Question

The length of Lead piping in the plant is 50 m long at a temperature of 160C. When hot water flows
through it the temperature of the pipe rises to 800C. The coefficient of linear expansion of lead is
29 10-6 0 K-1
i) Determine the change in length of the hot pipe.
ii) Determine the compressive force induced in the pipe if it is rigidly held and expansion is
prevented.

Answer 1

Answer on Question #72012-Physics-Molecular Physics-Thermodynamics

The length of Lead piping in the plant is 50 m long at a temperature of 16C. When hot water flows through it the temperature of the pipe rises to 80C. The coefficient of linear expansion of lead is 29 10-6 K-1

i) Determine the change in length of the hot pipe.

ii) Determine the compressive force induced in the pipe if it is rigidly held and expansion is prevented.

Solution

i)

$$dl = \alpha l \Delta T = 29 \cdot 10^{-6} \cdot 50 \cdot (80 - 16) = 0.0928 \, \text{m}.$$

ii)

$$F = \sigma A = \alpha T E A = 29 \cdot 10^{-6} \cdot 14 \cdot 10^{9} \cdot (80 - 16) \cdot \frac{\pi (0.025)^2}{4} = 12.75 \, \text{kN}$$