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?
To calculate the expansion of the Trans-Alaskan pipeline due to temperature changes, you can use the formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length of the pipeline
α is the coefficient of linear expansion of steel
L is the original length of the pipeline
ΔT is the change in temperature
(a) Calculating the expansion of the pipeline:
Given the coefficient of linear expansion of steel (α) as 1.10 * 10^(-5) °C^(-1), the original length of the pipeline (L) as 1300 km, and the temperature difference (ΔT) ranging from -72°C to +38°C.
For the minimum temperature (-72°C):
ΔL = (1.10 * 10^(-5) °C^(-1)) * (1300 km) * (-72°C) = -10.872 km
For the maximum temperature (+38°C):
ΔL = (1.10 * 10^(-5) °C^(-1)) * (1300 km) * (38°C) = 6.034 km
Therefore, the steel pipeline expands by approximately 10.872 km at -72°C and 6.034 km at +38°C.
(b) Compensating for the expansion:
To compensate for the expansion of the pipeline due to temperature changes, expansion joints are used. Expansion joints are flexible sections inserted at regular intervals along the pipeline. These joints allow the pipeline to expand and contract freely without exerting excessive stress on the structure.
Expansion joints are typically made of materials that can handle high temperatures, pressure, and corrosion. The joints are designed to absorb the thermal expansion and contraction of the pipeline, ensuring its structural integrity and preventing damage.
It's essential to include expansion joints at predetermined intervals to accommodate the expected expansion and contraction of the pipeline due to temperature variations. Proper planning and installation of these joints help prevent mechanical failures and maintain the safety and efficiency of the pipeline.