**1.1. Flows driven by a constant pressure gradient through a pipe of circular cross section**

When the flow of a Newtonian fluid in a pipe of circular cross section is driven solely by a constant pressure gradient, the resulting velocity distribution is a quadratic function of the radial distance from the axis of the pipe. The velocity profile of such a flow has, therefore, a parabolic distribution in which the maximum velocity occurs on the axis of the pipe. A graphical representation of this type of velocity is shown in Figure 1.

**Figure 1.** The parabolic velocity profile for flow driven by a constant pressure gradient in a circular pipe
