PHY 231 1 PHYSICS 231 Lecture 30: review Remco Zegers Walk-in hour: Monday 9:15-10:15 am Helproom.
PHY 231 1 PHYSICS 231 Lecture 24: Walking on water & other ‘magic’ Remco Zegers Walk-in hour:...
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Transcript of PHY 231 1 PHYSICS 231 Lecture 24: Walking on water & other ‘magic’ Remco Zegers Walk-in hour:...
PHY 2311
PHYSICS 231Lecture 24: Walking on water & other
‘magic’
Remco ZegersWalk-in hour: Thursday 11:30-13:30 am
Helproom
PHY 2312
P = P0+ fluidghh: distance between liquid surface and the point where you measure P
P0
P
h
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: B=wobject object= fluid
Pressure at depth h
Buoyant force for submerged object
Buoyant force for floating objecthB
w
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)
PHY 2313
Bernoulli’s equation
P1+½v12+gy1=
P2+½v22+gy2
P+½v2+gy=constant
The sum of the pressure (P), the kinetic energy per unit volume (½v2) and the potential energy per unit volume (gy)is constant at all points along a path of flow.
Note that for an incompressible fluid:A1v1=A2v2
This is called the equation ofcontinuity.
PHY 2314
Applications of Bernoulli’s law
The examples shown are with air, not with fluid.Remember that we derived this law for anincompressible fluid. Air is not incompressible,so the situation is typically more complicated…
But easier to show!
PHY 2315
Applications of Bernoulli’s law: moving a cart
No spin, no movementVair
Spin and movementP1 V1=Vair+v
V2=Vair-v P2
Near the surface of the rotating cylinder: V1>V2P1+½v1
2= P2+½v22
P1-P2= ½(v22- v1
2)P1-P2= ½[(vair-v)2-(vair+ v)
2]P2>P1 so move to the left
PHY 2316
Applications of Bernoulli’s law: the golf ball
P1
P2
Neglecting the small change in height between thetop and bottom of the golf ball:
P1+½v12= P2+½v2
2
P1-P2= ½(v22- v1
2)
P1
P2
P1-P2= ½(v22- v1
2)=0v2=v1
No pressure difference, no lift
P1-P2= ½(v2-v)2-(v1+ v) 2=0
P2>P1 so:Upward force: the ball goes higherand thus travels faster
PHY 2317
Not the whole story: the dimples in the golf ball reduce the drag
P1 P2 P1 P3
P3>P2 : there is less drag in case B
A B
The drag is the force you feel when you are biking. The pressure in front of you is higher than behind you, so youfeel a force against the direction of your motion.
PHY 2318
Demo
A floating globe
PHY 2319
Surface tension
R
Energy
0
R
2 liquid molecules
Two liquid molecules like tosit close to each other (energyis gained)
-Emin
PHY 23110
A bunch of liquid molecules
16
54
32
The molecule in the centergains 6 times Emin of energy.The summed energy is reduced by 6Emin
Inside the liquid
1
2 3
4
Near the surface of the liquid
The molecule near thesurface only gains 4 timesEmin of energy. The summedenergy is only reduced by4Emin.
It is energetically favorable to keepthe surface of the liquid as smallas possible
PHY 23111
Why does water make droplets on asurface and does not spread out?
The liquid surface is smallest:energetically favorable.
PHY 23112
Surface tensionIf you make the surface of the fluid larger, it tries to‘push’ back. The force with which this is done: Fs=Lwhere L is the length over which the force acts and is the surface tension. The force works parallel to thewater surface. Example: a needle on water
Top view
L
Fs Fs
FgHorizontal: Fscos-Fscos=0Vertical: Fssin+Fssin-Fg=0
=mneedleg/(2Lsin)
Units of : N/m=J/m2
Energy per unit surface
PHY 23113
Walking on water
The insect uses surface tension!
Surface tension depends on the type of liquid.
PHY 23114
Forces between molecules
Cohesive forces: forces between like moleculesAdhesive forces: forces between unlike molecules
Cohesive Adhesive
PHY 23115
More on surfaces
If cohesive forces are stronger than the adhesive oneslike 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 totalenergy of the system. The spreading will stop when thesurface tension becomes too strong.
PHY 23116
Same thing
Adhesive > CohesiveThe water wants tocover as much ofthe glass as its surface tension allows
Adhesive < CohesiveThe mercury wants tocover as little of the glassas its surface tension allows
PHY 23117
Capillary action
Fsurface tesion=L= 2rVertical (upwards) component:FSTvertical=2rcos
The weight of the liquid in the tube: w=Mg=r2gh
The liquid stops going up when:FSTvertical=wh=2cos/(gr)
If r very large: h very small!
PHY 23118
Viscosity
Viscosity: stickiness of a fluidOne layer of fluid feels a largeresistive force when slidingalong another one or along asurface of for example a tube.
PHY 23119
ViscosityContact surface A
fixed
movingF=Av/d
=coefficient of viscosityunit: Ns/m2
or poise=0.1 Ns/m2
PHY 23120
Poiseuille’s Law
How fast does a fluid flowthrough a tube?
Rate of flow Q= v/t=R4(P1-P2)
8L(unit: m3/s)
PHY 23121
Example
PP=106 Pa P=105 Pa
Flow rate Q=0.5 m3/sTube length: 3 m=1500E-03 Ns/m2
What should the radius of the tube be?
Rate of flow Q=R4(P1-P2)
8L
R=[8QL/((P1-P2))]1/4=0.05 m