The laminar hole pressure for Newtonian fluids
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For flows with wall turbulence the hole pressure, P H , was shown empirically by Franklin and Wallace (J Fluid Mech, 42, 33–48, 1970) to depend solely on R +, the Reynolds number constructed from the friction velocity and the hole diameter b. Here this dependence is extended to the laminar regime by numerical simulation of a Newtonian fluid flowing in a plane channel (gap H) with a deep tap hole on one wall. Calculated hole pressures are in good agreement with experimental values, and for two hole sizes are well represented by: (P H −P HS )/τ w = √(k 2 + c 2 R + 2 )−k, where the Stokes hole pressure P HS /τ w = s (b/H)3, k, c, s are fitted constants, and τ w is the wall shear stress.
KeywordsReynolds Number Wall Pressure Stoke Flow Hole Size Disturbance Pressure
This work was supported by NSF (grant number CTS-0326702). The authors gratefully acknowledge the advice and guidance of George Em Karniadakis during the course of this work.
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