# Stresses on Thin-walled Pressure Tanks

The circumferential stress, also known as tangential stress, in a tank or pipe can be determined by applying the concept of fluid pressure against curved surfaces. The wall of a tank or pipe carrying fluid under pressure is subjected to tensile forces across its longitudinal and transverse sections.

**Tangential Stress, σ_{t} (Circumferential Stress)**

Consider the tank shown being subjected to an internal pressure

*p*. The length of the tank is

*L*perpendicular to the drawing and the wall thickness is

*t*. Isolating the right half of the tank:

$2T = F$

$2(\sigma_t tL) = pDL$

$2t\sigma_t = pD$

**Longitudinal Stress, σ_{l}**

At the end of the tank, the total stress

*should equal the total fluid force*

*P*= σ_{T}_{l}A_{end}*F*at that end. Since the wall thickness

*t*is so small compared to internal diameter

*D*, the area

*A*of the wall is close to

_{end}*πDt*.

$P_T = F$

$\sigma_lA_{end} = \pi A_i$

$\sigma_l(\pi Dt) = p(\frac{1}{4}\pi D^2)$

$t\sigma_l = \frac{1}{4}p D$

Observe that the tangential stress is twice that of the longitudinal stress.

**Spherical Shell**

If a spherical tank of diameter *D* and thickness *t* contains gas under a pressure of *p*, the stress at the wall can be expressed as:

**Spacing of Hoops of Wood Stave Vessels**

It is assumed that the wood will not resist tension, only the hoops will resist all the tensile stress caused by the internal pressure *p*.

$F = 2T$

$pDs = 2 \sigma_t A_h$

where*s* = spacing of hoops*σ _{t}* = allowable tensile stress of the hoop

*A*= cross-sectional area of the hoop

_{h}*p*= internal pressure in the vessel

*D*= internal diameter of the vessel