Example How to Design Thin-Walled Vessel under Internal Pressure

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

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^oC. The material of construction will be plain carbon steel. Welds will be fully radiographed. A corrosion allowance of 2 mm should be used.

Solution

Design pressure, take as 10% above operating pressure = (16 – 1) × (1 + 10%) = 16.5 barg = 1.65 N/mm²

Design temperature = 300^oC

From table below, typical design stress is 85 N/mm².

Minimum thickness of cylindrical section

Minimum thickness of cylindrical section is calculated below.

Where:

e         = minimum thickness (mm)

P_i        = internal pressure (N/mm²)

D_i        = internal diameter of vessel (mm)

f         = design stress (N/mm²)

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

1. Try a standard dished head (torisphere):

Crown radius R_c = D_i = 1.8 m

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

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

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.