Algebra with math

Question

he 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

55

pounds per square inch if the diameter is

9

inches and the thickness is

0.15

inch.

Answer 1

Let S=stress, P=pressure, D=diameter, and T=thickness

S=kPD/T, k is constant of proportionality.

S=100 lbs/in², P=25 lbs/in² , D=5 in, T=0.75 in

.

100×0.75/(5×25)=k, 0.60=k

When P=55 lbs/in², D=9 in, and T=0.15 in

S=0.60×55×9/0.15 or 1,980 lbs/in²