Pipe Thickness Calculation Based on Pressure and Stress

To determine the minimum thickness of the pipe, we can use the formula for hoop stress in thin-walled pressure vessels. The hoop stress ($ \sigma_h $) is related to the internal pressure ($ p $), pipe diameter ($ D $), and wall thickness ($ t $) by the equation:

$ \sigma_h = \frac{pD}{2t} $

For the pipe to be safe, the calculated hoop stress must not exceed the permissible tensile stress ($ \sigma_{perm} $). Therefore, we set $ \sigma_h = \sigma_{perm} $ to find the minimum thickness.

Given:

• Diameter ($ D $) = 80 cm
• Internal Pressure ($ p $) = $ 20\ kg/cm^2 $
• Permissible Tensile Stress ($ \sigma_{perm} $) = $ 1000\ kg/cm^2 $

Calculating Minimum Pipe Thickness

We need to find the minimum thickness ($ t $). Rearranging the formula $ \sigma_{perm} = \frac{pD}{2t} $ to solve for $ t $, we get:

$ t = \frac{pD}{2\sigma_{perm}} $

Now, substitute the given values into the formula:

$ t = \frac{(20\ kg/cm^2) \times (80\ cm)}{2 \times (1000\ kg/cm^2)} $

$ t = \frac{1600}{2000}\ cm $

$ t = 0.8\ cm $

Thus, the minimum required thickness of the pipe is 0.8 cm.