CHAPTER 9 SOLID & FLUIDS
(9.39.10)
9.3 Density and Pressure
Density and can depend on temperature. Specific gravity .
Pressure in a fluid
At any particular depth, the pressure is constant throughout a fluid.


A 70kg man in a 5.0 kg chair tilts back so that all the weight is balanced on two legs of the chair. Assume that each leg makes contact with the floor over a circular area with a radius of 1.0 cm, and find the pressure exerted on the floor by each leg.
9.4 Variation of Pressure with Depth
In equilibrium, all points at the same depth must be at the same pressure. Otherwise a net force would be applied and the fluid would accelerate. 


Pick a volume of fluid a distance h below the surface:

P_{0} =1.013x10^{5} Pa at sea level
P increases with depth by an amount mgh.
NOTE that an increase in pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid (including the walls of the container) Pascal’s Principle
Worked Example:
At what depth in the ocean is the pressure twice that of the atmosphere alone (the density of seawater is about 1.02 kg m^{3})?
What to wear at a depth of 200m?
Can you think of other applications of this principle?
Two devices for measuring pressure:


opentube manometer 
barometer 
Manometer:
Note that P = absolute (true) pressure inside the bulb. PP_{0} is the gauge pressure, the pressure that is added to the atmospheric pressure to equal P.
Barometer:
1 atm. → pressure equal to a 0.76 m column of mercury at T=0°C and g=9.80665 m s^{2}.
You can read Torecelli’s own description of his barometer here.

Blood pressure is measured in terms of the column of mercury (in millimeters) that could be supported by the pressure inside the arteries at two times: maximum thrust by the heart, and when the heart is relaxed. These are normally about 120 mm and 80 mm, respectively.
Recent medical guidelines suggest that the familiar old “normal” 120/80 values are too high, and that somewhat lower values are desired! 
Exercise:
A collapsible plastic bag contains a glucose solution. If the average gauge pressure in the artery is 1.33x10^{4} Pa, what must be the minimum height h of the bag in order to infuse glucose into the artery? Assume that the specific gravity of the solution is 1.02. 

Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of fluid displaced by the object.
Sink or Float? Depends on Bw where w is the weight of the object.
For a completely submerged object, the volume of the object is the volume of displaced fluid,
For an object floating partially submerged on the surface,
A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm^{3}. If the pod has a radius of 6.00 cm and negligible mass, what is the mass of the frog? 

The density of ice is 920 kg/m^{3}n and that of seawater is 1030 kg/m^{3}. What fraction of the total volume of an iceberg is exposed?
9.7 Fluids in Motion
2 types of flow: laminar (streamline) & turbulent
Example: Numerical simulation of flow over a racing car. Here, the pressure is colorcoded, with blue being low pressure and red being high pressure. The flow lines are drawn in. Note that while the flow is laminar over much of the car, it breaks up into turbulent eddies behind the car.
For more neat simulations go here.
Ideal Fluids:
Equation of Continuity
For an incompressible fluid, flowing with no added “sources” or “sinks”:
Can you think of some examples of this principle?
Bernoulli’s Equation
Here, we will look at how the pressure changes in a laminar fluid flow.
Now, part of the work goes into changing the KE of the fluid, and part goes into changing the gravitational potential energy (mgh stuff).
Venturi Tube:
9.8 Other Applications
Aircraft Wing:
When air flows over the wing of an aircraft, the flow is faster over the more curved top than on the bottom, so that the pressure is lower on top than on the bottom. (Note: air is compressible, but the effect is small in this case and can be ignored). The tilt also aids lift. But turbulence disrupts the flow, diminishing the effect. 

Atomizer:

A stream of air passing over a tube dipped in a liquid causes the liquid to rise in the tube. Used in perfume atomizer bottles and paint sprayers.

Vascular Flutter:
The constriction in the blood vessel speeds up going through the constriction. The lower pressure causes the vessel to close, stopping the flow. Without flow, there is no Bernoulli effect, and blood pressure causes it to reopen. The process repeats.



Consider the portion of a home plumbing system shown in the figure to the left. The water trap in the pipe below the sink captures a plug of water that prevents sewer gas from finding its way from the sewer pipe, up the sink drain, and into the home. Suppose the dishwasher is draining, so that water is moving to the left in the sewer pipe. What is the purpose of the vent, which is open to the air above the roof of the house? In which direction is air moving at the opening of the vent, upward or downward? 
What is the net upward force on an airplane wing of area 20.0 m^{2} if the airflow is 300 m/s across the top of the wing and 280 m/s across the bottom?
A hypodermic syringe contains a medicine with the density of water. The barrel of the syringe has a crosssectional area of 2.50x10^{5} m^{2}. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude 2.00 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine’s flow speed through the needle. Assume that the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal. 

9.9 Surface Tension, Capillary Action, and Viscous Fluid Flow
The combined electrical attraction of molecules in a fluid gives rise to a force that tends to minimize the surface area of the fluid. This makes raindrops spherical. If they weren’t we would not see rainbows the way we do!
This surface tension γ acts like a local force along the surface of the fluid:
Note that the units are the same as the spring constant.
The surface tension can support small objects placed on top of the surface (such as a needle, which will float if placed carefully on the surface of still water), and hold back others from leaving it (this impedes evaporation from a body of water, for example).
The surface tension of a fluid can be measured with a device like that shown here. If the force required to break free of the water is F, then
where r is the radius of the hoop. (Here we need to factor of 2 because the surface tension exerts forces on the inside and the outside of the ring. 

The following table lists the surface tension of some common fluids.
Note that γ depends on temperature. At higher T, the
molecules are not as tightly bound together. You can also alter the surface
tension of fluids using additives.
When water sits on a surface or in a container, the shape the water takes depends on whether it is more strongly attracted to itself (cohesion) or to the “other” material (adhesion). 

Detergents wet allows water to penetrate clothes when washing and to spread over glass surfaces better.
Repellants water beads up & penetrates less.


Wetting pulls up Examples paper towels, sponges, mops, fingerprick blood samples 
Nonwetting pushes down 
A staining solution used in
a microbiology laboratory has a surface tension of 0.088 N/m and a density
1.035 times that of water. What must be the diameter of a capillary tube so
that this solution will rise to a height of 5 cm? (Assume a contact angle of
zero).
Viscosity the internal friction of a fluid. Resistance to shear stress.
Affects blood flow, squeezing Krazy Glue gel out of its tube, etc.
When is the onset of turbulence? Fluid flow in a pipe of diameter d:
9.10 Transport Phenomena
Net movement of a population across a “crosssection” by random walk from a region where the concentration is higher to a region where it is lower.
Osmosis
Movement of water from a region where its concentration is high, across a selectively permeable membrane, into a region where it is lower.
(READ THIS SECTION ON YOUR OWN)
Note use in artificial kidneys. Used in both hemodyalisis and paritoneal dialysis.
Resistive force on spherical object of radius r:
Terminal Speed net force goes to zero velocity is constant