Flow in a Circular pipe (Integral Analysis)

A classical example of a viscous incompressible flow includes the motion of a fluid in a closed conduit. It may be a pipe if the cross-section is round or duct if the conduit is having any other cross-section. The driving force for the flow may be due to the pressure gradient or gravity. In practical point of view, a pipe/duct flow (running in full) is driven mainly by pressure while an open channel flow is driven by gravity. However, the flow in a half-filled pipe having a free surface is also termed as open channel flow . In this section, only a fully developed laminar flow in a circular pipe is considered. Referring to geometry as shown in Fig. 5.4.1, the pipe having a radius is inclined by an angle with the horizontal direction and the flow is considered in x- direction. The continuity relation for a steady incompressible flow in the control volume can be applied between section ‘1' and ‘2' for the constant area pipe (Fig. 5.4.1).

Fig. 5.4.1: Fully developed flow in an inclined pipe.

(5.4.1)

Neglect the entrance effect and assume a fully developed flow in the pipe. Since there is no shaft work or heat transfer effects, one can write the steady flow energy equation as,

(5.4.2)