Internal Flow Applications

This chapter treats the flow rate-pressure gradient relationships for internal flow problems in general by considering ducts of noncircular cross sections such as concentric annulus, plane slit, partially filled pipes and valves and fittings. In practice, pipe networks include junctions (union, elbow, bends, tee-junctions, expansion and contraction of flow areas, etc.), flow control valves, globe, gate valves, and flow metering devices. Each of these contributes to the overall frictional pressure gradient in the system. For straight lengths of ducts, it is customary to introduce the hydraulic or equivalent diameter which replaces the pipe diameter in the definitions of the Reynolds number and friction coefficient, and one can then employ the familiar Moody chart to carry out flow calculations. For fittings and valves, the resulting friction losses are strongly influenced by the detailed design of the fittings, valves (partially or fully open, etc.), and the flow regime (laminar or turbulent). This contribution is expressed either in terms of an equivalent pipe length or in terms of a loss coefficient. Both approaches are presented here, though their precision is not as good as that of the Moody chart. Solved examples are presented herein for both Newtonian and non-Newtonian fluids spanning a variety of flow situations elucidating these ideas.