The pressure in a two-dimensional static hole at low Reynolds numbers

Abstract

A description is given of an arithmetical method for obtaining solutions for steady incompressible viscous flow at low Reynolds numbers in the form of expansions in powers of the Reynolds numbers. The method has been used to find a solution for the flow past the mouth of a two-dimensional static hole. The pressure in the hole is determined and it is shown that the disturbance to the flow caused by the hole produces an error in the pressure recorded in the hole. The error is positive and if it is expressed in non-dimensional form, i.e., (pressure error/½pU2), its magnitude decreases with increasing Reynolds number for the range for which the solution is valid. The theoretical results are compared with experimental results obtained for the error in the pressure recorded by a circular static hole.