PHYS 0212 Fluid Mechanics
1
Fluid Mechanics
This experiment has four parts:
2. Venturi Tube – Fluid velocity
1. Archimedes’ Principle – Why things float (or not)
3. Blood Pressure – Bernoulli’s equation
4. Diffusion and Osmosis – Fick’s law
A fluid is either a liquid or a gas.
Air and Water are both fluids.
Force
Pressure
Area
=
F
P
A
=
2
N
Units:
Pascal (Pa)
m
=
F
PA
=
Pressure as a function of depth in a fluid:
0
PP g
h
ρ
=+
0
Pressure at the top of the fluid
P
=
Density of the fluid
=
Depth
h
=
PHYS 0212 Fluid Mechanics
2
Archimedes’ Principle:
Picture a cube with sides
s
submerged in a fluid.
Force:
h
s
s
s
Pressure at the top of the cube:
0
top
PPg
h
(
)
2
0
top
top
F
PA P
g
hs
==
+
(
)
0
bottom
PP
g
h
s
+
(
)
()
2
0
bottom
bottom
F
PAP g
h
s
s
+
+
Pressure at the bottom of the cube:
Force:
The force on a vertical side
varies with the depth, but
the forces on opposite sides
cancel each other out.
top
F
bottom
F
side
F
side
F
B
bottom
top
F
FF
=−
Buoyant Force:
0
x
F
=
∑
s
2
A ss s
=×=
PHYS 0212 Fluid Mechanics
3
B
bottom
top
F
(
)
2
00
B
F
Pg
hg
s
h
s
ρρ
=+ + −−
3
B
F
gs
gV
(
)
(
)
22
B
F
h
s
sPg
h
s
+ −+
B
F
gV
=
Though this was derived for
the case of a cube but it is true
for any shape of the volume.
PHYS 0212 Fluid Mechanics
4
yy
F
ma
gV
mg
−
∑
Float
Vm
>
Sink
<
mass of water displaced by the object
V
=
mg
gV
Note that the buoyancy force does not depend on the depth of object
in the fluid.
?
Fm
a
=
=
∑
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View Full DocumentPHYS 0212 Fluid Mechanics
5
mass of balloon and air
volume of the balloon
density of water
weight > buoyant force
b
b
bB
b
bb
m
V
mg F
gV
mg
mV
ρ
=
=
=
>=
>
>
Is it possible for a balloon filled with air to sink in water?
b) No
a) Yes
()
(
)
3
32
3
kg
4
5
3
m
0
kg
m
ms
1000
0.1 m
1.013 10 Pa
11
0.01 kg
1000
9.80
4320 m
2.68 mi
o
b
PV
h
gm
h
π
×
=−
=
−
==
PHYS 0212 Fluid Mechanics
6
PHYS 0212 Fluid Mechanics
7
Cartesian Diver
Increase the pressure at
the top of the column of
water and the
volume
of
air inside the diver will
decrease.
Decrease the pressure at
the top of the column of
water and the
volume
of
air inside the diver will
increase.
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 Spring '08
 Naples
 Physics, Fluid Dynamics, mechanics, Osmosis, Buoyancy

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