When doing the application problem state the unknown quantit

When doing the application problem state the unknown quantity, present the working equation, in an orderly fashion solve the equation, circle the final answer, finally, give an intelligent conclusion. Failure to follow application problem directions will minimize partial credit for those problems. The stress S in the material of a pipe subject to internal pressure varies jointly with the internal pressure P and the internal diameter d of the pipe and inversely with the thickness t of the pipe. The stress is 100 pounds per square inch (psi) when the diameter is 5 inches, the thickness is 0.75 inch, and the internal pressure is 25 pounds per square inch. Find the thickness when the stress is 384 psi. the internal pressure is 40 pounds per square inch and the diameter is 8 inches.

Solution

S P

Sd

SPd

S1/t

combining we get

SPd/t

eliminating proportionality

S=k Pd/t

S/Pd/t=k

St/Pd=k

S₁t₁/P₁d₁=S₂t₂//P₂d₂

need to find t₂

t₂ =S₁t₁/P₁d₁ (P₂d₂₎ )/S₂

  =100*0.75/ 25 5(40*8)/384

=100*0.75(40*8)/25*5*384

t₂ =0.5 inch

thickness=0.5inch

thickness decreases from 0.75 inch to 0.5 inch as stress increases from 100 psi to 384 psi