Fluids

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Fluids

• Dr. Robert MacKay

Clark College
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Mass Density, r
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Weight Density, D
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Volume
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Some Densities
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Specific Gravity
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Pressure
Force
Pressure
Area
F
P
A
F P A
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Quick Quiz 14.1
Suppose you are standing directly behind someone
who steps back and accidentally stomps on your
foot with the heel of one shoe. Would you be
better off if that person were (a) a large
professional basketball player wearing sneakers
(b) a petite woman wearing spike-heeled shoes?
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Quick Quiz 14.1
Answer (a). Because the basketball players
weight is distributed over the larger surface
area of the shoe, the pressure (F / A) that he
applies is relatively small. The womans lesser
weight is distributed over the very small
cross-sectional area of the spiked heel, so the
pressure is high.
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Figure P14.62
In about 1657 Otto von Guericke, inventor of the
air pump, evacuated a sphere made of two brass
hemispheres. Two teams of eight horses each could
pull the hemispheres apart only on some trials,
and then "with greatest difficulty," with the
resulting sound likened to a cannon firing (Fig.
P14.62). (a) Show that the force F required to
pull the evacuated hemispheres apart is pR2(P0
P), where R is the radius of the hemispheres and
P is the pressure inside the hemispheres, which
is much less than P0. (b) Determine the force if
P 0.100P0 and R 0.300 m.
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Pressure with increasing depth
mrV wmg
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Barometer
Patms1.013x105 N/m2 1.013x105 Pa
1.013 bar 1 Atmosphere
1013 mb 760 mm Hg 29.92
in Hg 760 Torr 14.7 lb/in2
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manometer
Pgauge rgh
PabsPatmPgauge
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Quick Quiz 14.2
The pressure at the bottom of a filled glass of
water (? 1 000 kg/m3) is P. The water is
poured out and the glass is filled with ethyl
alcohol (? 806 kg/m3). The pressure at the
bottom of the glass is (a) smaller than P (b)
equal to P (c) larger than P (d) indeterminate
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Quick Quiz 14.2
Answer (a). Because both fluids have the same
depth, the one with the smaller density (alcohol)
will exert the smaller pressure.
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Archimedes Principle
Active Figure 1409
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Archimedes Principle
The Buoyant force acting on an object submerged
in a fluid equals the weight of fluid displaced
by the object.
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Buoyancy
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Buoyancy
m 100 g
400 g
V m/r 100 cm3
robj ?
500g
rf 1.00 g/cm3
?
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Buoyancy
m 100 g
400 g
V m/r 100 cm3
robj 5 g/cm3
500g
rf 1.00 g/cm3
?
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Buoyancy
m 100 g
400 g
V ?
robj8.0 g /cm3
500g
rf ?
?
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Buoyancy
m 100 g
V 500g/8.0 g /cm3 V62.5 cm3
400 g
robj8.0 g /cm3
500g
rf 100g/62.5 cm3 1.6 g /cm3
?
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Buoyancy
A 20,000,000 tonn ship Floats in salt water. (1
tonn1000kg) How much water does this
ship Displace?
Active Figure 1410
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QUICK QUIZ 14.2
(end of section 14.4)

• For a physics experiment, you drop three objects
  of equal mass into a swimming pool. One object
  is a piece of pine, the second object is a hunk
  of copper and the third object is a hunk of lead.
  The relationship between the magnitudes of the
  buoyant forces on these three objects will be
• Fcopper gt Fpine gt Flead,
• b) Fpine gt Fcopper gt Flead,
• c) Flead gt Fcopper gt Fpine or
• d) Fcopper gt Flead gt Fpine.

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(b). From Archimedes principle, the magnitude
of the buoyant force will be equal to the weight
of the water displaced. From Table 14.1, lead
and copper are more dense than water and will
therefore sink, while pine is less dense than
water and will therefore float. The buoyant force
for the pine must equal the weight, mg, of the
pine since these two forces balance. For
completely submerged objects, the buoyant force
will be equal to the weight of the water
displaced, mwg, and will be less for the denser
lead, because of its smaller volume, than for the
copper. In addition, the mass of the water
displaced will be less than the mass of the equal
volume of metal displacing it, so that mw lt m.
Therefore, the buoyant force on each metal is
less than the buoyant force on the pine.
QUICK QUIZ 14.2 ANSWER
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Buoyancy
A cubical block of wood has 30.0 cm sides.
If Its density is 600 kg/m3 how much of it is
submerged when floating in water?
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Buoyancy
A cubical block of wood has 30.0 cm sides.
If Its density is 600 kg/m3 how much mass must
be placed on its top to just barely submerge it?
M?
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Quick Quiz 14.6
A glass of water contains a single floating ice
cube as in the figure below. When the ice melts,
the water level (a) goes up (b) goes down (c)
remains the same
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Quick Quiz 14.6
Answer (c). The ice cube displaces a volume of
water that has a weight equal to that of the ice
cube. When the ice cube melts, it becomes a
parcel of water with the same weight and exactly
the volume that was displaced by the ice cube
before.
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A barge loaded with steel floats in a lock. If
the steel is then thrown overboard. Does the
water level in the lock a) go up b) go down
c) stay at the same level?
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Before H2O displaced W(boat)W(steel) After
H2O displaced W(boat)little more
A barge loaded with steel floats in a lock. If
the steel is then thrown overboard. Does the
water level in the lock a) go up b) go down
c) stay at the same level?
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Quick Quiz 14.5
An apple is held completely submerged just below
the surface of a container of water. The apple is
then moved to a deeper point in the water.
Compared to the force needed to hold the apple
just below the surface, the force needed to hold
it at a deeper point is (a) larger (b) the same
(c) smaller (d) impossible to determine
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Quick Quiz 14.5
Answer (b). For a totally submerged object, the
buoyant force does not depend on the depth in an
incompressible fluid.
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Continuity
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Equation of Continuity
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Volume rate of flow
Water flows out of a 1.0 inch hose at a speed of
2.0 ft/s. How long will it take this hose to
fill a 50 gallon drum?
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Quick Quiz 14.8
You tape two different sodas straws together
end-to-end to make a longer straw with no leaks.
The two straws have radii of 3 mm and 5 mm. You
drink a soda through your combination straw. In
which straw is the speed of the liquid the
highest? (a) whichever one is nearest your mouth
(b) the one of radius 3 mm (c) the one of
radius 5 mm (d) Neither the speed is the same
in both straws.
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Quick Quiz 14.8
Answer (b). The liquid moves at the highest
speed in the straw with the smaller cross
sectional area.
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Example

• A 1.0 inch diameter hose is connected to a 0.25
  in diameter nozzle. If the water shoots up in
  the air to a maximum height of 15.0 m, what is
  the flow rate (gallons/min) in the hose? (231
  in31 gallon)

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You would like to change the opening on the
nozzle of a fire hose so that the water exiting
the hose can reach a height that is four times
the present maximum height the water can reach.
To do this, you should decrease the cross
sectional area of the opening by a factor of a)
16, b) 8, c) 4 d) 2.
QUICK QUIZ 14.5
(end of section 14.5)
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QUICK QUIZ 14.5 ANSWER
(d). From the continuity equation, the velocity
of the water exiting the hose is inversely
proportional to the cross sectional area or v ?
1/A. However, the kinetic energy of the water
that exits the hose will be equal to the
potential energy of the water at its maximum
height (when you point the hose straight up),
or So to increase the height by a factor of
four, you must decrease the area by a factor of
2.
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Bernoullis Principle

• Where the fluid speed is high the internal
  pressure is low. based on the conservation of
  energy

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Bernoullis Principle
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Bernoullis Principle
http//www.aerospaceweb.org/question/aerodynamics/

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Bernoullis Principle
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Bernoullis Principle
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Bernoullis Principle
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Bernoullis Principle
A2
?m1
v1
A1
F1P1A1
?x1 v1?t
v2
?m2
F2P2A2
?m1 ?m2
?x2 v2 ?t
y2
y1
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Bernoullis Principle
0.0
0.0
V1 0.0
h1 h
h2 0.0 , P2P1
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Bernoullis Principle
0.0
0.0
V1 0.0
h1 h
h2 0.0 , P2P1
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Bernoullis Principle
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Bernoullis Principle
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Bernoullis Principle
(P1-P2)ALift
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Surface Tension
g L F
Water , g T 0.076 N/m 0C 0.072 N/m
20C 0.059 N/m 100 C
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Capillary Action
2 p r g r p r2 h g
r
h
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Viscosity
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Viscosity
Viscosity (Pa s) Fluid 0.0018
0C water 0.0010 20C
water 0.0003 100 C water 0.0040
37C blood
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Poiseuilles Law
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Stokes Law, terminal velocity of a sphere