two aspects of this extra pressure to consider – one is the increase in pressure di erential across the valve, but perhaps the greater one is the increase in pressure di erential between the inside of the vein and the outside tissue. The latter causes the vein to dilate (swell, increase its radius) as the tissue stretches until its tension can supply the pressure needed to confine the blood column.

Opposing this positively fed-back tendency to dilate, which compromises valves, which in turn increases the dilation to eventual destruction are things like muscle use (contracting surrounding muscles exerts extra pressure on the outside of veins and hence decreases the pressure di erential and stress on the venous tissue), general muscle and skin tone (the skin and surrounding tissue helps maintain a pressure outside of the veins that is already higher than ambient air pressure, and keeping one’s blood pressure under control, as the diastolic pressure sets the scale for the venous pressure during diastoli and if it is high then the minimum pressure di erential across the vein walls will be correspondingly high. Elevating one’s feet can also help, exercise helps, wearing support stockings that act like a second skin and increase the pressure outside of the veins can help.

Carrying the extra pressure below compromised valves nearly all of the time, the veins gradually dilate until they are many times their normal diameter, and significant amounts of blood pool in them – these “ropy”, twisted, fat, deformed veins that not infrequently visibly pop up out of the skin in which they are embedded are the varicose veins.

Naturally, gira es have this problem in spades. The pressure in their lower extremities, even allowing for their system of valves, is great enough to rupture their capillaries. To keep this from happening, the skin on the legs of a gira e is among the thickest and strongest found in nature – it functions like an astronaut’s “g-suit” or a permanent pair of support stockings, maintaining a high baseline pressure in the tissue of the legs outside of the veins and capillaries, and thereby reducing the pressure di erential.

Another cool fact about gira es – as noted above, they pretty much live with “high blood pressure” – their normal pressure of 280/180 torr (mmHg) is 2-3 times that of humans (because their height is 2-3 times that of humans) in order to keep their brain perfused with blood. This pressure has to further elevate when they e.g. run away from predators or are stressed. Older adult gira es have a tendency to die of a heart attack if they run for too long a time, so zoos have to take care to avoid stressing them if they wish to capture them!

Finally, gira es splay their legs when they drink so that they reduced the pressure di erential the peristalsis of their gullet has to maintain to pump water up and over the hump down into their stomach. Even this doesn’t completely exhaust the interesting list of gira e facts associated with their fluid systems. Future physicians would be well advised to take a closer peek at these very large mammals (as well as at elephants, who have many of the same problems but very di erent evolutionary adaptations to accommodate them) in order to gain insight into the complex fluid dynamics to be found in the human body.

Homework for Week 8

Problem 1.

Physics Concepts: Make this week’s physics concepts summary as you work all of the problems in this week’s assignment. Be sure to cross-reference each concept in the summary to the problem(s) they were key to, and include concepts from previous weeks as necessary. Do the work carefully enough that you can (after it has been handed in and graded) punch it and add it to a three ring binder for review and study come finals!

a) A 1 = 30 cm 2, v1 = 3 cm/sec, A 2 = 6 cm 2

b) A 1 = 10 cm 2, v1 = 8 cm/sec, A 2 = 5 cm 2

c) A 1 = 20 cm 2, v1 = 3 cm/sec, A 2 = 3 cm 2

H

In the figure above three flasks are drawn that have the same (shaded) cross sectional area of the bottom. The depth of the water in all three flasks is H, and so the pressure at the bottom in all three cases is the same. Explain how the force exerted by the fluid on the circular bottom can be the same for all three flasks when all three flasks contain di erent weights of water.

Problem 7.

y

L

y R

This problem will help you learn required concepts such as:

•Pascal’s Principle

•Static Equilibrium

so please review them before you begin.

A vertical U-tube open to the air at the top is filled with oil (density ρo) on one side and water (density ρw) on the other, where ρo < ρw. Find yL, the height of the column on the left, in terms

of the densities, g, and yR as needed. Clearly label the oil and the water in the diagram below and show all reasoning including the basic principle(s) upon which your answer is based.

Problem 8.

Pump?

Outflow

H

This problem will help you learn required concepts such as:

•Static Pressure

•Barometers

so please review them before you begin.

A pump is a machine that can maintain a pressure di erential between its two sides. A particular pump that can maintain a pressure di erential of as much as 10 atmospheres of pressure between the low pressure side and the high pressure side is being used on a construction site.

a)Your construction boss has just called you into her o ce to either explain why they aren’t getting any water out of the pump on top of the H = 25 meter high cli shown above. Examine the schematic above and show (algebraically) why it cannot possibly deliver water that high. Your explanation should include an invocation of the appropriate physical law(s) and an explicit calculation of the highest distance the a pump could lift water in this arrangement. Why is the notion that the pump “sucks water up” misleading? What really moves the water up?

b)If you answered a), you get to keep your job. If you answer b), you might even get a raise (or at least, get full credit on this problem)! Tell your boss where this single pump should be located to move water up to the top and show (draw a picture of) how it should be hooked up.

Problem 9.

This problem will help you learn required concepts such as:

•Archimedes Principle

•Weight

so please review them before you begin.

That it is dangerous to build a drain for a pool or tub consisting of a single narrow pipe that drops down a long ways before encountering air at atmospheric pressure was demonstrated tragically in an accident that occurred (no fooling!) within two miles from where you are sitting (a baby pool was built with just such a drain, and was being drained one day when a little girl sat down on the drain and was severely injured).

In this problem you will analyze why.

Suppose the mouth of a drain is a circle five centimeters in radius, and the pool has been draining long enough that its drain pipe is filled with water (and no bubbles) to a depth of ten meters below the top of the drain, where it exits in a sewer line open to atmospheric pressure. The pool is 50 cm deep. If a thin steel plate is dropped to suddenly cover the drain with a watertight seal, what is the force one would have to exert to remove it straight up?

Note carefully this force relative to the likely strength of mere flesh and bone (or even thin steel plates!) Ignorance of physics can be actively dangerous.

Problem 11.

A

P

BEER H

P0

a

h

R

This problem will help you learn required concepts such as:

•Bernoulli’s Equation

•Toricelli’s Law

so please review them before you begin.

In the figure above, a CO2 cartridge is used to maintain a pressure P on top of the beer in a beer keg, which is full up to a height H above the tap at the bottom (which is obviously open to normal air pressure) a height h above the ground. The keg has a cross-sectional area A at the top. Somebody has pulled the tube and valve o of the tap (which has a cross sectional area of a) at the bottom.

a)Find the speed with which the beer emerges from the tap. You may use the approximation A a, but please do so only at the end. Assume laminar flow and no resistance.

b)Find the value of R at which you should place a pitcher (initially) to catch the beer.

static pressure in the liquid is in balance with the vacuum that forms at the top of the tube and the ambient pressure of the surrounding air on the fluid surface of the reservoir at the bottom.

a)Suppose the fluid is water, with ρw = 1000 kg/m3. Approximately how high will the water column be? Note that water is not an ideal fluid to make a barometer with because of the height of the column necessary and because of its annoying tendency to boil at room temperature into a vacuum.

b)Suppose the fluid is mercury, with a specific gravity of 13.6. How high will the mercury column be? Mercury, as you can see, is nearly ideal for fluids-pr-compare-barometers except for the minor problem with its extreme toxicity and high vapor pressure.

Fortunately, there are many other ways of making good fluids-pr-compare-barometers.