The value of the average velocity Vavg at some stream cross-section is
determined from the requirement that the conservation of mass principle be
satisfied (Fig. 8–2). That is,
(8–1)
where m
.
is the mass flow rate, r is the density, Ac
is the cross-sectional area,
and u(r) is the velocity profile. Then the average velocity for incompressible
flow in a circular pipe of radius R can be expressed as
(8–2)
Therefore, when we know the flow rate or the velocity profile, the average
velocity can be determined easily.