The Trans-Alaskan pipeline is 1300 km long, reaching from Prudhoe Bay to the port of Valdez, and is subject to temperatures ranging from -72°C to +38°C.
(a) How much does the steel pipeline expand due to the difference in temperature? (The coefficient of linear expansion of steel is 1.10 10-5°C−1.)
____km
(b) How can one compensate for this expansion?
(a) To calculate how much the steel pipeline expands due to the difference in temperature, we need to use the formula:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length of the pipeline
α is the coefficient of linear expansion of steel
L0 is the initial length of the pipeline
ΔT is the difference in temperature
Given:
α = 1.10 * 10^(-5) °C^(-1)
L0 = 1300 km
ΔT = (38°C - (-72°C)) = 110°C
Substituting these values into the formula, we can calculate the change in length:
ΔL = (1.10 * 10^(-5) °C^(-1)) * 1300 km * 110°C
Simplifying:
ΔL = 1.43 km
Therefore, the steel pipeline expands by approximately 1.43 km due to the difference in temperature.
(b) To compensate for the expansion of the pipeline, various measures can be taken:
1. Expansion joints: These are flexible sections inserted at regular intervals along the pipeline. They allow the pipeline to expand and contract without causing stress or damage.
2. Anchoring and guides: Proper anchoring and guides can help control the direction and limit the movement of the pipeline due to expansion. This helps prevent buckling or excessive stress on the structure.
3. Pipe loops: The route of the pipeline can be designed with pipe loops, which are U-shaped sections that allow for expansion and contraction. This helps absorb the changes in length without causing problems.
4. Thermal insulation: Applying thermal insulation around the pipeline can help minimize temperature variations, reducing the expansion and contraction effects.
5. Lubrication: Using lubricants between the pipeline sections can reduce friction and facilitate the movement caused by expansion and contraction.
These techniques can help compensate for the expansion of the Trans-Alaskan pipeline and ensure its safe and efficient operation throughout the wide range of temperatures it experiences.