P o d s t a w y f i z y k i s e z o n 1
I X . M e c h a n i k a p By n w
A g n i e s z k a O b Bk o w s k a - M u c h a
A G H , W F I i S , K a t e d r a O d d z i a By w a D i D e t e k c j i C z s t e k ,
D 1 1 , p o k . 1 1 1
a m u c h a @ a g h . e d u . p l
h t t p : / / h o m e . a g h . e d u . p l / ~ a m u c h a
M e c h a n i k a p By n w
P AY N Y = C I E C Z E + G A Z Y
H y d r o s t a t y k a
H y d r o d y n a m i k a
% O p i s j e s t r |n y o d m e c h a n i k i b r y By s z t y w n e j ( z m i a n a k s z t a Bt u , [c i [l i w o [)
% W p By n a c h b r a k r e g u l a r n e g o u p o r z d k o w a n i a a t o m w i c z s t e c z e k ( j a k w
s i e c i k r y s t a l i c z n e j c i a B s t a By c h ) .
% P By n s u b s t a n c j a z d o l n a d o p r z e p By w u , p r z y j m u j e k s z t a Bt n a c z y n i a , w k t r y m
s i z n a j d u j e ,
% W p By n a c h w s p o c z y n k u n i e w y s t p u j |a d n e n a p r |e n i a [c i n a j c e .
% N a p By n y d z i a Ba j t y l k o s i By p r o s t o p a d Be d o i c h p o w i e r z c h n i . P o w i e r z c h n i a
u s t a w i a s i z a w s z e n o r m a l n i e d o s i By z e w n t r z n e j ( d o [w )
% Z a m i a s t w y z n a c z a m a s i s i B, o p i s u j e m y g s t o [ i c i [n i e n i e
2 A . O b Bk o w s k a - M u c h a
C i [n i e n i e
% C i [n i e n i e w a r t o [ s i By p r o s t o p a d Be j n a j e d n o s t k p o w i e r z c h n i :
5m 5A
"
5ؑ = = 1 5C5N
5z 5Z2
1 0 5 5C5N = 1 5O5N5_ ; 1 5N5a5Z = 1 0 1 3 , 2 5 !5C5N = 7 6 0 5Z5Z5;5T
% W e k t o r p o w i e r z c h n i - d Bu g o [ w e k t o r a 5Q5F j e s t
r w n a p o l u p o w i e r z c h n i 5Q5F, j e g o k i e r u n e k j e s t
p r o s t o p a d By d o p o w i e r z c h n i , a z w r o t n a
z e w n t r z p o w i e r z c h n i .
% S i Ba w y w i e r a n a p r z e z p By n n a t p o w i e r z c h n i :
5Q59 = 5] 5Q5F
55؎
% G s t o [ - 5F = - z a l e |y o d t e m p e r a t u r y ,
55}
c i [n i e n i a
3 A . O b Bk o w s k a - M u c h a
C i [n i e n i e w e w n t r z p By n u ( h y d r o s t a t y k a )
% C i [n i e n i e w y w i e r a n e p r z e z p By n
W E W N T R Z n a c z y n i a :
591 = 5] 5F
5f
n a g n i d o l n p o w i e r z c h n i
c i e n k i e g o w a l c a , o w y s o k o [c i 5Q5f,
5Q5f 5Q5Z
z n a j d u j c e g o s i n a g Bb o k o [c i 5f,
592 = ( 5] + 5Q5]) 5F
d z i a Ba j s i By :
591 = 5] 5F, 592 = 5] + 5Q5] 5F
5Q5Z 5T 5 5F5Q5f g
z m i a n a c i [n i e n i a w
5Q5] = = = 5 5T5Q5f
55ؑ
5F 5F
z a l e |n o [c i o d z m i a n y
= 5F 5؈
55ؚ
g Bb o k o [c i
% C i [n i e n i e h y d r o s t a t y c z n e c i e c z y n a
c i |a r w Ba [c i w y c i e c z y
g Bb o k o [c i y ( c a Bk u j e m y p o w y |s z e ) :
% c i [n i e n i e r o [n i e w r a z z g Bb o k o [c i ( n u r e k ) ,
5ؑ = 5ؑ5 5F 5؈ 5ؚ
% c i s n i e n i e m a l e j e z w y s o k o [c i ( t r e k i n g ) ,
% c i [n i e n i e j e s t j e d n a k o w e d l a p u n k t w n a t e j
s a m e j g Bb o k o [c i , n i e z a l e |y o d k s z t a Bt u
c i [n i e n i e a t m o s f e r y c z n e
n a c z y n i a ( p a r a d o k s h y d r o s t a t y c z n y ) .
4 A . O b Bk o w s k a - M u c h a
P o m i a r c i [n i e n i a
% D o p o m i a r u c i [n i e n i a b a r o m e t r
B a r o m e t r T o r r i c e l l e g o ( 1 6 4 3 ) p o m i a r c i s n i e n i a a t m o s f e r y c z n e g o z a
p o m o c r u r k i z r t e c i
5]54 = 5 5T !
5]55 = 5]5N5a5Z
5]54 = 5]55
5]5N5a5Z = 5 5T !
W s p Bc z e [n i e :
5 A . O b Bk o w s k a - M u c h a
B a r o m e t r y , m a n o m e t r y
% Z e w z g l d u n a r o d z a j p o m i a r u b a r o m e t r y m o |n a p o d z i e l i n a :
" b e z w z g l d n e w s k a z u j c i [n i e n i e a b s o l u t n e , c z y l i w o d n i e s i e n i u d o
p r |n i ,
" r |n i c o w e w s k a z u j r |n i c c i [n i e D,
" w z g l d n e ( m a n o m e t r y ) w s k a z u j c i [n i e n i e w z g l d e m c i [n i e n i a
o t o c z e n i a ( w z g l d n e ) i w i k s z e o d n i e g o ,
% M a n o m e t r y :
" h y d r o s t a t y c z n e ,
" s p r |y n o w e ,
" e l e k t r y c z n e
% P r |n i o m i e r z e
6 A . O b Bk o w s k a - M u c h a
C i [n i e n i e
% C i [n i e n i e p o d w o d p o k a |d y m z a n u r z e n i u o 1 0 m c i [n i e n i e z w i k s z a s i o
1 a t m .
5] = 5]0 + 5_5T!
5] = 1 0 1 3 !5C5N + ( 9 9 8 5X5T/ 5Z3 ) ( 1 0 5Z/ 5`2 ) ( 1 0 5Z) H" 1 5N5a5Z + 1 5N5a5Z
R e k o r d n u r k o w a n i a s w o b o d n e g o ( f r e e - d i v i n g ) t o p o n a d 2 7 0 m !
% Ao d z i e p o d w o d n e 2 0 0 - 4 0 0 m
% C i [n i e n i e a t m o s f e r y c z n e n a w y s o k o [c i H :
5 5]
5] = 5]0 5 5]5\5d 5T 5;
=
a l e :
5 0 5]0
5Q5] 5 0 5T
c o d a j e :
= - 5]
5Q! 5]0
w z r b a r o m e t r y c z n y
5F
- 5؈ 5ؑ5 5؉
4 0 0 0 m 2 7 0 0 m 3 0 0 m
5
5ؑ = 5ؑ55؆
r o z w i z a l u b s p r a w d z i !
7 A . O b Bk o w s k a - M u c h a
P r a w o P a s c a l a
% W z a m k n i t e j o b j t o [c i p By n u ( n i e [c i [l i w e g o ) z m i a n a c i [n i e n i a j e s t p r z e n o s z o n a
d o k a |d e g o m i e j s c a w p By n i e i d o [c i a n z b i o r n i k a ( p r a s a h y d r a u l i c z n a , h a m u l c e ,
c i [n i e n i e w o p o n i e j e s t w k a |d y m m i e j s c u j e d n a k o w e , i t p . )
591 592
5] = =
5F1 5F2
" M o |n a d z i a Ba m n i e j s z s i B w c e l u p o d n i e s i e n i a w i k s z e g o c i |a r u
( k o s z t e m d r o g i ) .
" P r z y r o s t c i [n i e n i a j e s t w k a |d y m m i e j s c u t a k i s a m , n i e z a l e |n y o d
g Bb o k o [c i
8 A . O b Bk o w s k a - M u c h a
P r a w o P a s c a l a - p r z y k Ba d y
5]0 + 5 1 !1 5T = 5]0 + 5 2 !2 5T
9 A . O b Bk o w s k a - M u c h a
P r a w o A r c h i m e d e s a
% N a c i a Bo z a n u r z o n e w c i e c z y d z i a Ba s i Ba g r a w i t a c y j n a g d y c i a Bo s i n i e
p o r u s z a m u s i o n a b y z r w n o w a |o n a p r z e z i n n s i B z w a n s i B w y p o r u
% S i Ba w y p o r u w y n i k a z r |n i c y c i [n i e D d z i a Ba j c y c h
n a g r n i d o l n p o w i e r z c h n i c i a Ba .
5] ! = 5]0 - 5 5T!
F 5d = 5] !2 A 2 - 5] !1 541
F 5d = 5 5T( !2 - !1 ) 54
5m5ؘ = 5F5؈5}
P R A W O A R C H I M E D E S A : n a c i a Bo z a n u r z o n e w p By n i e d z i a Ba s i Ba
w y p o r u , s k i e r o w a n a p i o n o w o d o g r y , a j e j w a r t o [ j e s t r w n a
c i |a r o w i w y p a r t e j p r z e z c i a Bo c i e c z y .
1 0 A . O b Bk o w s k a - M u c h a
P By w a n i e c i a B
% W a r u n k i p By w a n i a - g d y c i a Bo p By w a , w a r t o [
d z i a Ba j c e j n a n i e s i By w y p o r u 5m5ؘ j e s t r w n a
w a r t o [c i d z i a Ba j c e j n a n i e s i By c i |k o [c i .
595d = 5Z5T
5 5]B5f5[5b 5I5P5V5NB5N 5T = 5 5P5V5NB5N 5I5P5V5NB5N5T
5 5]B5f5[5b = 5 5P5V5NB5N
% S t a t k i p o w i n n y w y p i e r a c i e c z o c i |a r z e r w n y m w Ba s n e m u
c i |a r o w i .
5@5` 5T = 5 5d 5I 5T
5@
5`
z a n u r z e n i e j e s t p r o p o r c j o n a l n e d o 5I = , c z y l i z a l e |y o d g s t o [c i w o d y
5 5d
( t e m p , z a s o l e n i a )
1 1
h t t p : / / k u r c a b a t o m a s z 7 . w . i n t e r i a . p l / z a g a d n i e n i a / p l y w a n i e . h t m l
P By w a n i e c i a B
P r z y k B: J a k a c z [ o b j t o [c i g r y l o d o w e j w y s t a j e n a d p o w i e r z c h n i m o r z a ?
G s t o [ l o d u w y n o s i 9 2 0 k g / m 3 a g s t o [ w o d y m o r s k i e j 1 0 3 0 k g / m 3 .
C i |a r g r y l o d o w e j
5D5Y = 5 5Y5I5Y 5T
C i |a r o b j t o [c i 5I5d w y p a r t e j w o d y m o r s k i e j .
5D5d = 5 5d5I5d 5T
W a r u n e k p By w a n i a .
5 5Y5I5Y 5T = 5 5d5I5d 5T
5I5d 5 5Y 9 2 0
= = = 0 . 8 9
5I5Y 5 5d 1 0 3 0
5}5ؘ
O b j t o [ w y p a r t e j w o d y r w n a s i o b j t o [c i
z a n u r z o n e j c z [c i g r y l o d o w e j , c z y l i 8 9 % g r y
z n a j d u j e s i p o d w o d .
1 2 A . O b Bk o w s k a - M u c h a
S i Ba w y p o r u p o w i e t r z a
% N a k a |d e c i a Bo z n a j d u j c e s i w p o w i e t r z u p r z y
p o w i e r z c h n i Z i e m i d z i a Ba s i Ba w y p o r u r w n a c i |a r o w i
w y p a r t e g o p o w i e t r z a . C i a Bo o o b j t o [c i 1 m 3 w y p i e r a 1 m 3
p o w i e t r z a , k t r e g o c i |a r j e s t o k o Bo 1 2 N - k a |d e c i a Bo ,
w a |o n e p r z y p o w i e r z c h n i Z i e m i n a c i s k a n a w a g s i B o
o k . 1 2 N m n i e j s z o d i c h c i |a r u ( c o w a |y w i c e j t o n a
p u c h u c z y t o n a k a m i e n i ? ) p o p r a w k i n a p o m i a r m a s y &
% W e n t y l a c j a g r a w i t a c y j n a d z i a Ba d z i k i r |n i c y
t e m p e r a t u r y w e w n t r z i n a z e w n t r z b u d y n k u - % W y p e Bn i o n e g a z e m
l |e j s z e , c i e p Be p o w i e t r z e p By n i e k u g r z e , a n a b a l o n y , k t r e w z n o s z
j e g o m i e j s c e n a p By w a p o w i e t r z e z i m n i e j s z e - s i w p o w i e t r z u m a j a
c i |s z e . L a t e m t e m p e r a t u r y s i w y r w n u j - g s t o [ m n i e j s z n i |
w e n t y l a c j a p r z e s t a j e d z i a Ba p o w i e t r z e .
1 3 A . O b Bk o w s k a - M u c h a
D y n a m i k a p By n w
% D w a p o d e j [c i a d o o p i s u r u c h u p By n u :
" L a g r a n g e a o p i s u j e m y r u c h k a |d e j c z s t k i 5_ 5_0 , 5a ,
" E u l e r a w y z n a c z a m y g s t o [ i p r d k o [ w k a |d y m p u n k c i e , w k a |d y m
m o m e n c i e c z a s u : 5 ( 5_, 5a) , 5c 5a - z a m i a s t o p i s u , c o s i d z i e j e z k a |d
c z s t k - o p i s c o s i d z i e j e w o k r e [l o n y m p u n k c i e p r z e s t r z e n i .
P r d k o [ k a |d e g o p u n k t u c i e c z y w f u n k c j i
c z a s u p o l e w e k t o r o w e
" t o r k a |d e j c z s t k i t o l i n i a p r d u
" p r d k o [ j e s t s t y c z n a d o l i n i i p r d u ,
" s t r u g a w i z k a l i n i p r d u
1 4 A . O b Bk o w s k a - M u c h a
P o d z i a B p r z e p By w w
% P o d z i a B p r z e p By w w :
" s t a c j o n a r n y ( u s t a l o n y , l a m i n a r n y ) p r d k o [ p By n u w d o w o l n i e
w y b r a n y m p u n k c i e j e s t s t a Ba w c z a s i e t z n . k a |d a c z s t e c z k a
p r z e c h o d z c a p r z e z d a n y p u n k t z a c h o w u j e s i t a k s a m o - n i s k i e
p r d k o [c i p r z e p By w u .
" b e z w i r o w y - w |a d n y m p u n k c i e c z s t e c z k a n i e m a w y p a d k o w e j
p r d k o [c i k t o w e j .
" n i e [c i [l i w y - g s t o [ p By n u j e s t s t a Ba , z a z w y c z a j w c i e c z a c h , w g a z a c h
t y l k o p r z y b l i |e n i a
" n i e l e p k i o d p o w i e d n i k t a r c i a w c i a Ba c h s t a By c h
% D a l s z e r o z w a |a n i a d o t y c z p r z e p By w w : l a m i n a r n y c h , b e z w i r o w y c h ,
n i e [c i [l i w y c h , n i e l e p k i c h .
1 5 A . O b Bk o w s k a - M u c h a
R w n a n i e c i g Bo [c i s t r u g i
" W t a k i c h p r z e p By w a c h w e k t o r y p r d k o [c i s r w n o l e g Be d o k i e r u n k u
p r z e p By w u ( l i n i i p r d u ) .
" L i n i e p r d u s i n i e p r z e c i n a j .
" W s z y s t k i e c z s t k i c i e c z y p r z e p By w a j c e p r z e z d a n y p u n k t m a j w t e d y t e n
s a m w e k t o r p r d k o [c i .
M a s y p By n u p r z e c h o d z c e p r z e z d w a p r z e k r o j e
5F1 i 5F2 w t e j s a m e j j e d n o s t c e c z a s u 5a s t a k i e
s a m e :
5Z1 = 5 5F1 5c1 5a
5Z2 = 5 5F2 5c2 5a
a z a t e m :
5z5 5ؗ5 = 5z5 5ؗ5
j e s t t o p r a w o c i g Bo [c i s t r u g i
P r d k o [ p By n u n i e [c i [l i w e g o p r z y u s t a l o n y m p r z e p By w i e j e s t o d w r o t n i e
p r o p o r c j o n a l n a d o p o l a p r z e k r o j u s t r u g i
A . O b Bk o w s k a - M u c h a
1 6
P r a w o B e r n o u l i e g o
% T w i e r d z e n i e o p r a c y i e n e r g i i
p r a c a w y k o n a n a p r z e z
w y p a d k o w s i B j e s t r w n a
z m i a n i e e n e r g i i k i n e t y c z n e j .
P r a c a :
- w y k o n y w a n a p r z e z s i B c i |k o [c i :
5J5D = - 5Z5T !2 - !1 = - 5 5I 5T( !2 - !1 )
( s i Ba i p r z e m i e s z c z e n i e m a j p r z e c i w n e k i e r u n k i )
- w y k o n y w a n a n a d p By n e m :
5J5] = - 592 - 591 "5e = - ( 5]2 5F2 - 5]1 5F1 ) "5e = - ( 5]2 - 5]1 ) 5I
5J = 5J5D + 5J5C = - 5 5I 5T !2 - !1 - 5I( 5]2 - 5]1 )
1 7 A . O b Bk o w s k a - M u c h a
Z . K k o l
P r a w o B e r n o u l i e g o
1
Z m i a n a e n e r g i i k i n e t y c z n e j : 1 5Z5c2 2 - 5Z5c1 2
2 2
j e s t r w n a p r a c y :
1 1
- 5 5I 5T !2 - !1 - 5I 5]2 - 5]1 = 5Z5c2 2 - 5Z5c1 2
2 2
c z y l i :
5 5
5ؑ5 + 5F5ؗ55 + 5F5؈5؉5 = 5ؑ5 + 5F5ؗ55 + 5F5؈5؉5
5 5
5
P r a w o B e r n o u l i e g o
5ؑ + 5F5ؗ5 + 5F5؈5؉ = 55ؐ5؏5ؔ5ؕ
5
c i [n i e n i e h y d r o d y n a m i c z n e
1 8 A . O b Bk o w s k a - M u c h a
P r a w o B e r n o u l i e g o
% J e [l i c i e c z p By n i e w r u r z e p o z i o m e j :
1
5] + 5 5c2 = 5P5\5[5`5a
2
c i [n i e n i e d y n a m i c z n e
c i [n i e n i e s t a t y c z n e
s u m a c i [n i e n i a s t a t y c z n e g o i d y n a m i c z n e g o j e s t s t a Ba ( p r z y k B. : p a r a d o k s
h y d r o s t a t y c z n y )
5F5c = 5P5\5[5`5a, c z y l i g d y p r z e k r j j e s t m n i e j s z y , t o r o [n i e p r d k o [, a w i c c i [n i e n i e
5] m a l e j e
C i e c z p By n c w r u r z e o z m i e n i a j c y m s i p r z e k r o j u m a m n i e j s z e
c i [n i e n i e n a o d c i n k u g d z i e p r z e k r j j e s t m n i e j s z y .
P r a w o B e r n o u l i e g o m a z a s t o s o w a n i e d o p By n u i d e a l n e g o , n i e [c i [l i w e g o
p r z e p By w u l a m i l a r n e g o , b e z l e p k o [c i .
1 9 A . O b Bk o w s k a - M u c h a
M e c h a n i k a p By n w w |y c i u
% S t r u g a w o d y z w |a s i , g d y w z r a s t a j e s t p r d k o [.
% W | o g r o d o w y w i k s z a p r d k o [, g d y z m n i e j s z y m y o t w r
% W y p By w w o d y z e z b i o r n i k a :
1
5]0
5]0 = 5]0 + 5 5c2 - 5 5T!
2
5c = 2 5T!
!
% R o z p y l a c z e :
P r a w o T o r r i c e l l e g o
5ؗ
5]0
2 0 A . O b Bk o w s k a - M u c h a
P r a w o B e r n o u l i e g o w t e c h n i c e
% C i [n i e n i e j e s t n a j m n i e j s z e t a m , g d z i e
p r d k o [ j e s t n a j w i k s z a ( n u r k o w a n i e )
% S i Ba n o [n a s k r z y d Ba s a m o l o t u : s t r u g i
p o w i e t r z a s z a g s z c z o n e n a d s k r z y d Be m , a
r o z r z e d z o n e p o d n i m . J a k w i d a n a
r y s u n k u , c z s t e c z k i p o w i e t r z a ( l u b c i e c z y )
m a j c d o p r z e b y c i a w i k s z d r o g n a d
s k r z y d Be m , m a j t a m w i k s z s z y b k o [ n i |
p o d s k r z y d Be m
% S t r z y k a w k a
1
5]0 + 5 5c2 = 5]
2
p 0
p
)
2 ( 5] - 5]0
5c =
5
2 1 A . O b Bk o w s k a - M u c h a
h t t p : / / q b a k i t e . e u . i n t e r i o w o . p l / A e r o d y n a m i k a . h t m
D l a p i Bk a r z y
% W a l e c o b r a c a j c y s i w p r z e p By w a j c e j , l e p k i e j c i e c z y / p o d k r c o n a p i Bk a
" W n i e r u c h o m y m p By n i e ( p i Bc e n i e p d k r c o n e j ) o b r a c a j c e s i c i a Bo
p o w o d u j e o b r t p By n u z 5c5`,
" G d y p By n m a p r d k o [ 5c5S c i e c z u g r y j e s t s p o w o l n i a n i a 5c5T = 5c5S - 5c5` ,
n a d o l e p r z y s p i e s z a n a : 5c5Q = 5c5` + 5c5S
1 1
" C i [n i e n i a 5ؑ5؈ > 5ؑ5 :
5 5c5S - 5c5` 2 + 5]5T = 5 5c5` + 5c5S 2 + 5]5Q
2 2
" P o w s t a j e s i Ba M a g n u s a s k i e r o w a n a w d B ( e f e k t M a g n u s a )
2 2 A . O b Bk o w s k a - M u c h a
h t t p : / / w w w . f i z t a s z k i . p l / n o d e / 8 7
h t t p : / / w w w . i f . p w . e d u . p l / ~ b i b l i o t / a r c h i w u m / a d a m c z y k /
P o m i a r p r d k o [c i p r z e p By w u
% S t r u m i e D o b j t o [c i o w y : 5x = 5ؗ 5z
% P o m i a r p r d k o [c i p r z e p By w u :
" z w |k a V e n t u r i e g o ,
" r u r k a P r a n d l a ( r z e k i )
2 3 A . O b Bk o w s k a - M u c h a
P r z e p By w y t u r b u l e n t n e
% P r d k o [ w p r z e p By w i e
% P r z e p By w t u r b u l e n t n y
l a m i l a r n y m :
% P o p r z e k r o c z e n i u p e w n e j p r d k o [c i g r a n i c z n e j
s t r u m i e D z a m i e n i a s i n a w i r y p r z e p By w
t u r b u l e n t n y .
2 5c 5
5E5R = H" 2 3 0 0
% L i c z b a R e y n o l d s a -
5
o z n a c z a t u r b u l e n c j e
% L e p k o [ - 5<
2 4 A . O b Bk o w s k a - M u c h a
L e p k o [
% L e p k o [ t a r c i e p o m i d z y w a r s t w a m i c i e c z y . O p i s u j e s i By [c i n a n i a i s t n i e j c e
w p o r u s z a j c e j s i c i e c z y
% W r u r z e p r d k o [c j e s t n a j w i k s z a w [r o k u i m a l e j e p r z y [c i a n k a c h c i e c z
s k Ba d a s i z m a By c h w a l c o w a t y c h w a r s t w , k t r e p o r u s z a j s i z r |n y m i
p r d k o [c i m i - t a r c i e
% L e p k o [ 5< w a r t o [ s i By F , j a k n a l e |y p r z y Bo |y d o c i a Ba , a b y p o r u s z a Bo s i
z e s t a B p r d k o [c i v .
5Q5c
59 = 5 5F
5Q5g
% Z w i z e k l e p k o [c i z t u r b u l e n c j a m i .
2 5 A . O b Bk o w s k a - M u c h a
P o k a z y d o [w i a d c z e D
% D e m o n s t r a c j a p r a w a P a s c a l a .
% P a r a d o k s h y d r o s t a t y c z n y
% N u r e k K a r t e z j u s z a
% C i [n i e n i e d y n a m i c z n e w s t r u d z e c i e c z y - l e w i t u j c a p i Be c z k a
% P a r a d o k s a e r o d y n a m i c z n y
% P r a w o B e r n o u l i e g o
2 6 A . O b Bk o w s k a - M u c h a
P o d s u m o w a n i e
% C i [n i e n i e . P o m i a r .
% P r a w o c i g Bo [c i s t r u g i P a s c a l a , A r c h i m e d e s a . P r z y k Ba d y .
% R w n a n i e B e r n o u l i e g o . O p i s z j a w i s k .
% R o d z a j e p r z e p By w w .
% T u r b u l e n c j e .
% L e p k o [.
% L i c z b a R e y n o l d s a
2 7 A . O b Bk o w s k a - M u c h a
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