Tube and Cone Experiment
To show the difference between the effects of radial-expansion of fluid and fluid velocity, the author designed a simple experiment. This experiment is to blow air through two similar conduits, a tube and a cone. The cone allows the air to expand radially while the tube does not. In practice the cone collapses, demonstrating that radial-expansion induces lift. The tube shows no such effect. If the Bernoulli Principle were really applicable, both the tube and the cone would collapse.
You can try this at home
Get some soft paper, like newspaper, and make a tube about six inches long and about an inch in diameter. Also, make a cone about six inches tall and about five inches wide at the wide end and about an inch wide at the narrow end. Blow air through the tube. If Bernoulli's Principle applied, the tube would collapse since the fast air inside it would have lower pressure. The tube does not collapse so Bernoulli's Principle does not apply. Now blow air through the small end of the cone. The cone does collapse since the shape allows the air to radiate outward.
An early paper tube and paper cone experiment
Physics of Tubes and Cones
Since volume is proportional to the square of the radius, density and pressure are both inversely related to the square of the radius, per: P1 / P0 = r02 / r12. For a tube, r0 = r1. Therefore, P1 = P0 and this confirms the observation that there is no pressure decrease induced by high velocity air passing through a paper tube. Contrary to popular interpretations of Bernoulli's Principle, velocity, by itself, does not induce pressure decrease. Radially expanding flow through a cone, induces pressure decrease. For an inverted cone r0 > r1, and therefore P1 > P0; air flowing into the wide end of a cone does not cause it to collapse.
In practice, high-pressure compressible fluids, escaping through an orifice into a low-pressure area tend to expand, by radial Momentum, into a cone and induce even lower pressure. The shape of the cone depends on the compressibility of the fluid and the orifice exit velocity. Air tends to escape from an automobile tire into a radiating cone. Water, out of a faucet, tends to stay in a cylinder and may even taper, due to the effect of gravity to increase velocity.