Determine the gage pressure at the center of pipe A in pounds per square inch and in kilopascals
Calculation of Stress in Pipe A
Step 1: Let S represent the stress in the material of the pipe.
Step 2: Let P represent the internal pressure of the pipe.
Step 3: Let D represent the internal diameter of the pipe.
Step 4: Let T represent the thickness of the pipe.
The stress in the material of a pipe subject to internal pressure varies jointly with the internal pressure and the internal diameter of the pipe, and inversely with the thickness of the pipe. Introducing a constant of proportionality, k, the expression becomes:
S = kPD/T
Given that the stress is 100 pounds per square inch when the diameter is 5 inches, the thickness is 0.75 inch, and the internal pressure is 25 pounds per square inch. We can set up the equation as follows:
100 = (k à 25 à 5) / 0.75
Solving for k:
k = 75 / 125 = 0.6
Therefore, the equation representing the relationship becomes:
S = 0.6PD/T
If the internal pressure is 40 pounds per square inch, the diameter is 8 inches, and the thickness is 0.50 inch, then the stress would be:
S = (0.6 Ã 40 Ã 8) / 0.5
S = 384 pounds per square inch