HYDRODYNAMICAL PROBLEMS SUGGESTED BY PITOT'S TUBES.
[Proceedings of the Royal Society, A, Vol. xci. pp. 503 — 511, 1915.]
* THE general use of Pitot's tubes for measuring the velocity of streams
Qggests hydrodynamical problems. It can hardly be said that these are of Tactical importance, since the action to be observed depends simply upon Bernoulli's law. In the interior of a long tube of any section, closed at the irther end and facing the stream, the pressure must be that due to the velocity y) of the stream, i.e. ^pvs, p being the density. At least, this must be the ase if viscosity can be neglected. I am not aware that the influence of iscosity here has been detected, and it does not seem likely that it can be Bnsible under ordinary conditions. It would enter in the combination v/vl, rhere v is the kinematic viscosity and I represents the linear dimension of ie tube. Experiments directed to show it would therefore be made with nail tubes and low velocities.
In practice a tube of circular section is employed. But, even when viscosity i ignored, the problem of determining the motion in the neighbourhood of a ircular tube is beyond our powers. In what follows, not only is the fluid ipposed frictionless, but the circular tube is replaced by its two-dimensional nalogue, i.e. the channel between parallel plane walls. Under this head two roblems naturally present themselves.
The first problem proposed for consideration may be defined to be the ow of electricity in two dimensions, when the uniformity is disturbed by the cesence of a channel whose infinitely thin non-conducting walls are parallel > the flow. By themselves these walls, whether finite or infinite, would luse no disturbance ; but the channel, though open at the finite end, is sup-)sed to be closed at an infinite distance away, so that, on the whole, there no stream through it. If we suppose the flow to be of liquid instead of ectricity, the arrangement may be regarded as an idealized Pitot's tube,ment, suggested by the case of the mirror above referred to; the comparison was between a rectangular plate 2 inches x 1^- inches and an elongated strip '51 inch broad, the length of the strip being parallel to the needle, i.e. vertical in use. At first this length was a little in excess, but was cut down until the resistance balance was attained. For this purpose it seemed that equal areas were required to an accuracy of about one per cent., nearly on the limit set by the delicacy of the apparatus.