Bernoulli’s equation for unsteady and irrotational flow

02

2

tFzgput

s

Bernoulli’s equation for unsteady and irrotational flow

Bzgpus 2

2

Bernoulli’s equation for steady and irrotational flow

alternate form ofEuler’s equation zgpuu

tu

1

21 2

http://commons.wikimedia.org/wiki/File:Graphic1.png

Bzgpus 2

2

22

22

11

21

22hgpvhgpv

1. Venturi Tube

21212

12

21

21 hhgppvv

21

2211

UUAvAv

Continuity?

21212

12

21

21 hhgppvv

2211 AvAv

122

1 AAvv

2121

2

1

2222

121 hhgpp

AAvv

2

21

12

1

22

22 12

ghpghpAAv

21

22

22

11

22

1

2

AA

ghpghp

v

21

22

22

11

22

1

2

AA

hgph

gpg

v

21

22

2122

1

2

AAHHgv

21

22

212

1

2

AA

HHgv

http://en.wikipedia.org/wiki/Venturi_effect

21

22

212

1

2

AA

HHgv

Venturi Tube

2211 AvAv

Venturi Tube

21

22

212

1

2

AA

HHgv

2211 AvAv

http://en.wikipedia.org/wiki/Venturi_effect

Bzgpus 2

2h1

h2

2

221

21

22pupu

2211 hgphgp

21

21

2ghghu

u1 u2 = 0

121 2 hhgu

Pitot Tubez

http://www.aerospaceweb.org/question/instruments/q0251.shtml

Pitot tube

ρ

ρ

ρ

22

212

1

22pupu

ρ

http://www.lmnoeng.com/Tank/TankTime.htm

Bzgpus 2

2

Orifice in a Tank

atmatm phgpu

2

2

hgu 2

uaQ

51.08.061.098.0

h

h1

h2

u1 u2 = 0

121 2 hhgu

Pitot Tube

u 1 (m

/s)

h2 – h1 (m)

0.01

0.03

0.05

0.070

000000

00000

01

0.090

000000

0000

001

0.11

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0.20.40.60.8

11.21.41.61.8

22.22.4

Venturi Tube Video Pitot Tube Video