Water flows slowly and steadily through a red brass pipe from a hot source at A
ID: 1717992 • Letter: W
Question
Water flows slowly and steadily through a red brass pipe from a hot source at A into a tank at B held at a constant lower temperature of 25degree C. The system was initially stress-free when installed at 25 degree C. The air flowing around the pipe within the 2.4 meter gap between the two tanks provides the cooling, and the resulting temperature in the pipe can be approximated to vary as the square root of the distance away from B. Assume the walls of the tanks are fixed and immobile, and that the modulus and yield strength of the copper alloy remains constant. Find the source temperature A which will raise the stress level in the copper pipe to the yield point.Explanation / Answer
Tb = 298 K
T = Tb + k*sqrt(x) where x is the distance from B
at x = 2.4 m we have Ta = Tb + k * sqrt(2.4) = 298 + 1.55 * k K
assume yield strength = 70 MPa , E = 120 GPa , alpha = 16.5 * 10^-6
Thermal Stress = E * a * (Ta - Tb) = 120 * 10^9 * 16.5 * 10^-6 * 1.55k = yield stress
120 * 10^3 * 16.5 * 1.55 k = 70 * 10^6
k = 22.8087
Therefore Ta = 298 + 1.55 * sqrt(2.4) = 35.335 Celsius
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