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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 80 pounds per square inch if the diameter is 3 inches and the thickness is .2 inch.

Respuesta :

Answer:

720 pounds per square inch

Explanation:

If the stress in the material varies jointly with the internal pressure and the internal diameter and inversely with the thickness of the pipe, we can write the following equation

[tex]S=k\frac{PD}{T}[/tex]

Where S is the stress, P is the internal pressure, D is the diameter, T is thickness, and k is the constant of proportionality.

Then, we know that S = 100 when D = 5, T = 0.75 and P = 25. Replacing the values and solving for k, we get:

[tex]\begin{gathered} 100=k\frac{25(5)}{0.75} \\ \\ 100=k(166.667) \\ \\ \frac{100}{166.667}=k \\ \\ 0.6=k \end{gathered}[/tex]

Now, the equation for the stress is

[tex]S=0.6\frac{PD}{T}[/tex]

So, we can calculate the strees when P = 80, D = 3 and T = 0.2 as follows

[tex]\begin{gathered} S=0.6\cdot\frac{80(3)}{0.2} \\ \\ S=720 \end{gathered}[/tex]

Therefore, the answer is 720 pounds per square inch

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