Question
the 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 two-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches, we first need to determine the pipe's material density and its dimensions.
1. **Determine the Outside Diameter (OD) and the Wall Thickness**:
- For a nominal pipe size of 3.5 inches, the typical outside diameter is approximately 3.5 inches (which is roughly 88.9 mm).
- According to the ASME B36.10 standard for pipe dimensions, the wall thickness for Schedule 40 pipe with a 3.5-inch nominal size is approximately 0.216 inches (5.49 mm).
2. **Calculate the Inside Diameter (ID)**:
\[
\text{ID} = \text{OD} - 2 \times \text{Wall Thickness}
\]
\[
\text{ID} = 3.5 \text{ in} - 2 \times 0.216 \text{ in} \approx 3.068 \text{ in} \approx 77.9 \text{ mm}
\]
3. **Calculate the Volume of the Pipe**:
- The volume of a cylindrical pipe can be calculated using the formula:
\[
V = \pi \left( \left(\frac{OD}{2}\right)^2 - \left(\frac{ID}{2}\right)^2 \right) \times \text{Length}
\]
- Convert inches to meters (1 inch = 0.0254 m):
- OD = 3.5 inches = 0.0889 m
- ID = 3.068 inches = 0.0779 m
- Length = 2 meters
\[
V = \pi \left( \left(0.0889/2\right)^2 - \left(0.0779/2\right)^2 \right) \times 2
\]
\[
V \approx \pi \left( (0.04445^2) - (0.03895^2) \right) \times 2
\]
\[
V \approx \pi \left( 0.000197 \text{ m}^2 - 0.000152 \text{ m}^2 \right) \times 2
\]
\[
V \approx \pi \times 0.000045 \text{ m}^2 \times 2
\]
\[
V \approx 0.000283 \text{ m}^3
\]
4. **Calculate the Mass of the Pipe**:
- The density of common materials used for pipes (e.g., steel) is usually around \(7850 \, \text{kg/m}^3\).
\[
\text{Mass} = \text{Density} \times V
\]
\[
\text{Mass} \approx 7850 \, \text{kg/m}^3 \times 0.000283 \text{ m}^3 \approx 2.22 \text{ kg}
\]
Thus, the mass of a two-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches is approximately **2.22 kg**. Adjustments may be made if the material density differs, but this gives a good approximation for steel.
1. **Determine the Outside Diameter (OD) and the Wall Thickness**:
- For a nominal pipe size of 3.5 inches, the typical outside diameter is approximately 3.5 inches (which is roughly 88.9 mm).
- According to the ASME B36.10 standard for pipe dimensions, the wall thickness for Schedule 40 pipe with a 3.5-inch nominal size is approximately 0.216 inches (5.49 mm).
2. **Calculate the Inside Diameter (ID)**:
\[
\text{ID} = \text{OD} - 2 \times \text{Wall Thickness}
\]
\[
\text{ID} = 3.5 \text{ in} - 2 \times 0.216 \text{ in} \approx 3.068 \text{ in} \approx 77.9 \text{ mm}
\]
3. **Calculate the Volume of the Pipe**:
- The volume of a cylindrical pipe can be calculated using the formula:
\[
V = \pi \left( \left(\frac{OD}{2}\right)^2 - \left(\frac{ID}{2}\right)^2 \right) \times \text{Length}
\]
- Convert inches to meters (1 inch = 0.0254 m):
- OD = 3.5 inches = 0.0889 m
- ID = 3.068 inches = 0.0779 m
- Length = 2 meters
\[
V = \pi \left( \left(0.0889/2\right)^2 - \left(0.0779/2\right)^2 \right) \times 2
\]
\[
V \approx \pi \left( (0.04445^2) - (0.03895^2) \right) \times 2
\]
\[
V \approx \pi \left( 0.000197 \text{ m}^2 - 0.000152 \text{ m}^2 \right) \times 2
\]
\[
V \approx \pi \times 0.000045 \text{ m}^2 \times 2
\]
\[
V \approx 0.000283 \text{ m}^3
\]
4. **Calculate the Mass of the Pipe**:
- The density of common materials used for pipes (e.g., steel) is usually around \(7850 \, \text{kg/m}^3\).
\[
\text{Mass} = \text{Density} \times V
\]
\[
\text{Mass} \approx 7850 \, \text{kg/m}^3 \times 0.000283 \text{ m}^3 \approx 2.22 \text{ kg}
\]
Thus, the mass of a two-meter length of Schedule 40 pipe with a nominal diameter of 3.5 inches is approximately **2.22 kg**. Adjustments may be made if the material density differs, but this gives a good approximation for steel.