The Flow past a Pitot Tube at Low Reynolds Numbers. Part I. The Numerical Solution of the Navier-Stokes Equations for Steady Viscous Axi-symmetric Flow. Part II. The Effects of Viscosity and Orifice Size on a Pitot Tube at Low Reynolds Numbers

Abstract

Part I. In this Report numerical methods used to solve the Navier-Stokes equations for steady viscous two-dimensional flow are extended to include the case of axial symmetry. The equations and their finite difference approximations are derived working in cylindrical polar co-ordinates with the Stokes' stream function and the vorticity as variables. A new method of dealing with the boundary conditions is given. Part II. The effects of viscosity and orifice size on a blunt-nosed pitot tube have been theoretically investigated up to a Reynolds number of ten, where the Reynolds number has been based on the radius of the tube.