Post on 01-Jan-2016
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