# Line theory: Line pressure effects

OrcaFlex reports two different types of tension – the effective tension, $\Te$, and the wall tension, $\Tw$. These two are related by the formula $$\label{Tw} \Tw = \Te + (\peei\ai - \po\ao)$$ where

$\peei=$ internal pressure, calculated from the contents pressure, allowing for the static pressure head due to the instantaneous height difference between the point and the specified reference Z level.

$\po=$ external (i.e. surrounding fluid) pressure. This is assumed to be zero at and above the mean water level; below that level it is calculated allowing for the static pressure head due to the instantaneous height difference between the point and the mean water level.

$\ai=$ internal cross section area of the stress annulus, given by $\ai = \frac{\pi}{4} I\!D_\textrm{stress}^2$ where $I\!D_\textrm{stress}$ is the internal stress diameter of the line type.

$\ao=$ external cross section area of the stress annulus, given by $\ao = \frac{\pi}{4} O\!D_\textrm{stress}^2$ where $O\!D_\textrm{stress}$ is the external stress diameter of the line type.

 Note: OrcaFlex uses the stress diameters, not the line type diameters, to calculate $\ai$ and $\ao$. This is equivalent to assuming that the annulus between the stress OD and line type OD carries an axial load which matches the ambient external pressure, and the annulus between the stress ID and the line type ID carries an axial load which matches the ambient internal pressure.
 Warning: Before using the wall tension and stress results you should confirm that this model is suitable for the case you are modelling. We believe it is suitable for many cases of attached buoyancy and for non-structural linings, but it may not be suitable for bonded buoyancy or structural linings. If it is not suitable you should do your own separate calculation of wall tension and stresses.

## Explanation of wall tension formula

To understand this formula, and the difference between effective tension and wall tension, consider the axial forces acting at the mid-point of a segment. The nodes on either side represent a length of pipe plus its contents. More importantly, the forces on them are calculated as if the length of pipe represented has end caps which hold in the contents and which are exposed to the internal and external pressure. The diagram below illustrates these tension and pressure forces; the equation above is simply the force balance equation for this diagram.

 Figure: Tension and pressure forces
 Notes: Both effective tension and wall tension are relevant to the question of pipe buckling. For buckling of the pipe as an Euler strut, effective tension is the governing parameter – when it is negative the strut is in effective compression. On the other hand, local buckling of the pipe wall is determined by wall tension. (Note that OrcaFlex does not model local buckling, which depends critically on details of the pipe construction and is therefore beyond the scope of the program.) For cables, umbilicals and ropes, the internal pressure term $\peei\ai$ is not relevant. However, the external pressure term $\po\ao$ does still apply, and the actual tension in the cable is the wall tension $\Tw$ defined in (\ref{Tw}) above. For chains, neither of the pressure terms apply and the true tension in the chain is the effective tension $\Te$.