape with radius of 65 m.
2. Find the surface area of pond with an irregular square shape with length 68 m and 73 m
while the other two sides being 82 m and 87 m.
3. Find the surface area of a pond which is triangular in shape with angle 60°, 30° and 90°.
The base and height of the pond are 150 m and 165 m, respectively.
4. Find the surface area of a pond irregular in shape with following dimensions:
Length Width
a = 35 m u = 35 m
b = 49 m v = 41 m
c = 39 m w = 43 m
d = 35 m x = 39 m
e = 42 m y = 28 m
f = 28 m z = 29 m
Question 1. To find out Surface area of a rectangular pond of length 500 m and width 150 m.
Solution: 500 m
Given a rectangular pond:
Length = 500 m 150
Width = 150 m
Surface area of a rectangular pond = Length X width
= 500m X 150m
= 75000 m2
Answer: Surface area of the given rectangular pond =……….. m2 =...........acres = …… sq.feet
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