


FLUID PRESSURE p


Visualisation 



The oarfish may be the creature that
gave rise to the legends about "sea serpents". This long, skinny
fish, with its strangelooking head covered in protrusions and reaching
lengths perhaps as long as 15 m,



Life Life in the deep sea must adapt to unique conditions of low or no light, high pressure, low energy except at hot vents (superheated temperatures). One unexplained but fairly common feature of deep animals is gigantism (such as oarfish, the giant squid, etc.). Less than 1% of the deepsea has been explored. What might be left undiscovered? 
! 
Definition Fluid pressure _{}

! 
Provided that an object
immersed in a fluid is not moving, the force on each small part of the
contact surface is perpendicular to the surface so the interaction can be
described completely in terms of pressure. Fluid pressure always acts perpendicular to any surface irrespective of how
the surface is oriented. Pressure has no intrinsic direction of its own
(pressure is a scalar). The pressure within a uniform stationary fluid is the same at all points in the same horizontal plane. If there is
relative motion between the fluid and solid object, the force has components
parallel to the surface and the interaction is not simply described by the
pressure. 



Pressure increases with depth in a fluid


? 
How long can
your snorkel be?
Why
do your ears feel different when you dive into deep water? Why
does atmospheric pressure change as you go up a mountain? How
does a barometer work? 




 
! 
pressure at depth
h =
pressure acting on surface + pressure due to height
of liquid
p_{h} = p_{0} + F
/ A
F = weight of column liquid of cross sectional
area A
F = m g where m of liquid in column m = r V = r (A h)
F / A = r g h p_{h} = p_{0} +
r g h 

! 


Snorkelling 




? 
There is
a maximum depth at which a diver can breathe through a snorkel tube. The snorkel connects the air in the lungs
to the atmosphere at the surface. The pressure inside the lungs is atmospheric
pressure while outside the lungs (diver is immersed in water) the pressure is
greater than atmospheric pressure. As
the depth increases, so does the pressure difference tending to collapse the
diver’s lungs. Typically snorkel
tubes are 200 mm long. The
pressure outside the lungs at depths of 200 mm in seawater is: p_{h} = p_{atm} + r g h p_{h} = 1.013´10^{5} + (1030)(9.8)(0.200) Pa p_{h} = 1.033´10^{5} Pa Pressure
difference (outside – inside) Dp = 1.033´10^{5 }^{ }1.013´10^{5} Pa Dp = 2000 Pa The lungs cannot
withstand pressure differences greater than this. So for snorkel tubes > 200 mm the lungs collapse  a process
called lung squeeze. A scuba diver
breathing from compressed air tanks can operate at greater depths than can a
snorkeler, since the pressure of the air inside the scuba diver’s lungs is
increased to match the external pressure of the water by the scuba regulator. A scuba diver's lungs can rupture if he doesn't
breathe while surfacing? Why?
If a diver holds his breathe, the pressure inside the lungs is >
atmospheric pressure Þ lungs rupture. 
? 
You dive deep down into the
water. Does it matter whether it is in the ocean or a swimming pool? 




? 
Can we make a rough estimate of
atmospheric pressure?
What are meant by the terms high pressure and low
systems? What weather is associated with each of these? 

Crude model:
The atmospheric
pressure at ground level is due to weight of air above. Assume the air is in
a column of uniform density (r = 1.2 kgm^{3})
and the height of the column is equal the width of the troposphere (h
= 10 km).
p_{atm} = r g h
= (1.2)(9.8)(10^{4}) =
10^{5} Pa Actual value: p_{atm}
= 1.013´10^{5} Pa 
! ! 
Gas pressureA gas exerts a pressure on the walls of a
container because of the continual chaotic motion of the molecules of the
gas. For an ideal gas, the gas pressure can be described by the equations
(real gases resemble an ideal gas to some extent) p = N k T / V
= n R T / V where p
is the gas pressure (Pa), V is the volume of the gas (m^{3}), T
is the gas temperature (K), N is the number of molecule and n is
the number of moles of the gas (mol), k is the known as the Boltzmann constant and R the Universal gas constant. Boltzmann constant k = 1.38x10^{23} J.K^{1} ^{ } Universal gas constant R = 8.314 J.mol^{1}.K^{1} ^{ } k = R / N_{A } R = k N_{A } _{ } Avogadro's
constant N_{A }= 6.023x10^{23}
mol^{1} (constant volume) p = constant ´ T 

? 
How do we
breath?
The lungs are surrounded by a sealed thoracic cavity. According to
Boyle’s law an expansion of this cavity (volume increase) will result in a
decrease in the intrathoracic pressure. Since lung tissue is elastic they
expand with a decrease in pressure within the lungs. This decreased pressure
inside the lungs allows air to move into the lungs from the outside. This
event occurs when the diaphragm and intercostal muscles contract. 

! 
Isotherms for an ideal gas





Falling air Þ compressed
(adiabatic process) Þ rise in
temperature Þ
increase in evaporation Þ more water
vapour in the air 
How can you measure the pressure of a gas?


Manometer



Pressure at D p_{D} = p_{atm} Equilibrium Þ gas
pressure at A = pressure at point B
B and C are at the same level Þ p_{B}
= p_{C} = p_{A} But pressure at C p_{C} = p_{atm}
+ r g h where r is the density of the fluid within the arms
of the manometer \
absolute gas
pressure p_{A} = p_{atm} + r g h \
gauge gas pressure (p_{A}
 p_{atm}) = r g h Manometer measures gauge
pressure r g h 
? 
What is a simple way to measure atmospheric pressure?


! 
Mercury
Manometer


 

pressure at B p_{B} = p_{atm} pressure at A p_{A} = 0 (vacuum: mercury vapour pressure is
negligible) But p_{C} = p_{A}
+ r g h = 0 + r g h \ p_{atm} = r g h For example p_{atm} = 760 mmHg r = 13.6 ´ 10^{3} kg.m^{3} g = 9.8 m.s^{2} h = 760 mm = 760´10^{3} m p_{atm} = (13.6 ´ 10^{3})(9.8)(760´10^{3} ) Pa = 1.01´10^{5} Pa 
? 
How do you measure blood pressure?


See
Howstuffworks
sphygmomanometer



