Fluid Flow Near a Smooth Surface

Abstract

T T is known from model experiments tha t the -*• air in contact with the surface of a streamline body moves with it, and tha t the regions of easy flow which surround the body are connected to the surface through a relatively thin layer of air, within which the velocity falls to zero. I t is within this boundary layer tha t the resistance to motion is transmitted to the surface. A t speeds of flight, the flow in the boundary layer over the front part of a streamline body is regular, or as it is more often called, laminar, and the elements of fluid passing through any point in the layer behave in a simple and definite manner. At some distance beyond the nose of the body this regular motion breaks down, the movements of the elements become confused, and the flow is said to be turbulent. Measurements made with small Pitot tubes and hot-wire meters have shown tha t the velocity in a turbulent boundary layer falls rapidly as the distance from the surface diminishes. Viscous forces then predominate, and it has been suggested tha t the flow simulates more and more closely a streamline character as the surface is approached. The intensity of surface friction would then be given by the product of the velocity gradient at the surface and the coefficient of viscosity. To determine whether this relation held, Stanton made very careful measurements at the surface of a pipe in which the flow was turbulent. I t was known tha t a reliable measurement of the velocity gradient at the surface could not be obtained with a Pitot tube of the usual type, even when the diameter of the mouth was very small, since a sufficiently close approach to the surface would not be possible: or with an exceedingly fine hot wire, because in addition to the forced convection due to the wind stream there would be a loss of heat by conduction across the thin layer of air between the hot wire and the surface. To overcome these difficulties, an ingenious surface tube (Fig. 1), which had for its inner wall the surface of the pipe itself, was designed and used by Stanton. Because of the extreme smallness of the tube, a special method of calibration had to be devised to determine the effective distance from the surface corresponding to the speed calculated from the pressure measured at the mouth. The product of the measured velocity gradient at the surface and the coefficient of viscosity of the air was found to be in fairly close agreement with the intensity of surface friction. More recently, the intensity of friction on the surface of an aerofoil* has been determined at the National Physical Laboratory from measurements of velocity gradient taken with a particular form of Stanton tube constructed on the top of a circular rod designed to pass with a small clearance through holes drilled in the polished surface of a metal model. Three tubes were used. Photographs of the mouths of these tubes are given in Fig. 1. An interesting feature shown by the calibrations of these tubes is that the ratio of the effective distance to the width of opening increases as the width decreases. The effective distance of the smallest tube (No. 1) is in fact greater than the width of the opening (0.0020 inch), and the observations taken with this tube were not appreciably nearer the surface than those taken with the largest tube No. 3 (0.0044 inch). The distribution of frictional intensity was determined from measurements of velocity taken at 0.002 to 0.003 inch from the surface. The frictional drag of the aerofoil obtained from an integration of the frictional intensities was found to be in fairly