In hydraulics, pipe flow is commonly considered as a full-pipe pressuredriven flow occurring in closed conduits of a circular cross-section. The two basic equations that describe pipe flow are the continuity (or mass conservation) equation and the energy equation. Assuming incompressible fluid and considering a pipe with varying cross-sectional area, the continuity equation can be written as

Q = u1A1 = u2A2 = constant (4.1)

Q u

D u

D = = =1

4 4 pi pi

constant (4.2)

where Q is the volumetric discharge, ui is the uniform cross-sectional velocity, and Ai and Di are the cross-sectional area and pipe diameter, respectively, at point (i). However, in the majority of the applications the pipe cross-section is constant. Only in special cases (e.g. transitional sections connecting pipes of different diameter) does the pipe vary in diameter.