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I am studying fluid dynamics on my own and it is commom to see this assumption. I am asking this here because I didn't find any satisfactory answer. For example, I am studying a problem that is as follows

''Determine the form of a jet emerging from an infinitely long slit in a plane wall. Let the wall be along the $x$-axis in the $xy$-plane, and the aperture be the a segment in the $x$-axis, the fluid ocupying the half plane $y>0$. Far from the wall ($y\to\infty$) the fluid velocity is zero, and the pressure is $p_0$.''

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    $\begingroup$ The question is not so clear, please add some more information about your problem. If you are studying the problem of an object moving inside a fluid the assumption of constant velocity/pressure at infinity is due to experimental evidence: if an object is falling at 1km distance from you (observer), you don't feel any wind. $\endgroup$ – Matteo Nov 5 '17 at 21:43
  • $\begingroup$ Okay, I've edited. $\endgroup$ – Slayer147 Nov 5 '17 at 22:44
  • $\begingroup$ It is one possible boundary condition and part of the problem statement. If you want you may assume some other boundary condition. $\endgroup$ – Deep Nov 7 '17 at 4:47
  • $\begingroup$ 'Far from the wall ($y\rightarrow\infty$) the fluid velocity is zero, and the pressure is $p_0$' Choosing boundary conditions strategically can simplify the solution of a PDE significantly. In this case this specific boundary condition allows the jet to be solved with the use of a similarity solution. $\endgroup$ – nluigi Feb 1 '18 at 10:52
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In order for a PDE (read: the Navier-Stokes eqs.) to have a unique solution, it is necessary to impose adequate boundary conditions.

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