Solved problems in fluid flow concepts

Ex.1
Write the conservation-of-mass relation for steady flow through a streamtube (flow everywhere parallel to the walls) with a single one-dimensional exit 1 and inlet 2 (Fig. E3.3).
Solution
For steady flow Eq. (3.24) applies with the single inlet and exit
m?= ?1A1V1 = ? 2A2V2 = const
Thus, in a streamtube in steady flow, the mass flow is constant across every section of the tube.
If the density is constant, then
Q = A1V1 = A2V2 = const or V2 = A1 V1/A2
The volume flow is constant in the tube in steady incompressible flow, and the velocity increases as the section area decreases
Ex. 2:
For steady viscous flow through a circular tube (Fig. E3.4), the axial velocity profile is given approximately by:
Ex. 2:
For steady viscous flow through a circular tube (Fig. E3.4), the axial velocity profile is given approximately by:














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