In this post, I want to share a simple example on how to design thin-walled vessel under internal pressure. Please check my previous post about the method on how to estimate minimum thickness of vessel component (shell, flat end closures, domed head closures).

__Example__

__Example__

Estimate the thickness required for the component parts of the vessel shown in the diagram.

The vessel is to operate at a pressure of 16 bar (absolute) and design temperature of 300^{o}C. The material of construction will be plain carbon steel. Welds will be fully radiographed. A corrosion allowance of 2 mm should be used.

__Solution__

__Solution__

Design pressure, take as 10% above operating pressure = (16 – 1) × (1 + 10%) = 16.5 barg = 1.65 N/mm^{2}

Design temperature = 300^{o}C

From table below, typical design stress is 85 N/mm^{2}.

*Minimum thickness of cylindrical section *

*Minimum thickness of cylindrical section*

Minimum thickness of cylindrical section is calculated below.

Where:

*e * = minimum thickness (mm)

*P _{i} * = internal pressure (N/mm

^{2})

*D _{i}* = internal diameter of vessel (mm)

*f* = design stress (N/mm^{2})

Calculation of minimum thickness of cylindrical section:

*e *= 1.65 × 1800 / (2 × 85 – 1.65) = 17.64 mm

Add corrosion allowance = 17.64 + 2 = __19.64 mm__

*Domed head*

*Domed head*

**1. Try a standard dished head (torisphere):**

Crown radius *R _{c} *=

*D*= 1.8 m

_{i}Knuckle radius is 6% of *R*_{c} to prevent buckling = 0.108 m

A head of this size would be formed by pressing: no joints, so *J *= 1, then concentration factor (*C*_{s}) is

Minimum thickness for dished head (torisphere) is calculated using equation below:

Where:

*C _{s }*= stress concentration factor for torispherical heads

*R _{c} * = crown radius

*R _{k }*= knuckle radius

For formed heads (heads without joints), the joint factor *J* is assumed to be 1.0.

Then, minimum thickness for dished head is:

*e *= (1.65 × 1800 × 1.77) / [2 × 85 × 1 + 1.65 × (1.77 – 0.2)] = __30.47 mm__

**2. For standard ellipsoidal head, ratio major:minor axes = 2:1**

The minimal thickness necessary for this ratio can be determined using the equation below:

Then, minimum thickness is:

*e *= (1.65 × 1800) / (2 × 1 × 85 – 0.2 × 1.65) = __17.50 mm__

So, an ellipsoidal head would be probably the most economical.

*Flat head*

*Flat head*

For bolted cover with a full face gasket, take design constant *C _{p}* = 0.4

Take nominal plate diameter, *D _{e} *= 2 m

The minimum thickness of flat head is calculated using equation below:

Therefore, minimum thickness is:

*e *= (0.4 × 2000 × (1.65/85)^{0.5} = __111 mm__

This shows inefficiency of flat cover. The required thickness will be large.

__Free Spreadsheet__

__Free Spreadsheet__

Want to learn the calculation? Feel free to download the spreadsheet of the example above.

That’s all the example on how to design thin-walled vessel under internal pressure. I hope you find this post useful.