Fluid MechanicsFluid Mechanics

Lecture 2Lecture 2

Instructor: Prof. Zaher KuhailInstructor: Prof. Zaher Kuhail Eng. Tamer A. EshtawiEng. Tamer A. Eshtawi

Faculty: EngineeringDepartment: Civil EngineeringSemester: First semester 2006

University of Palestine

PressurePressure

Pascal’s Law

Example1Example1

Vertical Variation Of PressureIn A Fluid Under Gravity

Example 2Example 2

NW

WA

Fgh

A

F

PP

4468

101004

3.081.910001030

4

4002

2

1

1

21

2323

Solution:

Atmospheric pressure

The atmospheric air exerts a normal pressure upon all The atmospheric air exerts a normal pressure upon all surfaces with which it is in contact, and it is known as surfaces with which it is in contact, and it is known as atmospheric pressure.atmospheric pressure.

Gauge pressureGauge pressure

A gauge pressure can be given using height of any fluid.

Example 3Example 3

Pressure Measurement By Manometer

Manometers use the relationship between Manometers use the relationship between pressure and head to measure pressurepressure and head to measure pressure

1- Simple manometer1- Simple manometer

22 - -U-tube manometerU-tube manometer

Example 4Example 4

Solution

2

22

33

2211

/ 85.12010085.20.

..

/ 85.20/ 25.20846

16.0*81.9*106.1306.0*81.9*1085.0

21

mKNabsP

atmPgaugePabsP

mKNmNP

P

ghghP

PP

pipe

pipepipepipe

pipe

pipe

pipe

Example 5Example 5

Solution

2

22

33

2211

/ 27.8610073.13.

..

/ 73.13/ 13734

01.0*81.9*106.1304.0*81.9*101

0

21

mKNabsP

atmPgaugePabsP

mKNmNP

P

ghghP

PP

pipe

pipepipepipe

pipe

pipe

pipe

Advances to the “U” tube manometer

Single column manometersSingle column manometers

Vertical Single manometerVertical Single manometer

The volume that move from x-x to z-z datum =the volume that rise in right tube above x-x

datum

)()(

small very is A

a

)()(

)()(

21

1122

222211

2211

hghgP

hA

ahgh

A

ahgP

hhghhgP

PP

1

2

Inclined single column manometersInclined single column manometers

11

2

1

112

1122

222211

2211

sin

)()sin(

)()(

small very is A

a

)()(

)()(

21

hlg

Ph

hglgP

hghgP

hA

ahgh

A

ahgP

hhghhgP

PP

p

Example 2Example 2 The inclined manometer is filled The inclined manometer is filled

with oil that has a specific gravity with oil that has a specific gravity of 0.85 what angle a will yield a of 0.85 what angle a will yield a deflection 20 cm in the inclined deflection 20 cm in the inclined tube when the air pressure in the tube when the air pressure in the cistern is increased 600 N/m2 cistern is increased 600 N/m2

o

cmwithpressureIncrease

1.21

60085081.9sin2.0P

oil of drop thenglectingwith

tubein the 20N/m 600

increase

2

Solution:

ExampleExample

liquid of 28881.9800

5.64981

64981.5P

1.673756.2393

)5.0100

15.0(81.913600)5.0

100

13.0(81.9800

)5.0(81.913600)3.0(81.9800

21

1

m.g

Ph

P

P

hhP

PP

Solution

Differential manometersDifferential manometers

ghhgPhhgP

PP

datumAt

mercuryBBAA

)()(

21

x- x

11

ghhgPhhgP

PP

datumAt

mercuryBBAA

)()(

21

x- x

21

ExampleExample

ghgPhgP

PP

datumAt

mercuryBABB

)6.3()1(

21

x- x

Solution

mh

h

hh

hh

329.0

1255684.41342

1334166.1665057848207848

81.9136006.381.9160010110181.980010200 33

Inverted U-tube Differential Inverted U-tube Differential manometersmanometers

ghhgPhgP

PP

datumAt

liquidBBAA

)()(

21

x- x

21

1 2

ExampleExample

22

21

2

kN/m 8.18N/m 18835

15.081.98001.081.910003.081.9100019620

)()(

N/m 1962081.910002

21

x- x

B

B

liquidBBAA

A

P

P

ghhgPhgP

P

PP

datumAt

General Example 1General Example 1Example 1 The figure

Solution: w gasoline = 6.65 kN/m2 , w air = 0.0118 kN/m2

cm 0.857m 1057.8

100118.0 1065.63.18756.17610995.1

100118.0)018.03.0(1065.6018.081.9100010995.1

kN/m 995.130.01065.6

3

333

333

..

23

h

hh

hh

ghghghP

Also

whghP

airairgasogasowaterwatergauge

gauge

Example 2Example 2

23

23

2.

.

23

/38.602*81.9*10001080

/73.2073.1001080

/73.10081.9*13600*755.0

/806.0*81.9*106.13

)(0

21

mkNghPP

mkNP

mkNP

PPP

mkNP

hgP

PP

waterairL

abs

atm

atmairabs

air

mercurymercuryair

Solution:

Group work 1Group work 1

Group work 2Group work 2

Group work3Group work3