Measurements with a half-pitot tube

Abstract

The use of a half-pitot tube for measuring the surface friction of a fluid flowing past a smooth surface was introduced by the late Sir Thomas Stanton (1920). The sketch, fig. 1, shows how the method works. In fig. 1, A is the half-pitot. This is a pitot tube set facing the fluid, one wall of which could, in Stanton’s apparatus, be raised or lowered. The other wall is the smooth surface over which friction measurements are to be made. The difference in pressure between the fluid in the half-pitot tube and fluid in a tube connected to a hole ( C , fig. 1) in the surface is measured by means of a manometer M . To calibrate the instrument it was set up in a pipe through which fluid was flowing at a speed below the critical velocity. Under these conditions the distribution of velocity is parabolic across the section of the tube, and the tangential stress at the fluid surface is known. Stanton expressed his results in terms of an “effective distance” d '. This is the distance from the wall at which the velocity, v , is such that the pressure in the half-pitot, p , is equal to ½ρ v 2 . When d , the opening of the pitot, was large it was found that d '/ d was approximately ½. On the other hand, it was found that when d is very small d '/ d increases. Stanton’s measurements of corresponding values of d ' and d seem to indicate that d ' tends to a finite limit as d tends to zero, so that d '/ d would, in that case, tend to become infinite when d is very small. This conclusion cannot, however, be regarded as an experimentally established fact because the highest value of d '/ d obtained in Stanton’s experiments was only 2·2.