SURFACE AREAS OF CANAL CROSS-SECTIONS AND FARMS.pptx

TLE 7 EXPLORATORY

1. SURFACE AREAS OF CANAL CROSS-SECTIONS AND FARMS ELAINE JOY F. ANDAYA Teacher

2. 2 3/20/2023 Add a footer LEARNING OUTCOME 2 Perform basic workplace calculations PERFORMANCE STANDARDS  Calculations to be made are identified according to job requirements.  Correct method of calculation is determined.  Systems and units of measurement to be followed are ascertained.  Calculations needed to complete work task are performed using the four basic mathematical operations.  Appropriate operations are used to comply with the instruction.  Result obtained is reviewed and thoroughly checked.

3. 3 3/20/2023 Add a footer Determine the following pictures:

4. 4 3/20/2023 Add a footer PERFORM CALCULATION It is important to be able to measure and calculate surface areas. It might be necessary to calculate, for example, the surface area of the cross-section of a canal or the surface area of a farm.

5. Determination of the Surface Areas of Canal Cross-Sections The most common shape of a canal cross-section is a trapezium or, more truly, an "up-side-down" trapezium. 5 3/20/2023 Add a footer

6. 1. Canal Cross-Sections The area (A B C D), hatched on the drawing, is called the canal cross-section and has a trapezium shape. Thus, the formula to calculate its surface is similar to the formula used to calculate the surface area of a trapezium. 6 3/20/2023 Add a footer

7. Formula: whereby: base (b) = bottom width of the canal top line (a) = top width of the canal canal depth (h) = height of the canal (from the bottom of the canal to the top of the embankment) 7 3/20/2023 Add a footer Surface area of the canal cross-section = 0.5 (base + top line) x canal depth = 0.5 (b + a) x h ..... (6)

8. Wetted Cross-Section of a Canal The area (A B C D), hatched on the drawing, is called the wetted canal cross-section. It also has a trapezium shape and the formula to calculate its surface area is: 8 3/20/2023 Add a footer

9. Formula: Surface area of the wetted canal cross-section = 0.5 (base + top line) x water depth = 0.5 (b + a1) x h1 ..... (7) whereby: base (b) = bottom width of the canal top line (a1) = top width of the water level water depth (h1) = the height or depth of the water in the canal (from the bottom of the canal to the water level). 9 3/20/2023 Add a footer

10. Example: Calculate the surface area of the cross-section and the wetted cross-section, of the canal shown in next figure. 10 3/20/2023 Add a footer

11. 11 3/20/2023 Add a footer Canal cross-section: base (b) =1.25 m top line (a) =3.75 m canal depth (h) = 1.25 m Formula: A = 0.5 x (b + a) x h Canal wetted cross-section: base (b) = 1.25 m top line (a1) = 3.25 m water depth (h1) =1.00 m Formula: A = 0.5 x (b + a1) x h

12. 12 Activity 1: Calculate the surface area of the cross-section and wetted cross-section 3/20/2023 Add a footer 1. 2.

13. 13 Generalization: 3/20/2023 Add a footer What are the two surface areas of a canal? Canal cross-section and canal wetted cross-section What is the formula for canal cross-section? What is the formula for canal wetted cross-section? Formula: A = 0.5 x (b + a1) x h Formula: A = 0.5 x (b + a) x h

14. Activity 2: Calculate the surface area of the cross-section and wetted cross-section. (notebook) 14 3/20/2023 Add a footer 1. Canal cross-section: b = 3.50 m a = 4.50 m h = 2.50 m Canal wetted cross-section: b = 3.50 m a1 = 4.00 m h1 = 2.00 m 2 . Canal cross-section: b = 4.50 m a = 4.50 m h = 3 .50 m Canal wetted cross-section: b = 4 .50 m a1 = 5 .00 m h1 = 3.00 m 3 . Canal cross-section: b = 5.00 m a = 7.00 m h = 4 .00 m Canal wetted cross-section: b = 5.00 m a1 = 6.00 m h1 = 3.00 m 4 . Canal cross-section: b = 10 m a = 15 m h = 7 m Canal wetted cross-section: b = 10 m a1 = 13 m h1 = 5 m 5 . Canal cross-section: b = 15 m a = 12 m h = 8 m Canal wetted cross-section: b = 15 m a1 = 10 m h1 = 6 m

15. 15 3/20/2023 Add a footer f or your participation!

16. 16 3/20/2023 Add a footer Determine the following pictures:

17. Determination of the Surface Area of a Farm

18. 18 3/20/2023 Add a footer It may be necessary to determine the surface area of a farmer's field. For example, when calculating how much irrigation water should be given to a certain field, the size of the field must be known. When the shape of the field is regular and has, for example, a rectangular shape, it should not be too difficult to calculate the surface area once the length of the field (that is the base of its regular shape) and the width of the field have been measured.

19. Field of Regular Shape 19 3/20/2023 Add a footer EXAMPLE: Length of the field =50 m Width of the field = 30 m What is the area of the same field, expressed in hectares? A hectare is equal to 10 000 m. Thus, the formula to calculate a surface area in hectares is:

20. Field of Irregular Shape 20 3/20/2023 Add a footer In this case, the field should be divided in several regular areas (square, rectangle, triangle, etc.).

21. 21 3/20/2023 Add a footer Division of Irregular Field into Regular Areas Surface area of the square: As = length x width Surface area of the rectangle: Ar = length x width Surface area of the triangle: At = 0.5 x base x height Total surface area of the field: A = As + Ar + At

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