FLUID PRESSURE p

 

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Visualisation

 

 

The oarfish may be the creature that gave rise to the legends about "sea serpents". This long, skinny fish, with its strange-looking 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 deep-sea has been explored. What might be left undiscovered?

 

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Definition Fluid pressure

 

 

 

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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.

 


 


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Pressure increases with depth in a fluid

 

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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?

 

 


 

 

 


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pressure at depth h =

pressure acting on surface + pressure due to height of liquid

 

ph = p0 + 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

 

ph = p0 + r g h

 

 

 

 

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Snorkelling

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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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 divers lungs. Typically snorkel tubes are 200 mm long.

 

The pressure outside the lungs at depths of 200 mm in seawater is:

ph = patm + r g h

ph = 1.013105 + (1030)(9.8)(0.200) Pa

ph = 1.033105 Pa

Pressure difference (outside inside)

Dp = 1.033105 - 1.013105 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 divers 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 lungs rupture.

 

 

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You dive deep down into the water. Does it matter whether it is in the ocean or a swimming pool?

 


 

 


 

 

 

 

 


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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).

 

patm = r g h = (1.2)(9.8)(104) = 105 Pa

 

Actual value: patm = 1.013105 Pa

 

 

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Gas pressure

A 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 (m3), 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 / NA R = k NA

 

Avogadro's constant NA = 6.023x1023 mol-1

 

Gas laws (fixed quantity of gas)

Boyle's Law (constant temperature) p = constant / V

Charles Law (constant pressure) V = constant T

(constant volume) p = constant T

 

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How do we breath?

 

The lungs are surrounded by a sealed thoracic cavity. According to Boyles law an expansion of this cavity (volume increase) will result in a decrease in the intra-thoracic 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.

 

 

 

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Isotherms for an ideal gas

 


 

 

 


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Rising air expands (adiabatic process) fall in temperature decrease in evaporation less water vapour in the air (great deserts)

Falling air compressed (adiabatic process) rise in temperature increase in evaporation more water vapour in the air

 

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How can you measure the pressure of a gas?

 

 

 

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Manometer

 


 

 

 

 

 

 

 

 

 


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Pressure at D pD = patm

 

Equilibrium gas pressure at A = pressure at point B

pA = pB

 

B and C are at the same level pB = pC = pA

 

But pressure at C pC = patm + r g h

 

where r is the density of the fluid within the arms of the manometer

 

\              absolute gas pressure pA = patm + r g h

 

\ gauge gas pressure (pA - patm) = r g h

 

Manometer measures gauge pressure r g h

 

 

 

 

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What is a simple way to measure atmospheric pressure?

 

 

 

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Mercury Manometer

 

 

 

 


pressure at B pB = patm

 

pressure at A pA = 0 (vacuum: mercury vapour pressure is negligible)

 

B and C are at the same level pB = pC = patm

 

But pC = pA + r g h = 0 + r g h

 

\ patm = r g h

 

For example patm = 760 mmHg

 

r = 13.6 103 kg.m-3

g = 9.8 m.s-2

h = 760 mm = 76010-3 m

patm = (13.6 103)(9.8)(76010-3 ) Pa = 1.01105 Pa

 

 

 

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How do you measure blood pressure?

 

See Howstuffworks

 

sphygmomanometer

 


 


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