Determine the gage pressure at the center of pipe A in pounds per square inch and in kilopascals.

the stress is 384 pounds per square inch.

Step-by-step explanation:

Let S represent the stress in the material of the pipe.

Let P represent internal pressure of the pipe.

Let D represent internal diameter of the pipe.

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

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. It means that

100 = (k × 25 × 5)/0.75

125k = 100 × 0.75 = 75

k = 75/125 = 0.6

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 × 40 × 8)/0.5

S = 384

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