# Loss factor of steel pipes

The loss in steel pipes is given in the IEC by two empirical formulae, one for cables where the cores are bound in close trefoil formation and the other where the cores are placed in a more open configuration (cradled) on the bottom of the pipe. We calculate the ratio of the pipe inside diameter to cable outside diameter and if this ratio is larger than 3, cradled configuration is assumed otherwise triangular.

To be noted:

• The loss-factor is per phase.
• The IEC notes that these formulae have been empirically obtained in the United States of America and at present apply only to steel pipe sizes and steel types used in that country.
• The formulae given apply to a frequency of 60 Hz. For lower frequencies, the induced current in the ferromagnetic steel pipe will be lower and for higher frequencies it will be higher. So for other frequencies, each formula is multiplied by a correction factor. For 50 Hz, the factor is 0.760 and for 16.7 Hz it is 0.147.
• Symbol
$\lambda_{3}$
Formulae
 $\frac{1.0 \cdot 10^{-5} \left(- 0.001485 Di_{d} + 0.0115 s_{c}\right)}{R_{c}}$ three single-core cables in trefoil in magnetic steel pipe $\frac{1.0 \cdot 10^{-5} \left(0.00226 Di_{d} + 0.00438 s_{c}\right)}{R_{c}}$ three single-core cables in cradled formation in magnetic steel pipe $\frac{\sqrt{15} f^{2} \sqrt{\frac{1}{f}}}{1800}$ multiplication factor for other frequencies than 60 Hz $0$ steel pipe is non-magnetic
Related
$Di_{d}$
$R_{c}$
$s_{c}$
Used in
$f_{SHF}$
$I_{c}$
$T_{eq}$
$W_{h}$
$W_{p}$