Let the fluid enter with velocity v₁ and at the left end. Let A₁ be the area of cross section and P₁ be the liquid pressure. Let it flow out of a constriction with v₂, and let P₂ , A₂ be the pressure and area of the cross section at the constriction.

Dynamical lift

Consider a ball in spin motion about a horizontal axis and let the ball also have translational motion in horizontal direction but perpendicular to the axis of spin motion as show in fig.8a moving in otherwise still air.

If we consider the frame of reference in which the center of the ball is at rest then air will flow and pass the ball in the opposite direction as shown in Fig.8b.

Now at 'H' velocity of air is increased by the spin of the ball and at 'L' velocity of air is decreased by the spin of the ball.

Therefore pressure at H is decreased and is increased at L according to Bernoulli's equation. As a result net force F acts on the ball from the direction of L to H direction, i.e., the ball is lifted vertically upwards. The lift off of an aeroplane is based on this principle.

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Index

8.1 Hydrostatic pressure in a fluid
8.2 Pascal's Law
8.3 Archimedes' Principle
8.4 Moving Fluids & Bemoulli's Equation

Chapter 9