### Pressure Vessel ,Thin Wall Hoop and Longitudinal Stresses

**Mechanics of Materials **

**Pressure Vessel Design and Calculators **

For the thin-walled assumption to be valid the vessel must have a wall thickness of no more than about one-tenth (often cited as one twentieth) of its radius. The classic equation for hoop stress created by an internal pressure on a thin wall cylindrical pressure vessel is:

- σ
_{θ}= PD_{m }/2t for the Hoop Stress

Thin Wall Pressure Vessel Hoop Stress Calculator

where:

*P* = is the internal pressure

*t* = is the wall thickness

*r* = is the inside radius of the cylinder.

Dm = Mean Diameter (Outside diameter - t). Mean diameter of OD and ID...

σ_{θ} = is the hoop stress.

The hoop stress equation for thin shells is also approximately valid for spherical vessels, including plant cells and bacteria in which the internal turgor pressure may reach several atmospheres.

Inch-pound-second system (IPS) units for *P* are pounds-force per square inch (psi). Units for *t*, and *d* are inches (in). SI units for *P* are pascals (Pa), while *t* and *d*=2*r* are in meters (m).

Longitudinal Stress Thin Walled Pressure Vessel:

When the vessel has closed ends the internal pressure acts on them to develop a force along the axis of the cylinder. This is known as the axial or longitudinal stress and is usually less than the hoop stress.

Though this may be approximated to

Where:

- P = Pressure

d = Mean Diameter (Outside diameter - t). Mean diameter of OD and ID...

t = Wall Thickness

= Logitudinal Stress

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