1. Purdue University, Physics 220
Lecture 16
Fluids
Lecture 16
Purdue University, Physics 220

2. Purdue University, Physics 220
States of Matter
Solid
Hold Volume
Hold Shape
Liquid
Adapt Shape
Gas
Adapt Volume
Fluids
Compressible/uncompressible
Lecture 16
Purdue University, Physics 220

3. Purdue University, Physics 220
Pressure
Pressure = Fnormal / A
Scalar
Units:
Pascal (Pa) = N/m2
Atmosphere: 1 atm = kPa
1 atm ~ 10 N/cm2 ~ 15 lb/in2
Force due to molecules of fluid colliding with container.
Change in Impulse = Dp
Lecture 16
Purdue University, Physics 220

4. Purdue University, Physics 220
Pascal’s Principle
A change in pressure at any point in a confined fluid is transmitted everywhere in the fluid
Hydraulic Lift
DP = F1 / A1 on right
DP = F2 / A2 on left
Since DP is same, set equal
F1 / A1 = F2 / A2
F2 = F1 (A2 / A1)
Can get LARGE force!
Volume is conserved A1d1 = A2d2
d2 = d1 A1 / A2
Work is the SAME:
W = Fd
F2 d2 = F1(A2/A1)*d1 (A1/A2) = F1 d1
Lecture 16
Purdue University, Physics 220

5. Purdue University, Physics 220
Gravity and Pressure
Consider a small “piece” of the fluid
Draw Forces on the fluid element
y-direction:
P2 A – mg – P1 A = 0
P2 A – (rAd)g – P1 A = 0
P2 – (rd)g – P1 = 0
P2 = P1 + rgd
Pressure under fluid P = Patmosphere + rgd
Basically “weight of air + weight of fluid” y x
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Purdue University, Physics 220

6. Purdue University, Physics 220
Density
Mass density of an object of mass m and volume V
Density = Mass/Volume
 = m/V
Units = kg/m3
Densities of some common things (kg/m3)
Water g/cm3
Ice g/cm3 (floats on water)
Blood g/cm3 (sinks in water)
Lead , g/cm3
Copper g/cm3
Mercury 13, g/cm3
Aluminum g/cm3
Wood g/cm3 (floats on water)
Air g/cm3
Helium g/cm3
Uranium 19, g/cm3
Lecture 16
Purdue University, Physics 220 1

7. Purdue University, Physics 220
Pressure versus Depth
For a fluid in an open container:
The pressure is the same at a given depth, independent of shape of the container
The fluid level is the same in a connected container
Lecture 16
Purdue University, Physics 220

8. Purdue University, Physics 220
iClicker
Two identical “light” containers are filled with water. The first is completely full of water, the second container is filled only ½ way. Compare the pressure each container exerts on the table.
A) P1 > P2 B) P1 = P2 C) P1 < P2
Under water P = Patmosphere + r g h
P = F/A
= mg / A
Cup 1 has greater mass, but same area
Example w/ container of water? Double water double weight, calculate using density, see how A disappears. 1 2
Lecture 16
Purdue University, Physics 220

9. Purdue University, Physics 220
Atmospheric Pressure
Basically weight of atmosphere!
Air molecules are colliding with you right now!
Pressure = 1105 N/m2 = 14.7 lbs/in2
Example 1: Disc r = 2.4 in
A = p r2 = 18.1 in2
F = P A
= (14.7 lbs/in2 )(18.1 in2)
= 266 lbs
Example 2: Sphere r = 0.1 m
A = 4 p r2 = m2
F = 12,000 N (over 2,500 lbs)!
Lecture 16
Purdue University, Physics 220

10. Purdue University, Physics 220
Atmospheric Pressure
You buy a bag of potato chips in Lafayette and forget them (un-opened) under the seat of your car. You drive out to Denver Colorado to visit a friend for Thanksgiving, and when you get there you discover the lost bag of chips. The odd thing you notice right away is that the bag seems to have inflated like a balloon (i.e. it seems much more round and bouncy than when you bought it).
How can you explain this ?
Due to the change in height, the air is much thinner in Denver. Thus, there is less pressure on the outside of the bag of chips in Denver, so the bag seems to inflate because the air pressure on the inside is greater than on the outside. PL PU
In Lafayette PU PD
In Denver
Lecture 16
Purdue University, Physics 220

11. Purdue University, Physics 220
Pressure and Depth
Barometer: a device to measure atmospheric pressure
Pressure at points A and B is the same
PA = Atmospheric Pressure
PA = PB = 0 + r g h = r g h h
p2=patm
p1=0
Measure h, determine patm
Example: Mercury
 = 13,600 kg/m3
patm = 1.05 x 105 Pa
 h = m = 757 mm = 29.80” (for 1 atm) A B
Lecture 16
Purdue University, Physics 220

12. Purdue University, Physics 220
Question
Suppose you have a barometer with mercury and a barometer with water. How does the height hwater compare with the height hmercury?
A) hwater is much larger than hmercury
B) hwater is a little larger than hmercury
C) hwater is a little smaller than hmercury
D) hwater is much smaller than hmercury h
p2=patm
p1=0
Lecture 16
Purdue University, Physics 220

13. Purdue University, Physics 220
Question
Is it possible to stand on the roof of a five story (50 foot) tall house and drink, using a straw, from a glass on the ground?
A) No
B) Yes
p=0 pa h
Evacuate the straw by sucking
How high will water rise?
no more than h = Pa/g = 10.3m = 33.8 feet
no matter how hard you suck!
Lecture 16
Purdue University, Physics 220

14. Purdue University, Physics 220
Lecture 16
Purdue University, Physics 220

15. Purdue University, Physics 220
Manometer
A device to measure gas pressure
PB = PB’ = PC + gd
P = PB - PC = gd
The difference in mercury level d is a measure of the pressure difference.
Start from beginning.
Lecture 16
Purdue University, Physics 220

16. Purdue University, Physics 220
iClicker A B
Two dams of equal height prevent water from entering the basin. Compare the net force due to the water on the two dams.
A) FA > FB B) FA=FB C) FA< FB
F = P A, and pressure is rgh. Same pressure, same area same force even though more water in B!
Lecture 16
Purdue University, Physics 220

17. Archimedes’ Principle
Determine force of fluid on immersed cube
Draw FBD
FB = F2 – F1
= P2 A – P1 A
= (P2 – P1)A
= r g d A
= r g V
Buoyant force is weight of displaced fluid!
A fluid exerts an upward buoyant force on a submerged object equal in magnitude to the weight of the volume of fluid displaced by the object
Lecture 16
Purdue University, Physics 220

18. Purdue University, Physics 220
Sink or Float
The buoyant force is equal to the weight of the liquid that is displaced
If the buoyant force is larger than the weight of the object, it will float; otherwise it will sink
We can calculate how much of a floating object will be submerge
Object is in equilibrium
FB = mg y
Lecture 16
Purdue University, Physics 220

19. Archimedes’ Principle
Does an object float or sink?
F = (fluid-solid) gV
fluid > solid F > 0 object rises
fluid = solid F = 0 neutral buoyancy
fluid < solid F < 0 object sinks
Lecture 16
Purdue University, Physics 220

20. Purdue University, Physics 220
Archimedes Example
A cube of plastic 4.0 cm on a side with density = 0.8 g/cm3 is floating in the water. When a 9 gram coin is placed on the block, how much does it sink below water surface?
S F = m a
Fb – Mg – mg = 0
r g Vdisp = (M+m) g
Vdisp = (M+m) / r
h A = (M+m) / r
h = (M + m)/ (r A)
= (51.2+9)/(1 x 4 x 4) = 3.76 cm mg Fb Mg h
Transparency
M = rplastic Vcube
= 4x4x4x0.8
= 51.2 g
Lecture 16
Purdue University, Physics 220

21. Purdue University, Physics 220
Illustration y
Lecture 16
Purdue University, Physics 220