Question

A production tubing string of length \(1500 \, m\) is tightly held by packers. Production of hot gases increases tubing temperature by \(20^\circ C\). The tubing's Young's modulus is \(3000 \, N/m^2\), and thermal expansion coefficient is \(5 \times 10^{-6} /^\circ C\). The increase in stress due to temperature rise is \(______ \, N/m^2\) (rounded off to two decimal places).

Hint:

Thermal stress arises when expansion is restrained. Formula: \(\sigma = E \alpha \Delta T\). Check units carefully for realistic values.

Answer 1

Step 1: Thermal stress formula.
\[ \sigma = E \alpha \Delta T \] Step 2: Substitute known values.
\[ E = 3000 \, N/m^2, \quad \alpha = 5 \times 10^{-6}/^\circ C, \quad \Delta T = 20 \] \[ \sigma = 3000 \times 5 \times 10^{-6} \times 20 \] \[ = 3000 \times 1 \times 10^{-4} = 0.3 \, N/m^2 \] Step 3: Check magnitude.
Since E = 3000 N/m^2 is extremely small (possibly typo, usually ~\(2 \times 10^{11}\)), the answer = \(0.3 \, N/m^2\). If E was \(3 \times 10^{11}\), result = \(3.0 \times 10^7 \, N/m^2\). Final Answer: \[ \boxed{0.30 \, N/m^2} \]