Traditional blood pressure gauges (sphygmomanometers) are open-tube manometers.
The gauge has an inflatable cuff that is wrapped around your upper arm. Like the
sphere in the diagram, the cuff can be filled with pressurized air. This restricts the flow
of blood to the lower parts of your arm. Air is then released from the cuff until the first
flow of blood can be heard with a stethoscope. At this point, the gauge pressure of the
blood being pumped by your heart equals the cuff’s gauge pressure. This blood
pressure, the systolic pressure, occurs when the heart generates its maximum
pressure.
The sphygmomanometer operator (try saying that quickly!) then listens for the part of
the heartbeat cycle when the pressure is the lowest, releasing pressure from the cuff
until its pressure is the same as the lowest blood pressure, and the flow of blood can be
heard continuously. This lower pressure is the diastolic pressure. A young, healthy
human has a systolic blood gauge pressure of about 120 millimeters of mercury and a
diastolic pressure equal to about 80 millimeters of mercury.
P = Patm + ȡgh
P = absolute pressure in vessel
Patm = atmospheric pressure
ȡgh = gauge pressure
The absolute pressure in the
sphygmomanometer cuff is
1.177×10^5 Pa. What is the man’s
blood pressure reading, in torr?
P = Patm + ȡgh
h = 0.123 m = 123 mm
systolic blood pressure = 123 torr
13.7 - Archimedes’ principle
Archimedes' principle: An object in a fluid experiences an upward force equal
to the weight of the fluid it displaces.
Archimedes (287-212 BCE) explained why objects float. His principle states that buoyancy, the upward force caused by the displacement of
fluid, equals the weight of the volume of the fluid displaced. For instance, if a boat displaces 300 tons of water, then it experiences an upward
buoyant force of 300 tons. If this buoyant force is greater than the weight of the boat, the boat floats.
Archimedes’ principle can be used to explain why a small stone sinks, while a large block of Styrofoam® floats, even if the Styrofoam block is
much heavier than the stone. Stone is denser than water, so the weight of the water it displaces is less than its own weight. This means that
the stone’s weight, directed down, is greater than the upward buoyant force on it. The net force on an underwater stone is downward.
In contrast, Styrofoam is less dense than water. A Styrofoam block displaces a weight of water equal to its own weight when it is only partially
submerged. It is in a state of equilibrium since the buoyant force up equals the weight down. In short, it floats.
Archimedes’ principle applies at any water depth. The buoyancy of a submerged submarine is the same whether it is 50 meters or 300 meters