# 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 Ã 25 Ã 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