Question
mass of a two metre length of schedule 40 pipe, nominal pipe 3.5 inches, is
Answers
GPT-4o mini
To calculate the mass of a 2-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches, we first need to determine the outer diameter, wall thickness, and material density.
1. **Outer Diameter**: For a nominal pipe size of 3.5 inches in Schedule 40, the outer diameter is approximately 3.94 inches (or 100 mm).
2. **Wall Thickness**: The wall thickness for a Schedule 40 pipe with a 3.5-inch nominal diameter is about 0.216 inches (or about 5.49 mm).
3. **Inner Diameter**: The inner diameter can be calculated as:
\[
\text{Inner Diameter} = \text{Outer Diameter} - 2 \times \text{Wall Thickness} = 3.94 - 2 \times 0.216 \approx 3.51 \, \text{inches}
\]
4. **Volume Calculation**: The volume of the pipe can be calculated by finding the volume of the outer cylinder and subtracting the volume of the inner cylinder:
\[
V = \pi \times \left(\left(\frac{\text{Outer Diameter}}{2}\right)^2 - \left(\frac{\text{Inner Diameter}}{2}\right)^2\right) \times \text{Length}
\]
Converting lengths to meters:
- Outer Diameter = 0.1 m
- Inner Diameter = \( \frac{3.51 \, \text{inches} \times 0.0254 \, \text{m/in}}{1} \approx 0.089 \, \text{m} \)
- Length = 2 m
Now calculate the volume:
\[
\text{Outer Radius} = \frac{0.1}{2} = 0.05 \, \text{m}
\]
\[
\text{Inner Radius} = \frac{0.089}{2} \approx 0.0445 \, \text{m}
\]
\[
V = \pi \times \left((0.05)^2 - (0.0445)^2\right) \times 2
\]
\[
V \approx \pi \times \left(0.0025 - 0.00197625\right) \times 2
\]
\[
V \approx \pi \times 0.00052375 \times 2 \approx 0.003287 \, \text{m}^3
\]
5. **Density**: The density of typical steel pipe is about 7850 kg/m³.
6. **Mass Calculation**: Using the density to find the mass:
\[
\text{Mass} = \text{Density} \times V \approx 7850 \, \text{kg/m}^3 \times 0.003287 \, \text{m}^3
\]
\[
\text{Mass} \approx 25.8 \, \text{kg}
\]
Therefore, the mass of a 2-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches is approximately **25.8 kg**.
1. **Outer Diameter**: For a nominal pipe size of 3.5 inches in Schedule 40, the outer diameter is approximately 3.94 inches (or 100 mm).
2. **Wall Thickness**: The wall thickness for a Schedule 40 pipe with a 3.5-inch nominal diameter is about 0.216 inches (or about 5.49 mm).
3. **Inner Diameter**: The inner diameter can be calculated as:
\[
\text{Inner Diameter} = \text{Outer Diameter} - 2 \times \text{Wall Thickness} = 3.94 - 2 \times 0.216 \approx 3.51 \, \text{inches}
\]
4. **Volume Calculation**: The volume of the pipe can be calculated by finding the volume of the outer cylinder and subtracting the volume of the inner cylinder:
\[
V = \pi \times \left(\left(\frac{\text{Outer Diameter}}{2}\right)^2 - \left(\frac{\text{Inner Diameter}}{2}\right)^2\right) \times \text{Length}
\]
Converting lengths to meters:
- Outer Diameter = 0.1 m
- Inner Diameter = \( \frac{3.51 \, \text{inches} \times 0.0254 \, \text{m/in}}{1} \approx 0.089 \, \text{m} \)
- Length = 2 m
Now calculate the volume:
\[
\text{Outer Radius} = \frac{0.1}{2} = 0.05 \, \text{m}
\]
\[
\text{Inner Radius} = \frac{0.089}{2} \approx 0.0445 \, \text{m}
\]
\[
V = \pi \times \left((0.05)^2 - (0.0445)^2\right) \times 2
\]
\[
V \approx \pi \times \left(0.0025 - 0.00197625\right) \times 2
\]
\[
V \approx \pi \times 0.00052375 \times 2 \approx 0.003287 \, \text{m}^3
\]
5. **Density**: The density of typical steel pipe is about 7850 kg/m³.
6. **Mass Calculation**: Using the density to find the mass:
\[
\text{Mass} = \text{Density} \times V \approx 7850 \, \text{kg/m}^3 \times 0.003287 \, \text{m}^3
\]
\[
\text{Mass} \approx 25.8 \, \text{kg}
\]
Therefore, the mass of a 2-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches is approximately **25.8 kg**.