Exact Solutions to the Navier-Stokes Equation
Unsteady Flow in a Tube
Consider flow in a circular tube subject to a step change in
pressure as shown in Figure 4. The Navier-Stokes equation reduces to
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(37)
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Introducing dimensionless variables,
,
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(38)
|
we find
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(39)
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Figure 4. Schematics of flow in a tube subject to step
change in pressure. |