Peter's Physics Pages

An Introductory Physics Course with Peter Eyland
Lecture 10 (Pressure)

In this lecture the following are introduced:
• Solids, fluids, plastics and plasmas
• Pressure as the intensity of force
• Pressure at a depth in a liquid
• Pascal's principle and hydraulics
• How a vacuum is not nothing
• Air pressure and its measurement

Solids, fluids, plastics and plasmas.

There are four states of matter.
A solid holds its shape.
A fluid flows to take the shape of its container (i.e. a liquid or a gas).
A plastic can be moulded or shaped (clay).
A plasma is an ionised gas (eg flame, stars).

Pressure is the intensity of force.

An intensity is a concentration of something and will be a ratio.

The unit of pressure is the Pascal, named after Blaise Pascal, inveterate gambler, philosopher, mathematician, and scientist.
He was born in Clermont-Ferrand, France in 1623 and died in 1662 (age 39).

Pressure from a solid due to gravity

The force of gravity acts so that solids exert a downward force through the area they occupy.
The same force can have a different intensity and produce different effects

Elephants walk quietly and can sneek up on people because of the relatively low pressure from their feet.

Example:
An African elephant has a mass of 5500kg, and has four (approximately) circular feet with diameter 0.3m. Find the pressure each elephant foot exerts on the ground when standing.

Example:
A 60kg woman is wearing square "stiletto" heels with 10mm sides. Find the pressure on the floor as half her weight acts through one heel.

Pressure in a liquid

The pressure in a liquid, increases with depth, because of the increasing weight of the liquid above it.

The difference in pressure between the bottom area and the top is found by the weight pressing down through that area.

One might think that because there is a greater weight of water above the left hand shape there would be a greater pressure at the bottom. Also, the smaller weight of water above the right hand shape might mean a smaller pressure at the bottom. However, even though the weights are different and the areas are the same for each shape, the pressure at the bottom is the same for all three cases. This is because the sides of the left hand shape support the water a little and the sides of the right hand shape push down a little. The pressure at the bottom of each vertical tube thus depends on the height of water not the shape or quantity of water.

Farmers have sometimes (incorrectly) thought that the force on a dam wall depends on the volume of water behind it, instead of the height of the water at the wall.

Torricelli demonstrated that pressure increases with depth because the speed of efflux increases with depth:

Example:
The pressure just under the surface of the ocean is 101.3 kPa. If sea water has a density of 1030 kg.m-3, find the depth where the pressure has doubled.

A diver 10m underwater will not be crushed because the pressure on their body has doubled.
What happens is that their internal body pressures also increase, thus pushing outwards.

More internal pressure means that more air will dissolve into the blood stream. A sudden decrease in pressure will cause the dissolved air to come out of solution in the form of bubbles. When Nitrogen bubbles are caught in the joints, this causes people to bend over and double-up in pain, hence this is called "the bends". The person needs to be re-pressurised so that the Nitrogen dissolves again, then they can be slowly de-pressurised.

What happens if you step (or are pushed) out of a space shuttle into the vacuum of space when you haven't got any protective gear on?

Pascal's principle

Pascal's principle states that a change in pressure is transmitted throughout a liquid without loss.
The "Cartesian diver" inside a sealed plastic bottle.
Any increase in pressure by pressing on the the side of the bottle is added to the pressure on the diver so that the diver descends. Hydraulics are applications of this principle.

The Hydraulic jack:

Compressed air forces an increase in the oil pressure in the smaller tube. This increase in pressure is transmitted through the fluid. The ratio of the areas of the cylinders gives the ratio of the forces.

Hydraulic brakes:

The force of the foot on the pedal increases the pressure in the brake lines (pipes). This is transmitted through the liquid without loss to magnify the force on the brake pads. Note: if there is any air in the brake lines, the foot pressure will compress that air without increasing the pressure at the brake pads.

In the early Renaissance, the argument about whether or not a vacuum could exist, reappeared. The Scholastics insisted (with Aristotle) that a vacuum was logicaly impossible. They said the Universe would sooner fall apart than to permit an abhorred Nothing in its midst!
For example,Descartes said if everything were removed from a vessel, then the sides must immediately touch for a vessel cannot contain "Nothing"! The problem was that they identified vacuum (emptiness) with "nothing" (Latin: nihil).

Galileo noticed that "it was not possible, either by pump or any other machine working on the principle of attraction, to lift water a hair's breath above 18 cubits (10.3 m)".
He is said to have commented that Nature's abhorrence of a vacuum was limited to this height :).

Air Pressure

The air, in which we are immersed, has mass and weight so it also exerts a pressure on us, not only downwards but also sideways.

The inertia of the air pushing down.

The egg in a bottle sucked inside when the air inside is cooled

collapsing can when heated then stoppered.

Measuring air pressure

In 1644 Evangelista Torricelli (one of Galileo's pupils) suggested an experiment of inverting a tube of mercury into a bowl of mercury.

He noticed that the Mercury fell a little bit and left a void above it. He said the void at the top was vacuum and the mercury was held up by outside air pressure. The height of the Mercury would then give the air pressure relative to vacuum and as above, Pressure=ρgH.

Pascal, in Rouen (1647), was convinced by Torricelli's conclusions and leaped into the controversy when he saw he could make some money. Pascal performed experiments with tubes of various diameters, in which the space for the void now either bulging or narrow. He inclined his tubes till the void disappeared and then reappeared. He put a bladder inside the top. Every time the height remained constant while the empty space varied enormously. Arguing against a vacuum in the Torricelli tubes, the "Plenists" in the town said the apparent void was simply Mercury vapour, which expanded to fill the space.

To put things to the test, Pascal constructed two tubes of glass, each 14m long. He bound them to ships' masts and made pivots at the centres. He filled one with water and stoppered it. He then inverted it into a tub of water and removed the stopper. The water fell to 10.3m. He asked the Plenists what would happen if wine should be used in the test.

The Plenists said that wine was more volatile than water and would release more vapours and so would fall further in the tube. After bets were organised, Pascal filled the second tube with red wine.

The wine stood higher than the water, not lower.

air pressure = density x gravity x height
Wine is less dense than water, so to keep the product of density and height the same, the less dense wine must stand higher.

Standard Air Pressure

Because of density differences, 10.3 m of water is equivalent to 760 mm of Mercury. Standard atmospheric pressure is set equal to this.

Standard Air Pressure = 760 mm Hg = 760 torr = 1 Atmosphere.

In other units:

Air pressure is not constant. Higher pressures usually indicate fine weather and the pressure falls as storms approach.

Cautionary Tale
One man made a barometer to check on weather changes.
He made it with water in a glass tube, and it was so long that it stuck out through the roof of his house. He put the small outline figure of a woman in it, so that he could easily see the height of the water. The figure rose out of the roof and disappeared back inside as the weather changed. He was quite proud of this until the locals were so spooked by the mysterious flying figure, that they burned him as a witch.

Summarising:

Pressure (the intensity of force) is force/area and measured in Pascal.
Pressure at a depth in a liquid:

Pascal's principle states that a change in pressure is transmitted throughout a liquid without loss.
A vacuum is space that is emptied of matter, but it is not "nothing" because it has properties.
Standard Air Pressure =1 Atmosphere =760mm Hg =760torr =101.3kPa

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