2. FLUID MECHANICS
Static of fluid (fluid at rest)
Density
Pressure Fluid
Buoyancy Force
Dynamic of fluid (fluid in motion)
The Equation of Continuity
Equation
is a substance that can flow; it conforms to the boundaries of its container
5. density
Ex6 Mercury has relative density 13.6, determine density of mercury.
13.6 ✗ 103 K
8
/µ
3
6. FLUID MECHANICS
Pressure in Fluid
is a substance that can flow; it conforms to the boundaries of its container
lhspa=
1
อั๋
Nlm
ว
ใน pg
EP =
PaePg
7. pressure in fluid
Pressure : P (N/m2)
is force per unit area applied in a direction
perpendicular to the surface of an object.
P =
Atmospheric Pressure : Pa (N/m2)
is the approximate average pressure of the
atmosphere at sea level.
Pa =
8. pressure in fluid
Gauge Pressure : Pg (N/m2)
is depends on density of liquid and depth
but not on horizontal dimension.
Pg =
Absolute Pressure : P (N/m2)
is total pressure
P = Pa + Pg
1Pa
tpg
t
ความ
ลึ
ก
9. pressure in fluid
Ex6 A room has floor dimensions of 3.5 m x 4.2 m and a height of 2.4 m.
a) What does the air in the room weigh when the air pressure is 1.0 atm?
b) What
head, which we take to have an area of 0.040 m2?
a) W =
MG
ะ
fVG = [ 1.21)[3.5 ✗ 4.2× 2.4) 4.8) = 418N
b) F =
PA =
(1.013×105) 10.0407 =
4 ✗ 103 N
10. Ex6 3 Estimate the pressure exerted on your eardrum due to the water when you are
swimming at the bottom of a pool that is 5.0 m deep.
pressure in fluid
หวน
pg
=
fgh= (103)[9. 8) (5) ะ 4.9 ✗104 Pa
11. Ex6 Water is filled to a height H behind a dam of width w. Determine the resultant
force exerted by the water on the dam.
pressure in fluid
Pg =
¥ F.gg
W
หั๋
F =
BA Fygwti
Fegg
HA
df =
ggd
HCHW )
น①
2s
fdk =
gg
Hพ ⑨
แ{
F =
fgw
รู๋
Hdtl
ง②eg
12. pressure in fluid
law
change in the pressure applied to a fluid is transmitted undiminished
to every point of the fluid and to the walls of the container
A B C D
PA = PB = PC = PD
sameg
Connect
} EP = constant
sameh
13. pressure in fluid
Ex6 Water is filled in manometer. If h = 2 m, determine pressure C.
Pc =
คู
+ Patm = Patmt / 9.6
ยุ
ะ 105+19.6g
=
|05+ 19600
=
| 19,600
Pa
2 ะ
งํ๊
d
Pc
14. Ex6 Barometer is filled with mercury (no air inside barometer). If h = cm, find
atmospheric pressure (in SI unit). (Density of mercury = x 103 kg/m3)
pressure in fluid
ไตรอบ
ๆ
ะ
Pa
(13.6×103)(9. 8) 175.9 2) ะ
Pa
%
Pa =
101,186Pa
ยํ๊
→
15. Ex If PA = 9 atm, oil = 0.8 x 103 kg/m3 and Hg = 13.6 x 103 kg/m3, determine h
in oil.
pressure in fluid
oil
Mercury
s 9
P✗
=
[t Sghi 1
อั๋
+ (13.6×103) (9.8) (อ.
3)
Px= 100000+39984 = 139984
[ |39984) t (อ . 8 ✗เอ 3) [9.8) h ะ 9 ✗105
hr 96.94 M
Pxy
16. Ex6 A novice scuba diver practicing in a swimming pool takes enough air from his
tank to fully expand his lungs before abandoning the tank at depth L and swimming to
the surface, failing to exhale during his ascent. At the surface, the difference p
between the external pressure on him and the air pressure in his lungs is 9.3 kPa.
From what depth does he start? What potentially lethal danger does he face?
pressure in fluid
17. Ex6 The U-tube in Fig. contains two liquids in static equilibrium: Water of density =
998 kg/m3 is in the right arm, and oil of unknown density is in the left. Measurement
gives l = 135 mm and d = 12.3 mm. What is the density of the oil?
pressure in fluid
อ .
แ5m ° " " "
i.µ
=
ญู้
t Pmter
8cmYdtl
)
ะ
#erYll
=
µ
3
Soile 998
อ_
รุ่
5
ญํ่
Soi| = 914.66 "
Jlrp
ttrnetcoee
oarosrosnroe
18. pressure in fluid
Hydraulic Lever
A given force applied over a given distance
can be transformed to a greater force applied
over a smaller distance.
PA = PB
( )A = ( )B
Fd A
19. pressure in fluid
Hydraulic Lever
A given force applied over a given distance
can be transformed to a greater force applied
over a smaller distance.
PA = PB
( )A = ( )B
20. pressure in fluid
Ex6 1 Using hydraulic to elevate kg car, find
a) Minimum compressive force (A1 = 10 cm2 and A2 = 0.25 m2)
b) If compression is cm, how height of the car from starting point?
1500 ✗9.8
"
กั๋
กู
ฅฺ
→
ig =
gg
Fg = 58.8 N
b)
-
.
.
. .
.
⇐
.
0.1A 1
=
Agh
0.1 ( 10 ✗1
จั
4) =
[ 0.25) h
อ . 1
{ } n h =
4 ✗ 1
อั
4m µ
21. Ex6 1 In a car lift used in a service station, compressed air exerts a force on a small
piston that has a circular cross section of radius 5.00 cm. This pressure is transmitted
by a liquid to a piston that has a radius of 15.0 cm.
A) What force must the compressed exert to lift a car weighing 13300 N?
B) What air pressure produces this force?
pressure in fluid
a)
ใน →
รฺญุ๋
iEแi
ญุ่
33
ำ
¥
→ F =
1477.78N
b) p =
กั๋
=
133 00 ×
5
ะ_T
ฑิ๊
°
ฐํ๊ะ
P ะ
188251.94
Pa-Lr.in
ขอ
m
/
22. ⑨ ก
ลุ่
ม 7
รุ
จิ
รา๙
Pwine =
µ
5
สึ
ร
วิ
ช
ญ์
Cfgh)พµ
=
µ
5 ณ
ฐาน
(984) (9.8) h ะ
1อ
5
ฃื้ฏื๊
ine
h ะ 10.37 m
*
⑤ Pmercvng =
1อ
5
Cggh)
หg
=
เ
อ๋
( 13.6×10ำ (9.8) hi µ
5
h ะ
0.75 M
h
Hg
< hwine → there will absolutelyhave a vacuum
*
⑨ จาก 8 =
ตู
เอ ✗ เ
อ้
4 V =
§
=
Ofyonns
= 104 m
3
5 ✗ 1
อ้
4
1
อั
4 ะ (5✗ เอา4) 1
ด้
T N
d ะ
0.2 M M
µ
⑤
ทุ
e-
ร+
ะ
Prigµ
④
µ { ② #89
หุ
หํ๋
☒1
"
rign
(13.6×103) h ะ
เอ
3
µ
13.6h = h
Vc = V
@
[ ×
ษู้
4) h = C#¢4) ( อ.
2- 13.6h)
2
2h ะ 0.2 -13.6h
h ะ 0.013 m
*
24. Buoyancy Force : Fb (N)
exists because the pressure in the surrounding water.
Buoyancy force is directed upward
and has a magnitude equal to the weight of the fluid that has been displaced by the body.
Buoyancy force
25. Buoyancy force
Buoyancy Force : Fb (N)
exists because the pressure in the surrounding water.
Buoyancy force is directed upward
and has a magnitude equal to the weight of the fluid that has been displaced by the body.
26. Buoyancy force
EX6.12 A block of density 800 kg/m3 floats face down in a fluid of density 1200
kg/m3. The block has height H = 6 cm. By what depth h is the block submerged?
mg
=
&
0.06
m =
จม
g
V =
f-
ร่
วม →
8
จ้
☒ µะ ☒
% ยา
µ
2 (อ.
อ แ = 3h
0.06 =
f=
ผู๊
^
ะ h =
0.044
*
ซื๊
lffluid
=
120 จ
27. Buoyancy force
EX6.13 Fifteen kilogram gold is attached with string as shown in figure. Determine
tension when the gold is submerged in water. density of gold = x 103 kg/m3)
V =
ธุ๊
=
µ
หื๊
µ
3
โT
T =
mg
-
FB
T ะ
15 (9. 8)
-
(103) 1
ฐิ๋
µ
) ( 9.9
T =
139.38 N
โ FB
I.
28. Buoyancy force
EX6.14 An object has 100 N and 90 N weight when measured in air and water,
respectively. What is its volume?
FB = 100-90 =
10N = 103 V1 9. 8)
ปะ 0.00| มา
ย
29. Buoyancy force
EX6.15 Archimedes supposedly was asked to determine whether a crown made for the
king consisted of pure gold. According to legend, he solved this problem by weighing
the crown first in air and then in water as shown in Figure. Suppose the scale read
7.84 N when the crown was in air and 6.84 N when it was in water. What should
Archimedes have told the king?
Frg ะ
1 N =
gvg
1 =
( เอ3) V [9. 8)
V =
1
ทาง
crown
µ
3
✗ 9.8
Vcrowri
ง
ฒิ๊
=
µ
3
×
นาง=
""
า
d
8gal
=
19.3✗
103kg1m3
Scrowi 7.68 ✗103 kgln
3
30. Buoyancy force
EX6.16 An iceberg floating in seawater as shown in Figure is extremely dangerous
because most of the ice is below the surface. This hidden ice can damage a ship that
is still a considerable distance from the visible ice. What fraction of the iceberg lies
below the water level? ทา
§
=
8¥
ฏุ่
→
gv =
9ร
-
"
จม
ficet 0.917 ✗103 kgm3
ษู
=
ฐู๋
=
¥ *
31. Buoyancy force
EX6.17 An ice floats above water 0.2 m. After an airplane with mass kg stop on
this ice, the sheet of ice start to sink in the water. What is the minimum area of the
sheet of ice which can hold the airplane. (density of ice = kg/m3)
① before landing ② after landing
FB ะ
WAF + WICE
EF = 0
8-¥% ""
4""
""
fttttt
mg=
# ¥$
|03AM ะ 1000 + 920AM 92#H ะ 1000 HfH -0.
2)
A =
'
,
ญื๊ H =
หื
=
§
i. A =
ร่
ฐะ 5
ท้
#
32. Buoyancy force
EX6.1 A hollow cylinder iron has g and g when measure in air and water,
respectively. If the relative density of iron is 11.3, determine volume of air inside this
cylinder. ↳
fimi 11.3 ✗ 103 kghis
FB ะ
75g
N
FB =
f.
รยg
75 = 103 ไปจม
นม ะ
75 ✗ เอง m
3
นะ 7.5 ✗ 1
จิ๋
ต
3
33. Buoyancy force
EX6.1 A wood with mass kg and density kg/m3 floats in water, determine
a) Volume of wood above the water
b) Attached mass making the wood sink in water.
34. FLUID MECHANICS
The Equation of Continuity
is a substance that can flow; it conforms to the boundaries of its container
35. The Equation of Continuity
Fluid Flow
can be characterized as being one of two main types.
Steady (laminar)
- Each particle follows a smooth path.
- The paths never cross each other.
- Every fluid particle arriving at a given
point in space has the same velocity.
Turbulent
- Above a certain critical speed,
fluid flow becomes turbulent.
- The flow is irregular flow
characterized by small whirlpool-like.
laminar flow
laminar flow
36. The Equation of Continuity
Fluid Flow
can be characterized as being one of two main types.
Steady (laminar)
- Each particle follows a smooth path.
- The paths never cross each other.
- Every fluid particle arriving at a given
point in space has the same velocity.
Turbulent
- Above a certain critical speed,
fluid flow becomes turbulent.
- The flow is irregular flow
characterized by small whirlpool-like.
37. The Equation of Continuity
Fluid Flow
can be characterized as being one of two main types.
Steady (laminar)
- Each particle follows a smooth path.
- The paths never cross each other.
- Every fluid particle arriving at a given
point in space has the same velocity.
Turbulent
- Above a certain critical speed,
fluid flow becomes turbulent.
- The flow is irregular flow
characterized by small whirlpool-like.
38. The Equation of Continuity
Fluid Flow
can be characterized as being one of two main types.
Steady (laminar)
- Each particle follows a smooth path.
- The paths never cross each other.
- Every fluid particle arriving at a given
point in space has the same velocity.
Turbulent
- Above a certain critical speed,
fluid flow becomes turbulent.
- The flow is irregular flow
characterized by small whirlpool-like.
39. The Equation of Continuity
Ideal Fluid Flow
The motion of real fluids is very complex and not fully understood,
we make some simplifying assumptions in our approach.
Steady (laminar)
All particles passing through a point have the same velocity.
Nonviscous
Internal friction is neglected. An object moving through the fluid experiences no
viscous force.
Incompressible
The density of an incompressible fluid is constant.
Irrotational
The fluid has no angular momentum about any point. If a small paddle wheel
placed anywhere in the fluid does not rotate about the center of mass.
40. The Equation of Continuity
Equation of continuity for fluids
Consider ideal fluid flow, in the same time interval,
the mass of fluid that passes point 1
must equal the mass that passes point 2
0in ะ
Qout
AM ะ A
ห้
2
41. The Equation of Continuity
EX6. Figure shows how the stream of water emerging from a faucet necks down
as it falls. This change in the horizontal cross-sectional area is characteristic of any
laminar falling stream because the gravitational force increases the speed of the
stream. Here the indicated cross-sectional areas are A0 = 1.2 cm2 and A = 0.35 cm2.
The two levels are separated by a vertical distance h = 45 mm. What is the volume
flow rate from the tap? (1.2 ×
/
เอา4) หะ (0.354
#) ทา
ชำห้
+2gh
ริ๋
-e U =
vu42C9.TT#ExiTf,t
ชะ โหด
2g
h
Uะ 0.00286 mls
Q =
อ§
_g
( 0.00286) = 0.0098
m
%
u
ช
42. The Equation of Continuity
EX6. A gardener uses a water hose to fill a 30 L bucket. The gardener notes that it
takes 1 min to fill the bucket. A nozzle with an opening of cross-sectional area 0.500
cm2 is then attached to the hose. The nozzle is held so that water is projected
horizontally from a point 1.00 m above the ground. Over what horizontal distance can
the water be projected?
43. Bernoulli s Equation
EX6.2 A swimming pool (H m x L 1 m x D m) needs water inside m
height. Using 5 water pipes (diameter cm) with speed of water m/s in each pipe,
how long does it take to reach 2.1 m?
ษุ
{f้gคค~g_
~
6
ัั
/4=
¥= Ar
#
ศั้
ภื๊%
*
⇐
t =
3208.56 s
44. Bernoulli s Equation
EX6.2 A syringe (diameter cm) can extrude water with speed cm/s at the tip of
syringe, as shown in figure. If water pass through the syringe with rate cm3 in 1
second, find d (cm) and v (m/s).
ไหลออก
Cl =
A |
ทุ
-
_
Azy
5 × เ
อ้
°
m
3
T
%¥ |418✗ 1
อั้
) ะ
c
%
ณื๋
%
¥
ทุ๋
=
5 × µ
-
เ
ปาน
5 × เอา
6
ชุ
E 2.55×1
อั
น1s
d-
-0.00595m
dะ 5.95 mn
46. Daniel Bernoulli has derived the relationship between fluid speed, pressure,
and elevation.
+ gh + P = constant
47. Bernoulli s Equation
Daniel Bernoulli has derived the relationship between fluid speed, pressure,
and elevation.
48. Bernoulli s Equation
Bernoulli effect
The vertical component force on airplane wing is called lift.
The curvature of the wing surfaces causes the pressure above the wing to be
lower than that below the wing due to the Bernoulli effect.
+ g + = + g +
+ = +
- = -
P = - )
A x P = A x - )
49. Ex6.2 The horizontal constricted pipe, known as a Venturi tube, can be used to
measure the flow speed of an incompressible fluid. Determine the flow speed at point 2
if the pressure difference P1 - P2 is known.
50. EX6.2 An enclosed tank containing a liquid of density r has a hole in its side at a
distance y1 from the bottom. The hole is open to the atmosphere, and its
diameter is much smaller than the diameter of the tank. The air above the liquid is
maintained at a pressure P. Determine the speed of the liquid as it leaves the hole
when the level is a distance h above the hole.
51. Bernoulli s Equation
EX6.2 Ethanol of density 791 kg/m3 flows smoothly through a horizontal pipe that
tapers in cross-sectional area from A1 = 1.2x10-3 m2 to A2 = A1/2. The pressure
difference between the wide and narrow sections of pipe is 4120 Pa. What is the
volume flow rate RV of the ethanol?
52. Bernoulli s Equation
EX6.2 In the old West, a desperado fires a bullet into an open water tank, creating a
hole a distance h below the water surface. What is the speed v of the water exiting
the tank?
53. EX6.28 A tank of water is full filled by water. At the position above the bottom of
this tank 10 cm has a hole (diameter = cm) which releases water in to a square
container (4m x 4m x 2m). How long does it take to full fill the container.
