PHYSICS 231 Lecture 24: Walking on water

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PHYSICS 231Lecture 24 Walking on water other
magic

• Remco Zegers
• Walk-in hour Thursday 1130-1330 am
• Helproom

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P0
Pressure at depth h
P P0 ?fluidgh h distance between liquid
surface and the point where you measure P
h
P
Buoyant force for submerged object
B ?fluidVobjectg Mfluidg wfluid The
buoyant force equals the weight of the amount of
water that can be put in the volume taken by the
object. If object is not moving Bwobject
?object ?fluid
Buoyant force for floating object
The buoyant force equals the weight of the amount
of water that can be put in the part of the
volume of the object that is under
water. ?objectVobject ?waterVdisplaced h
?objectVobject/(?waterA)
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Bernoullis equation
P1½?v12?gy1 P2½?v22?gy2 P½?v2?gyconstant
The sum of the pressure (P), the kinetic energy
per unit volume (½?v2) and the potential energy
per unit volume (?gy) is constant at all points
along a path of flow.
Note that for an incompressible
fluid A1v1A2v2 This is called the equation
of continuity.
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Applications of Bernoullis law
The examples shown are with air, not with
fluid. Remember that we derived this law for
an incompressible fluid. Air is not
incompressible, so the situation is typically
more complicated But easier to show!
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Applications of Bernoullis law moving a cart
No spin, no movement
Vair
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Applications of Bernoullis law the golf ball
Neglecting the small change in height between
the top and bottom of the golf ball
P1½?v12 P2½?v22 P1-P2 ½?(v22- v12)
P1
P1-P2 ½?(v22- v12)0 v2v1 No pressure
difference, no lift
P2
P1
P1-P2 ½?(v2-v)2-(v1 v) 20 P2gtP1 so Upward
force the ball goes higher and thus travels
faster
P2
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Not the whole story the dimples in the golf ball
reduce the drag
The drag is the force you feel when you are
biking. The pressure in front of you is higher
than behind you, so you feel a force against the
direction of your motion.
A
B
P1
P2
P1
P3
P3gtP2 there is less drag in case B
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Demo
A floating globe
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Energy
Surface tension
Two liquid molecules like to sit close to each
other (energy is gained)
0
-Emin
R
R
2 liquid molecules
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A bunch of liquid molecules
Inside the liquid
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1
5
4
2
3
The molecule in the center gains 6 times Emin of
energy. The summed energy is reduced by 6Emin
It is energetically favorable to keep the surface
of the liquid as small as possible
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Why does water make droplets on asurface and
does not spread out?
The liquid surface is smallest energetically
favorable.
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Surface tension
If you make the surface of the fluid larger, it
tries to push back. The force with which this
is done Fs?L where L is the length over which
the force acts and ? is the surface tension. The
force works parallel to the water surface.
Example a needle on water
Top view
Fs
Fs
?
L
Fg
Horizontal Fscos?-Fscos?0 Vertical
Fssin?Fssin?-Fg0 ?mneedleg/(2Lsin?)
Units of ? N/mJ/m2 Energy per unit surface
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Walking on water
The insect uses surface tension!
Surface tension depends on the type of liquid.
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Forces between molecules
Cohesive forces forces between like
molecules Adhesive forces forces between unlike
molecules
Adhesive
Cohesive
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More on surfaces
If cohesive forces are stronger than the adhesive
ones like molecules in the drop try to stay
together to reduce the total energy of the
system if adhesive forces are stronger the drop
will spread out to reduce the total energy of the
system. The spreading will stop when the surface
tension becomes too strong.
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Same thing
Adhesive gt Cohesive The water wants to cover as
much of the glass as its surface tension allows
Adhesive lt Cohesive The mercury wants to cover as
little of the glass as its surface tension allows
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Capillary action
Fsurface tesion?L ?2?r Vertical (upwards)
component FSTvertical?2?rcos? The weight of
the liquid in the tube wMg??r2gh The liquid
stops going up when FSTverticalw h2?cos?/(?gr)
If r very large h very small!
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Viscosity
Viscosity stickiness of a fluid One layer of
fluid feels a large resistive force when
sliding along another one or along a surface of
for example a tube.
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Viscosity
Contact surface A
moving
F?Av/d ?coefficient of viscosity unit
Ns/m2 or poise0.1 Ns/m2
fixed
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Poiseuilles Law
How fast does a fluid flow through a tube?
?R4(P1-P2)
(unit m3/s)
Rate of flow Q ?v/?t
8?L
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Example
Flow rate Q0.5 m3/s Tube length 3 m ?1500E-03
Ns/m2
PP106 Pa
P105 Pa
What should the radius of the tube be?