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. 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. Find the stress when the internal pressure is 40 pounds per square inch if the diameter is 8 inches and the thickness is 0.50 inch.

Answer: 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