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On substitution of this expression for the pressure function into the second Navier-Stokes equation we may deduce a system which is formally identical to that arising from the standard boundary layer approximation for axially symmetric pipe flow, namely (9).
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Under these assumptions, along with the usual boundary layer approximation, the governing equations for the flow in cylindrical coordinates are as follows (Mukhopadhyay and Ishak 2012) and (Saffman 1962): {kern15pt} {fontsize{8.5}{frac{partialigned} {frac{partial w}{partial z}}+{frac{1}{r}}{frac{partial (ru)}{partial r}}=0, end{aligned}}} (1).
All results are valid for the diffusive boundary layer approximation.
The boundary layer approximation is used commonly as an effective approach for simplification of the laminar wall jet problems.
Content includes kinematics, macroscopic balances for linear and angular momentum, the stress tensor, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows.
The practical effects of boundary layer approximation in the resulting controller design are examined.
Boundary layer approximation provides the dependence of the statistical moments of the RTD on Péclet number.
The thin acoustic boundary layer approximation has been made in determining fluid vorticity in the vicinity of solid boundaries.
The equation of motion for wave-free flow of the falling liquid film and the convective-diffusion equation for mass transfer in the falling liquid film, based on the boundary layer approximation, were solved simultaneously.
The boundary layer approximation and the small magnetic Reynolds number assumptions are used.
The boundary layer separates from the surface at s = s c, and beyond this value, the boundary layer approximation is no longer valid.
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CEO of Professional Science Editing for Scientists @ prosciediting.com