Abstract:
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.