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Full text of "Scientific Papers - Vi"

1914]
FLUID  MOTIONS
239
closely along the edges, give the right kind of tube, and may be made airtight with pasted paper or with sealing-wax. Perhaps a square section requiring four pieces is best. It is worth while to remark that there is no stretching of the cardboard, each side being merely bent in one dimension. A model is before you, and a study of it forms a simple and useful exercise in solid geometry.
Another form of the experiment is perhaps better known, though rather more difficult to think about. A tube (fig. 3) ends in a flange. If I blow through the tube, a card presented to tlie flange is drawn up pretty closely, instead of being blown away as might be expected. When, we consider the
Pig. 8.
J?ig. 4.
matter, we recognize that the channel between the flange and the card through which the air flows after leaving the tube is really an expanding one, and thus that the inner part may fairly be considered as a contracted place. The suction here developed holds the card up.
A slight modification enhances the effect. It is obvious that immediately opposite the tube there will be pressure upon the card and not suction. To neutralize this a sort of cap is provided, attached to the flange, upon which the objectionable pressure is taken (fig. 4). By blowing smartly from the mouth through this little apparatus it is easy to lift and hold up a penny for a short time.
The facts then are plain enough, but what is the explanation ? It is really quite simple. In steady motion the quantity of fluid per second passing any section of the tube is everywhere the same. If the fluid be incompressible, and air in these experiments behaves pretty much as if it were, this means that the product of the velocity and area of cross-section is constant, so that at a narrow place the velocity of flow is necessarily increased. And when we enquire how the additional velocity in passing from a wider to a narrower place is to be acquired, we are compelled to recognize that it can only be in consequence of a fall of pressure. The suction at the narrows is the only result consistent with the great principle of conservation of energy;ory can give a satisfactory account.length.