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An engincer has specificd that a sewage pipe for a certain building must have a grade of \(3 \% .\) How much vertical clearance must the construction crew leave for a sewage pipe that must carry waste a horizontal distance of 200 feet?

Short Answer

Expert verified
The vertical clearance must be 6 feet.

Step by step solution

01

Understand the Grade Percentage

The grade of a pipe indicates the slope or incline. A grade of 3% means that for every 100 feet of horizontal distance, the pipe drops 3 feet vertically.
02

Calculate Vertical Clearance per Foot

Since a 3% grade means a vertical drop of 3 feet per 100 feet, it can be expressed as a ratio: \[ \frac{3 \text{ feet}}{100 \text{ feet}} = 0.03 \text{ feet per foot} \]
03

Calculate the Total Vertical Clearance

To find the total vertical clearance for 200 feet of horizontal distance, multiply the horizontal distance by the rate of vertical drop: \[ 200 \text{ feet} \times 0.03 \text{ feet per foot} = 6 \text{ feet} \]
04

Conclusion

The construction crew must leave a vertical clearance of 6 feet for the sewage pipe to maintain a 3% grade over a horizontal distance of 200 feet.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Grade Percentage
In construction, the term 'grade percentage' is used to describe the slope or incline of a pipe. This is especially important in sewage systems as it ensures proper flow. A grade percentage is essentially the vertical drop over a specified horizontal distance, expressed as a percent. For example, when a sewage pipe has a grade of 3%, it means that for every 100 feet of horizontal distance, the pipe drops 3 feet vertically. This ratio is critical for designing systems that eliminate waste efficiently.
To calculate the vertical drop per foot in this case, you simply divide the vertical distance by the horizontal distance, resulting in a ratio of \( \frac{3 \text{ feet}}{100 \text{ feet}} = 0.03 \text{ feet per foot} \). This 0.03 value helps you determine the vertical clearance needed for any given horizontal distance.
The grade percentage is crucial for engineers designing pipe systems because improper slopes can cause blockages by not allowing gravity to assist in moving the waste material.
Importance of Vertical Clearance
Vertical clearance in a sewage system refers to the amount of vertical space that the pipe needs to drop to maintain the specified grade percentage over a horizontal distance. This is important because correct vertical clearance ensures that sewage flows smoothly, preventing back-ups and blockages.
To find the vertical clearance needed, you multiply the horizontal distance by the grade percentage expressed as a decimal. For instance, with a 3% grade over 200 feet, the calculation is: \( 200 \text{ feet} \times 0.03 \text{ feet per foot} = 6 \text{ feet} \). This means that the pipe must drop 6 feet over a horizontal distance of 200 feet.
Understanding and correctly calculating vertical clearance guarantees that sewage systems are efficient and functional, adhering to the design specifications of engineers.
Slope Calculation for Sewage Pipes
The slope calculation verifies that the pipe maintains the necessary incline for proper sewage flow. Correct slope calculation prevents issues like stagnant water or sewage backflow.
To calculate the slope, you need to know two things: the grade percentage and the horizontal distance. For a pipe with a grade of 3% spanning a horizontal distance of 200 feet, use the formula: vertical distance = horizontal distance \( \times \) grade percentage.
Using our example, the calculation is: \( 200 \text{ feet} \times 0.03 \text{ feet per foot} = 6 \text{ feet} \). This calculation tells us the pipe needs to drop 6 feet over 200 feet.
  • Step 1: Convert the grade percentage to a decimal: 3% = 0.03.
  • Step 2: Multiply this decimal by the horizontal distance: 200 \( \times \) 0.03 = 6 feet.
This straightforward method helps ensure that every part of the sewage system is designed to function correctly, preventing common problems associated with improper slopes.

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