3-ΛΥΜΕΝΑ-ΡΕΥΣΤΑ.pdf
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Transcript of 3-ΛΥΜΕΝΑ-ΡΕΥΣΤΑ.pdf
-
1
3:
1:
1.
. p
p
.
h
,
.
,
) 2 1y y .
) 0p p gh , .
) p 0p .
.
.
p gh , 0p .
0p gh p (1).
, h ,
P.
gh p, (1)
. (1) .
-
2
2.
;
) , .
) , .
) ,
.
.
.
. ,
.
h, .
Pgh P h
g
.
,
.
-
3
1.
=1 g/cm3. , p0=1,01310
5 N/m2. g=9,81 m/sec2.
h,
gh
(p=0) . . , .
5
20
0 3
6 3 2
1,01310p mp p gh h
10 kg mg9,81
10 m s
h 10,32 m
-
4
2.
U (). 1= 10 cm
2 2= 5 cm2 (
). 100 g . .
) .
) h, .
: 1=13,6 g/cm3
2=1 g/cm3.
) ( C.G.S).
h2
2 2 2 2 2 2 2 222 2
3
m 100grm V m h h h h 20cm
g1 5cmcm
.
) . x h :
x h 2 1V V x A h x 2h (1)
0p 2 2 0gh p 1 3
21 2 2 1 2
13
g1cmg h x h 3h h h h 20cm
g33 13,6
cm
20h cm 0,49 cm
40,8 .
: 15/12/2015
:
: ,
-
1
3:
2:
1.
,
.
) .
) .
) .
.
. ,
=, .
-
2
2.
.
2 9 cm/s.
) 1= 3 cm/s ) 1 = 9 cm/s ) 1= 27 cm/s .
.
.
1=32.
:
1 2 21 1 2 11 2 2 3 9 3cm / s
-
3
3.
1,
(
) 1.
2
3,
2 3 .
) 1 2 3
) 1 1 2 2 3 3
) 1 2 3
.
.
t,
.
21 13 32m Vm m V V
t t t t t t
1 2 3 1 1 2 2 3 3
-
4
4.
.
.
)
) .
) .
.
.
==,
. -
(-=W ) , m
.
-
5
5.
( )
.
. .
,
)
)
)
.
.
. 1, 3
.
:
1 3 3 (1)
:
1 3 3 (2)
(1) (2) .
-
6
1
300 m3
10 . 2 m/s.
.
) .
) .
.
) , 300 m3 10
. :
3 3V 300 m m0,5
t 600 sec sec
) :
3
2
m0,5
secA A 0,25 mm
2 sec
-
7
2
30 L/min 1.
2, 2= 1/5.
h=1,8 m
s=6 m. :
)
.
) .
) .
) .
.
g=10 m/sec2.
) :
2
2
1 2h 2 1,8 mh gt t t t 0,6 sec.
m2 g10
sec
) :
s ms t 10
t sec
)
, . :
3 3
4 2 2
2 2 2 2
30 10 m
60 sec 0,5 10 m 0,5 cmm
10 sec
) :
2 21 1 2 2 1 1
1
m2 sec
-
8
3
,
. ,
.
. =1,2 cm
1=40 cm/s.
r=210-4 cm,
2=0,05 cm/s .
.
.
1 2
.
, 22 r .
, :
2 22 2 2 1
1 1 2 2 1 2 1 2 2
2
R r r2 4r
2
9
24
40 cm1,2 cm
sec 7,2100,05 cm
4 2 10sec
5-10
.
: 10/11/2015
: ,
: ,
-
1
3:
3: BERNOULLI
1.
.
,
.
, hB, , h,
. h > h.
. h < h
. h = h
.
.
Bernoulli 1 2
.
2 21 1 2 2
1 1p p (1)
2 2
,
, 2 > 1 . (1) p2 h.
-
2
2.
.
h.
. =
B. 2
2gh
. 2gh
.
.
,
.
-
3
3.
1
2 1 = 22.
h
1 2 2 = 21.
. 1 2
. 1 = 2
. 1 = 22
. 2 = 21.
.
.
= .
Toriccelli,
h
. , ,
.
1 = 1 2 = 2 = 21 2 = 21.
-
4
4.
,
,
.
. .
.
.
.
Bernoulli, ,
, . ,
()
.
.
-
5
5.
,
h
.
.
. .
. .
.
.
Bernoulli
(
)
.
,
.
2 2
A B B
1 1p p gy
2 2
pA = patm = 0. p = patm = 0.
atm atm
0 p 0 p gy y 0
Bernoulli .
.
-
6
6.
,
E
> .
. .
. .
. .
.
.
, .
.
( Bernoulli) =+(U/V)
(U/V) . >,
(U/V)
-
7
1
h = 0,2m ,
=3*10-4m2.
.
.
( Torricelli).
. .
. h
.
patm,
g = 10m/s2.
. Bernoulli ,
,
.
, .
2 2
1 1p gh p
2 2
, ,
pA = pB = patm
, =0.
2
1gh 2gh
2
Torricelli .
h.
.
: 2m m
2 10 0,2m 2
s s
-
8
. :
3
4 2 3m m L
3 10 m 2 0,6 10 0,6s s s
. H 2gh
2 2gh 2 2gh h 4h 0,8m
-
9
2
(
Ventouri). 1
1 2
2. ,
h
= 10cm.
. 1 2.
. 1 2.
. N 1.
.
g = 10m/s2 , = 1000 kg/m3
. 1 2 :
1 1
1 1 2 2 2
2
AA A (1)
A
2 1
3
. .
. , pB
p1 .
1 B
p p . p = patm + gh1 , p1 = patm + gh1 , (2)
p2 = patm + gh2 , (3)
p1 p2 = g(h1 - h2) , (4)
: 3 21 2
p p 10 N / m
. Bernoulli
1 2.
, gh
.
-
10
2 2 2 21 1 2 2 1 2 2 11 1 1
p p p p , (5)
2 2 2
(5),(1)
2
2 1
1 2 1 2
2
1p p 1 , (6)
2
(4) (6) 1
2
1 2 2
1
2
m2 10 0,1m
2gh s
3 1A
1
A
1=0,5 m/s
-
11
3
.
( )
.
h = 10cm.
.
.
. .
: = 1,25 kg/m3, = 1000 kg/m
3 , patm =
105N/m2 g = 10m/s2.
Bernoulli
A B.
2 2A A B B
1 1p p
2 2
, pA = patm = 0
2 2 5B A atm B A 21 N
p p p 0,625 10
2 m
, (1)
. .
.
B atmp p p gh , (2)
(1),(2)
3
2
A A A
3
kg2 1000 0,1m
2 gh1 mmgh 40
kg2 s1,25
m
:
Pitot .
-
12
4
h = 5m. H
= 10cm2.
= 10m/s. :
.
( )
. .
. .
. () .
. : = 1000kg/m3, g = 10m/s2.
. ,
( )
, = = 10m/s.
. Bernoulli
.
2 2
B B B
4
B B3 2 2
1 1p p gh , ( )
2 2
kg m Np p gh 1000 10 5m p p 5 10
m s m
. .
B 4 2
3 2
p p dVdW dW kg m mgh A 1000 10 5m 10 10 m 10
dt dt dt m s s
dW500W
dt
: .
. () :
dWP
dt
-
.
Ww .
-
13
2 2
w
2
1 1m 0 W W m 0 W m gh
2 2
1W m m gh
2
, P :
2 2
2
4 2
2 3
dW 1 dm 1P gh gh A
dt 2 dt 2
1 m m kg mP 10 10 5m 1000 10 10 m 10 P 1000W
2 s s m s
-
14
5
, Boeing 737
.
= 70m2 .
,
,
= 756km/h,
= 684km/h. :
.
.
. .
. Boeing 737 ,
= 20.
o: = 1,25kg/m3, patm = 10
5N/m2, 20 = 0,94
A. ernoulli , ,
= .
2 2 2 2
A A A A
2 2 2 2
B B B B
1 1 1p p p p
2 2 2
1 1 1p p p p
2 2 2
:
2 2 21 N
p p 5000
2 m
B. , F,
A B
F p p 2A
2 .
2A B 2
NF p p 2A 5000 140m F 700.000N
m
-
15
. F
, .
w F F 700.000N 0,94 w 658.000
: 11/01/2016
:
: ,
-
1
3:
4:
1.
, 2
, 1
F
w .
.
, 1
.
. F
1 .
.
1.
. F
.
.
.
,
F
( ) .
1 , . ,
, F
.
-
2
2.
.
.
.
(ii).
.
,
( )
.
, W=(p-p) V.
W>0 p-p>0 ,
. p=p+gh.
, h . (ii).
: 3/11/2015
:
: ,
