In flow through tube banks, there occur irreversible energy changes due to friction. These energy changes are manifested as pressure losses over the bank. The calculation of these pressure changes is vital to the design of the circulation system (pumps, fans, natural circulation). Conversely, the energy changes are associated with forces in the individual tubes in the bank. These forces are important in assessing and calculating phenomena such as tube vibration. Although the pressure losses and forces on the tubes are clearly linked, it

is convenient to treat them separately in the present context, dealing first with the forces on die tubes.

A. Drag on a tube in a bank

Flow of a fluid through a tube bank generates 3 force on each separate tube, the direction of which is not necessarily coincident with that of the flow. The total drag force is the sum of the skin friction and the form drag. Its longitudinal component is known as the drag force F_x and the transverse component as the lift force F_y. The forces on a tube in a bank may be described in terms of the skin friction coefficient c_f and the drag coefficient c_D. The skin friction coefficient is defined (Achcnbach, 1969, Cebeci and Bradshaw, 1977) by

\[\label{eq1} c_{f}=\frac{2\tau_{wx} }{\rho u^2} \tag{1}\]