What is the thickness needed for a blank, unstayed, full-hemispherical head with a radius of 700 mm under a pressure of 4000 kPa?

To determine the thickness required for a blank, unstayed, full-hemispherical head under a specific internal pressure, several factors must be considered, including the internal pressure, the radius of the head, and the material's allowable stress.

The formula used for calculating the thickness of a hemispherical head subjected to internal pressure is derived from the principles of pressure vessel design. Specifically, the thickness ( t ) necessary can be expressed as:

[ t = \frac{P \cdot R}{2 \cdot S} ]

Where:

• ( P ) is the internal pressure (in Pascals),

• ( R ) is the radius of the head (in meters),

• ( S ) is the allowable stress of the material (in Pascals).

In this case, substituting the values provided:

• The radius ( R ) is 700 mm (or 0.7 m),

• The internal pressure ( P ) is 4000 kPa (or 4,000,000 Pa).

For a typical material used in such applications, you would have a standard allowable stress value. Assuming a value for the allowable stress typically used in engineering calculations, substituting these quantities into the formula would yield a