The value of the average velocity Vavg at some streamwise 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.
The value of the average velocity Vavg at some streamwise cross-section isdetermined from the requirement that the conservation of mass principle besatisfied (Fig. 8–2). That is,(8–1)where m.is the mass flow rate, r is the density, Acis the cross-sectional area,and u(r) is the velocity profile. Then the average velocity for incompressibleflow 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 averagevelocity can be determined easily.
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