# Viscous fluid flowing around obstacle: would it deflect earlier?

Consider a viscous fluid, flowing linearly (say, with velocity $\vec u = [1,0]$ everywhere). Then an obstacle is put in the flow. Would a highly viscous fluid start deflecting around the obstacle earlier (more up-stream) than one with low viscosity?

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The dominant cause behind the fluid deflecting before reaching an obstacle is sound wave propagation. One might guess then that there is little, if any, change with the viscosity of the fluid. In fact, for high Reynolds numbers that is indeed the case. For low Reynolds numbers I can't say that I know what will happen. The question really needs to be asked with regard to both Mach number and Reynolds number. – SimpleLikeAnEgg Feb 28 '14 at 18:45
For stokes-flow ($Re << 1$, $M << 1$) there is an analytic solution for flow over a sphere (see "Viscous Fluid Flow" by White). It turns out that the solution is entirely independent of the fluid's viscosity. I think you should rephrase your question to indicate fixed, moderate, Mach numbers and moderate Reynolds numbers. That is probably the range where what you are asking can occur. My intuition as to the how the deflection varies with Reynolds number isn't quite able to answer your question though. – SimpleLikeAnEgg Feb 28 '14 at 19:13