Problem 7: Calculate the Depth of Excavation

Given:

• Volume of excavation: $70 \, \text{m}^3$
• Surface area of the excavation: $5 \, \text{m} \times 4 \, \text{m}$

Solution: The volume of the excavation is given by: $\text{Volume} = \text{Surface Area} \times \text{Depth}$

Substitute the known values: $70 = (5 \times 4) \times \text{Depth}$

Simplify: $70 = 20 \times \text{Depth}$

Solve for depth: $\text{Depth} = \frac{70}{20} = 3.5 \, \text{m}$

Answer: The depth of the excavation is 3.5 meters.

Problem 8: Calculate the Minimum Width of the Trench

Given:

• Diameter of the pipe: $150 \, \text{mm} = 0.15 \, \text{m}$

To allow installation, a trench must accommodate the pipe width plus some clearance. Typically, a minimum clearance of $0.15 \, \text{m}$ on either side of the pipe is standard.

The minimum width of the trench is: $\text{Minimum Width} = \text{Diameter of Pipe} + 2 \times \text{Clearance}$

Substitute the values: $\text{Minimum Width} = 0.15 + 2 \times 0.15 = 0.15 + 0.30 = 0.45 \, \text{m}$

Answer: The minimum width of the trench is 0.45 meters.

Do you want further clarifications or step-by-step breakdowns?

Related Questions:

1. How would the trench width change if the clearance was increased to $0.2 \, \text{m}$?
2. What is the total surface area of the excavation if the depth is known?
3. If the volume of excavation is increased to $100 \, \text{m}^3$, what would the depth be for the same surface area?
4. How does pipe diameter influence trench width requirements in other projects?
5. Why is clearance important when designing trenches for pipe installations?

Tip: Always confirm units (meters, millimeters, etc.) to avoid errors during calculations.