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As you correctly point out there is a pressure gradient behind the object that causes the flow to return to its original path. As to why that pressure gradient exists, image what would happen if the flow continued straight after bending round the object. Behind the cylinder there would be no fluid as it is blocked by the cylinder, essentially there would ...


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I recommend Turbulence: The Legacy of A. N. Kolmogorov by Uriel Frisch. It explains how turbulence is a top-down behavior, large scale turbulence in turn causes turbulence at smaller and smaller scales. This continues until a small enough scale is reached where the energy from the turbulence serves to create more heat on the molecular level. Because of this ...


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The porosity is needed if you are interested in the flow velocity within the porous medium. If you look at $Q/A$ this is also a velocity but with reference to the void or empty channel, as $A$ represents void and matrix. To get the velocity within the medium (in straight flow direction) one needs to correct $A$ by the porosity or void fraction $n$: ...


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The continuity equation only means that the mass flow rate in equals the mass flow rate out. It does not mean that that flow rate never changes; flow in and flow out can both change simultaneously. For a given pressure drop (pressure upstream minus pressure downstream), the flow rate is proportional to the 4th power of radius, according to the ...



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