# Fluid mechanics navier stokes flow around geometry

by joshmccraney
Tags: flow, fluid, geometry, mechanics, navier, stokes
 P: 327 hey pf! i am studying fluid mechanics and was wondering if any of you are familiar with a flow around some geometry? for example, perhaps a 2-D fluid flowing around a circle? if so please reply, as i am wondering how to model the navier-stokes equations. i'll be happy to post the equations and my thoughts if you would like me to? for the record, i am using white's book, and while it is great, i have not seen any examples dealing with 2-D flow around geometry. so far it's been flow in between plates and against a wall. thanks so much for your support and interset! josh
 P: 14 Take a look at this site: http://www.math.nyu.edu/faculty/childres/chpseven.PDF
 PF Gold P: 1,491 The problem is that in general you can't find a solution to the Navier-Stokes equations analytically, especially external flows. There are some that are possible, like laminar flow over a flat plate (the Blasius solution), but these are relatively few and far between. Except at very low Reynolds number, the 2-D flow around a circle (or cylinder, for example) is one such flow where an analytical solution is not possible for a viscous flow. You have to deal with flow separation and an unsteady wake (for example, try Googling von Kármán vortex street).
 P: 327 Fluid mechanics navier stokes flow around geometry thanks you guys! hey bonehead, what do we consider "very low Re number"? would it be possible to model, say, syrup sliding over a plate with a slight angle as a low reynolds number, or is this too fast?
 PF Gold P: 1,491 That depends on the context. With a cylinder in a viscous flow, very low Reynolds number in regards to whether Stokes flow is valid is typically considered to be $Re \ll 1$. It doesn't really make sense to just ask what constitutes very low Reynolds number in a random situation since you aren't really specifying in that case what physical phenomenon you are hoping to capture or avoid. For example, in Stokes flow, very low Reynolds number represents the region where the assumptions used in deriving it are valid.

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