Aristotele di Stagira (384-322 a.C.) Archimede di Siracusa (287-212 a.C.) Erone di Alessandria (II-I a.C.)

I PRECURSORI

Il RINASCIMENTO

Leonardo da Vinci (1452-1519)

LA SCIENZA NUOVA

Galileo Galilei (1564-1642)

LA FLUIDOSTATICA

B. Pascal (1623-1662)

S. Stevino (1548-1620)

E.Torricelli (1564-1642)

IL PENSIERO MATEMATICO SI APPLICA ALLA FLUIDODINAMICA

I. Newton (1643-1727)

D. Bernoulli (1700-1782) L. Eulero (1707-1783)

J-L. Lagrange (1736-1813)

P-S. Laplace (1749-1827)

J-B Le Rond D’Alembert (1717-1783)

LA FLUIDODINAMICA SPERIMENTALE

Edme Mariotte (1620-1684) Christian Huyghens (1629-1695)

Henri Pitot (1695-1771)Pressione statica e dinamica in un flusso

Benjamin Robins (1707-1751)La bilancia a braccio ruotante

2vL

Frank H. Wenham (1824-1908)La prima galleria del vento

"I think the paper just read is one of great interest and importance, especially as it points out the true mechanical explanation of the curious problem, as to how and why it is that birds of the most powerful flight always have the longest and narrowest wings.“The Duke of Argyll, after Wenham’s presentation of his paper “Aerial locomotive” to the Aeronautical Society (London) in 1866

Bilancia aerodinamica a braccio ruotante(Benjamin Robins, 1730)

Il tubo di Pitot

Henri Pitot, 1732

Ludwig Prandtl (1930)

Tubo di Pitot-Prandtl

Galleria del vento dei fratelli Wright (riproduzione)

Claude Louis Marie Henri Navier (1785-1836)

Sir George Gabriel Stokes (1819-1903)

LE EQUAZIONI DETERMINISTICHE DEL FLUIDO LE EQUAZIONI DETERMINISTICHE DEL FLUIDO REALEREALE::

EQUAZIONI DI NAVIER-STOKESEQUAZIONI DI NAVIER-STOKES

“Con la sua (di Eulero) scoperta tutta la meccanica dei fluidi è stata ridotta ad una questione di sola analisi e, se le equazioni si proveranno mai integrabili, le caratteristiche del flusso, e il comportamento del fluido sotto l’azione delle forze, sarà determinato per ogni circostanza” (Lagrange, 1788)

OSBORNE REYNOLDS (1842-1912)

"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? And why turbulence? I really believe he will have an answer for the first.“ Werner Heisenberg (1901-1976)

DISTINZIONE REGIME LAMINARE (“diretto”) E TURBOLENTO (“sinuoso”)

UL

Re

HERMANN HELMHOLTZ (1821-1894)I FLUSSI VORTICOSI

L’equazioni di Navier-Stokes: irrisolvibili (analiticamente) se non in particolari condizioniLa viscosità c’è ma non si sa come trattarla

“When the complete mathematical problem looks hopeless, it is recommended to enquire what happens when one essential parameter of the problem reaches the limit zero” (Ludwig Prandtl, 1948)

Ludwig Prandtl (1874-1953)“..his ability to establish systems of simplified equations whichexpressed the essential physical relations and dropped thenonessentials was unique, I believe, even when compared with hisgreat predecessors in the field of mechanics - men like LeonhardEuler and d’Alembert” (Theodore Von Kármán, 1954, about Prandtl)

Prandtl had “the ability to see the solution of equations without going through the calculations” (Werner Heisenberg)

Prandtl:“No, I strive to form in my mind a thorough picture… the equations come only later when I believe I have understood…[and are] good means of proving my conclusions in a way that others can accept.”

L’IPOTESI DELLO STRATO LIMITEL’IPOTESI DELLO STRATO LIMITEThird International Mathematics Congress, Heidelberg, 1904

GLI UOMINI CON LE ALIGLI UOMINI CON LE ALI

“Der Vogelflug als Grundlage der Fliegekunst” (1889) (Il volo degli uccelli come base per il volo)

Otto Lilienthal(1848-1896)

Orville Wright(1871-1948)

Wilbur Wright(1867-1912)

Gli uomini di azioneThe “chauffeurs” (S.P. Langley)• Concezione statica

dell’aeroplano• Si progetta e si prova• Si fa pilotare agli altri• Mancano il controllo e la

manovrabilitàThe “airman” (i fratelli Wright)

• Concezione dinamica dell’aeroplano

• Si prova e si progetta• Si impara a pilotare da se• I movimenti dell’aeroplano

sono controllati e si possono effettuare manovre

““Nobody will fly for a thousand years!”Nobody will fly for a thousand years!”

Wilbur Wright, 1901, in a fit of dispairWilbur Wright, 1901, in a fit of dispair

““....the first in the history of the world in which the first in the history of the world in which a machine carrying a man had raised itself by a machine carrying a man had raised itself by its own power into the air in full flight, had its own power into the air in full flight, had sailed forward without reduction of speed sailed forward without reduction of speed and had finally landed at a point as high as and had finally landed at a point as high as that from which it startedthat from which it started” ”

Orville Wright, 1903Orville Wright, 1903describing their first flightdescribing their first flight

• Ipotesi del continuo• La particella di fluido• Pressione totale, statica e dinamica• Sforzo di taglio • Viscosità e condizione di non-slittamento• Strato limite (ipotesi di Prandtl)• Regimi fluidodinamici: laminare e turbolento• Similitudine fluidodinamica