Extra Column Dispersion - Dispersion in Tubular Conduits > Page 24
There is, however, a limit to which (r) can be reduced as, from Poiseuille's equation, the pressure drop across the tube is given by,
Thus, as ,
Thus, the pressure drop across the connecting tube increases inversely as the fourth power of the tube radius. It is clearly inadvisable to dissipate a significant amount of the available pressure across a connecting tube, and so there will be a lower limit to which (r) can be reduced in order to minimize dispersion.
Changing the length of the connecting tube, however, has the same effect on both dispersion and pressure drop. Reducing (l) will linearly reduce dispersion and at the same time linearly reduce the pressure drop across the connecting tube. It follows, that reducing the length of the connecting tube is the best method of controlling conduit dispersion as, by making (l) as small as possible, both the dispersion and the pressure drop can be minimized.