Calculation of Storm Water Pipe Fall (Y2) assessment

Based on the diagram, calculate the fall (Y ₂ ) required when installing a typical storm water pipe

Make the following assumptions:
Use as reference 1% gradient when installing the storm water pipe.

Use the formula below:
Y2 = X2 (Y1) / X1

Note:

Storm water pipe gradient = 1% = 1:100
X ₁ = 100
Y ₁ = 1

X ₂ = pipe run length along horizontal
Y ₂ = Fall

Referring to the image below, calculate the slope/gradient of the driveway. Express your answer as a percentage.

You will need to calculate the rise first, then use the formula below:

Rise/Run x 100

You are setting out the batter boards on site.

Based on the image below, calculate the angle θ between the top of the board and the indicated slope. Enter your answer in the box provided, and include a screenshot of the data you entered using the upload option.

Use the tangent formula below:
TAN θ = Opposite / Adjacent

Note:
Opposite = 800mm

Assessment Summary and Requirements

The assessment had three main components: calculating the required fall for a storm water pipe, determining the percentage gradient of a driveway, and calculating the angle of a slope for setting out batter boards. The key learning objectives were to apply formulas for gradient, slope, and trigonometry (specifically, the tangent function) to solve practical construction-related problems.

Approach and Process

An academic mentor guided the student through the assessment using a step-by-step approach, ensuring a thorough understanding of each section.

1. Section 1: Storm Water Pipe Calculation

   • The mentor first explained the concept of a gradient in construction, emphasizing that a 1% gradient means a fall of 1 meter for every 100 meters of horizontal run (1:100).

   • The student was then asked to identify the given values from the provided diagram and formula (

     Y2=X2(Y1)/X1

     ). The mentor clarified that X1 is the horizontal run (100) and Y1 is the fall (1), while X2 is the length of the pipe run and Y2 is the unknown fall to be calculated.

   • The student was then able to substitute the values into the formula to find the correct fall (

     Y2

     ).

2. Section 2: Driveway Slope Calculation

   • The mentor introduced the formula for calculating a slope as a percentage: (

     Rise/Run×100

     ).

   • The student was guided to first calculate the rise from the provided diagram by subtracting the final elevation from the initial one.

   • Once the rise was determined, the student was able to substitute both the rise and the given run into the formula to calculate the percentage slope of the driveway.

3. Section 3: Batter Board Angle Calculation

   • For this section, the mentor explained the fundamentals of trigonometry and the purpose of the tangent formula (

     TAN θ=Opposite/Adjacent

     ) in determining angles.

   • The student was guided to identify the "Opposite" side (the vertical distance, 800mm) and the "Adjacent" side (the horizontal distance) from the diagram.

   • The mentor emphasized the importance of correctly identifying the adjacent side and not confusing it with the hypotenuse. The student was then able to substitute the values into the formula to find the angle (

     θ

     ).

   • The final step was to use the inverse tangent function (

     tan−1

     ) to solve for the angle, and the student was instructed to provide a screenshot of their final answer.

Outcome and Learning Objectives

The guided, step-by-step process allowed the student to successfully complete all parts of the assessment. The final outcome demonstrated a solid understanding of fundamental construction principles. The learning objectives covered were:

• Mathematical application: The student learned to apply specific formulas for gradient and slope, and the trigonometric tangent function, to real-world construction scenarios.

• Reading and interpreting diagrams: The student developed the skill of extracting essential data (measurements, rise, run, opposite, adjacent) directly from technical drawings and diagrams.

• Problem-solving: The approach helped the student break down complex problems into manageable steps, fostering a systematic and logical approach to problem-solving.

• Conceptual understanding: Beyond just calculating, the student gained a deeper understanding of what gradients, slopes, and angles mean in the context of construction and site setting-out.

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