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 the temperature difference, we can use the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length of the pipeline
α is the coefficient of linear expansion of steel
ΔT is the change in temperature
(a) Calculating the expansion:
Given:
L = 1300 km (1300,000 meters)
α = 1.10 * 10^(-5) °C^(-1)
ΔT = (38°C - (-72°C)) = 110 °C
Using the formula, we can calculate the expansion:
ΔL = (1300,000 m) * (1.10 * 10^(-5) °C^(-1)) * (110 °C)
= 157,300 meters
Therefore, the steel pipeline expands by approximately 157,300 meters.
(b) Compensating for expansion:
To compensate for the expansion of the pipeline, expansion joints are used. Expansion joints are flexible sections inserted at various intervals along the pipeline. These joints can expand and contract with changes in temperature without causing damage to the pipeline.
Expansion joints allow the pipeline to expand and contract freely while maintaining its integrity. They can absorb the thermal expansion and prevent stress-related issues such as buckling or structural failure.
By installing expansion joints along the pipeline, they can accommodate the change in length due to temperature variations, ensuring the safety and proper functioning of the pipeline.
(a) To calculate how much the steel pipeline expands due to the difference in temperature, we can use the following formula:
ΔL = L * α * ΔT
Where:
ΔL - Change in length of the pipeline
L - Length of the pipeline (1300 km)
α - Coefficient of linear expansion of steel (1.10 * 10^-5 °C^-1)
ΔT - Difference in temperature (38°C - (-72°C) = 110°C)
Let's plug in the values and calculate:
ΔL = 1300 km * 1.10 * 10^-5 °C^-1 * 110°C
ΔL = 1.43 km
Therefore, the steel pipeline expands by approximately 1.43 km.
(b) To compensate for the expansion of the pipeline, a technique called "thermal expansion joints" can be used. These joints are designed to absorb the expansion and contraction of the pipeline caused by temperature changes. They allow the pipeline to expand and contract without damaging the structure or causing any leaks. Thermal expansion joints typically consist of flexible sections that can accommodate the movement of the pipeline while maintaining its integrity. They are strategically placed along the pipeline to account for the expected expansion and contraction.