Plate Theory and Extensions - The Compressibility of the Mobile Phase > Page 20

Consider the column depicted in Figure 3.

Figure 3. Pressure and Velocity Distribution Along a Packed Column

The column may be packed or an open tube but in this example, a packed column will be specifically considered. Let the column have a length (L) and inlet and outlet pressures and inlet and outlet velocities of (P_i), (P_o), (u_i) and (u_o), respectively. The pressure and velocity at a distance (x) from the front of the column will be defined as (P_x) and (u_x), respectively. According to D'Arcy's equation for fluid flow through a packed bed, at any point in the column,

                                                                           (22)

                         where (h) is the viscosity of the gas, 

                           and (K) is a constant.

(The D'Arcy equation is the equation that describes the flow of fluid through a packed bed and its derivation will be found in most physics textbooks dealing with the Properties of Matter. If a capillary column is considered, then the Poiseuille's equation for fluid flow through an open tube would be used and this will also be found in the same type of reference).