Fluid (ของไหล)

Page 1


Ideal fluid 1. 2. 3. 4.

(Steady flow) (Irrotational flow) (Incompressible flow) (Nonviscous flow)


Steam line


tube of flow


P Q v1 v2 A1 A2 P Q

Q

t v∆t A1 v2

P

∆m1 = ρ1∆V1 = ρ1 A1v1∆t

v1 1 P t A1 v1


∆t → 0

P ∆m1 dm1 = ρ1 A1v1  → = ρ1 A1v1 ∆t → 0 ∆t dt

Q

dm2 = ρ 2 A2 v2 dt

Q

dm1 dt

v2

(Mass flux)

P v1

A1 A2 1

dm2 dt


ρ1 = ρ 2 = ρ

dm1 dm2 = dt dt

Q

v2

ρ v1 A1 = ρ v2 A2

ρ Av =

P v1

A1v1 = A2 v2


(Mass flux) 1

dm Rm = = Ď Av dt Volume flow rate

dV RV = = Av dt


x? (cm3/s) x

( x + 4 + 8 + 4 + 5) − ( 2 + 6 ) = 0 x + 21 − 8 = 0 → x = −13

13 cm3/s


Daneil Bernoulli

Hydrodynamica .. 1738 .. 1700 - 1782


A1 A2 y1 y2

A1 V1 p 1 A2 V2 p 2


() p1A1 p2A2 (a) (b) W1 = p1 A1∆l1 , W2 = − p2 A2 ∆l2 W = W1 + W2 = p1 A1∆l1 + ( − p2 A2 ∆l2 )

∆V = A1∆l1 = A2 ∆l2

∆l2 ∆l1

 m ∆V = ρ


p1 A1∆l1 + ( − p2 A2 ∆l2 )

(

∆l2

1 2  1 2  =  mv2 + mgy2 ÷−  mv1 + mgy1 ÷ 2  2 

m 1 2 1 2 p1 − p2 ) − mg ( y2 − y1 ) = mv2 − mv1 ρ 2 2

1 2 1 2 p1 + ρ v1 + ρ gy1 = p2 + ρ v2 + ρ gy2 2 2

∆l1

1 2 p + ρ v + ρ gy1 = 2


A1v1 = A2 v2 A1 v2 = v1 > v1 A2

()

1 2 1 2 p1 + ρ v1 = p2 + ρ v2 2 2

1 p2 = p1 − ρ ( v22 − v12 ) < p1 2


F

v1

v2


v1 p1 v2 p2 1 2 1 2 p1 + ρ v1 = p2 + ρ v2 2 2

F

v1

1 p2 − p1 = ρ ( v12 − v22 ) > 0 2 A

v2

1 F = ( p2 − p1 ) A = ρ ( v12 − v22 ) 2


A1v1 = A2 v2 A1 v2 = v1 > v1 A2

()

1 2 1 2 p1 + ρ v1 = p2 + ρ v2 2 2

1 p2 = p1 − ρ ( v22 − v12 ) < p1 2


F

v1

v2


v1 p1 v2 p2 1 2 1 2 p1 + ρ v1 = p2 + ρ v2 2 2

F

v1

1 p2 − p1 = ρ ( v12 − v22 ) > 0 2 A

v2

1 F = ( p2 − p1 ) A = ρ ( v12 − v22 ) 2


6,000 60

0.60 ×105 Pa 4,000

F = ( p2 − p1 ) A 2 F = 2 ( p2 − p1 ) A = mg

2 × ( 0.60 ×105 − p1 ) × 60 = 6, 000 × 9.8 p1 = 5.95 × 104 Pa


Spoiler Spoiler () N

fs

air

W 2

2

mv fs = = Âľs N r

v,p v p

W 2


Down force Down force 4 2 ....

air

Spoiler N W 2

fs

W 2

..

mv 2 fs = = Âľs N r


1 .. 2537 .

?


Aerodynamics F1

Downforce F1


A0

(A1) down force

A1


...

Formula 1


Venturi meter ď ˛Aa


12

1 2 1 2 p1 + ρ v1 = p2 + ρ v2 2 2 1 1 2 2 p1 − p2 = ρ ( v2 − v1 ) = ρ ( v 2 − V 2 ) 2 2

vV AV = av

A v= V a 21 2   1 A 2 p1 − p2 = ρV  2 − 1÷ 2 a 


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