# 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).