Weird Science

Bernoulli’s Principle in Action: The Mystery of the Floating Ball

Polish ver­sion is here

Ber­no­ulli's prin­ci­ple is one of the fun­da­men­tal equ­a­tions of fluid dyna­mics for ideal flu­ids. It was for­mu­la­ted by Daniel Ber­no­ulli in 1738.

This prin­ci­ple applies under the fol­lo­wing assump­tions:

The equ­a­tion then takes the fol­lo­wing form:

Ilustracja

where:

em - energy per unit mass of the fluid,

ρ (rho) - fluid den­sity,

v - fluid velo­city at the con­si­de­red point,

h - hei­ght in the refe­rence sys­tem where poten­tial energy is mea­su­red,

g - gra­vi­ta­tio­nal acce­le­ra­tion,

p - fluid pres­sure at the con­si­de­red point.

Ana­ly­zing the equ­a­tion leads to an inte­re­sting conc­lu­sion: if we con­si­der a pipe with a vary­ing cross-sec­tio­nal area thro­ugh which an incom­pres­si­ble fluid flows in a lami­nar man­ner, it logi­cally fol­lows that the flow velo­city will be higher where the pipe's cross-sec­tio­nal area is smal­ler. This results in a less intu­i­tive effect: the pres­sure within the fluid is lower where the flow is faste­r—that is, at the pipe's con­stric­tion! This phe­no­me­non is known as the hydro­dy­na­mic para­dox.

Expe­ri­ment

Let’s take a ping-pong ball. It is light eno­ugh to be sui­ta­ble for our expe­ri­ment. We also need a source of com­pres­sed air. An old-style vacuum cle­a­ner with a hose attach­ment at the air outlet is ideal. A hair­dryer (with the highest pos­si­ble air­flow set­ting) can also be used. Direct the stream of fast-moving air upward and place the ball in it. The ball will start to levi­tate within the air­flow. You can see this effect in my video below:

How do we explain this? Air beha­ves simi­larly to an ideal fluid, so we can rea­so­na­bly apply the equ­a­tion above. The air from the vacuum cle­a­ner moves at high speed rela­tive to the sur­ro­un­ding air. This results in a pres­sure drop within the air­flow. The pres­sure dif­fe­rence between the inside of the air­flow and the sur­ro­un­ding air keeps the ball suspen­ded within the stream.

Have fun expe­ri­men­ting! :)

Fur­ther rea­dings:

Marek Ples

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