Module 1
in
Pressure Liquids
Pascal Gunsch Cor-Jan Heijlema Lotte van den Heuvel Maarten Hoogstad Tom de Roon Michael van der Spek
ď ˇ
http://www.youtube.com/watch?v=yd7E9CW8dPE&feature=g-allu&context=G2695f30FAAAAAAAAAAA
MOLECULES Pressure ( ) is caused by the force ( ) of the direction of molecules hitting a surface ( ) In mathematical language, we could say that: = = pressure, = force of direction molecules, = surface area
In a liquid, this principle works exactly the same. The water/other liquids molecules exert force on a certain surface. The only difference is, that the molecules are in a liquid state, meaning that they can move. Therefore, they will always spread to keep the pressure equal. That is why the pressure acts in all directions.
ARCHIMEDE’S PRINCIPLE It all started around 2250 years ago, with the physician Archimedes. For that time, he was a very good physician, who meant a lot for the city of Syracuse, where he lived. He invented, for example, a device to stop foe ships attack the harbour. He did this by placing mirrors in such a position, that they focussed the sun rays on the ships, which then caught fire. Due to his works, King Hiero II asked him whether he could find a way to discover if his crown is of made of gold or a mixture, without damaging it. Archimedes accepted the challenge. At first, he thought and thought but could not solve it. It was such a stressful situation, that he decided to take a bath. While taking a bath, he noticed that the level of the water rose as he got in, and fell as he got out. He realised, that he could measure the volume of the crown. The submerged crown would displace a volume equal to that of the crown. And, since density is a substance property, he could use it to determine whether it was real gold or not. He should simply apply the formula: ρcrown =
crown water
(ρ = density, = mass, = volume) And do exactly the same for a regular shaped piece of gold, to obtain its density. After that, he would just use a simple but famous ratio table. ρcrown = ρgold ⇒
crown water
=
gold gold
If ρcrown < ρgold, the crown would be a mixture with less dense metals (e.g. silver). Archimedes was so excited, that he took to the streets. He was so excited, that he had forgotten to dress (naked) and he was screaming “Eureka!” (Gr. εὕρηκα! I have found it!). After testing, he indeed found that the crown was not pure gold. But now, what is Archimedes’ Law? Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. — Archimedes of Syracuse Or, as a formula: = – = buoyant force, = weight of the object, =weight of the displaced fluid
PROPULSIONS OF A BOAT Common means of boat propulsions are: motor power human power (rowing, paddling etc.) wind power (sailing)
Buoyancy A floating boat displaces its weight in water. The material of the boat hull may be denser than water, but if this is the case then it forms only the outer layer. If the boat floats, the mass of the boat (plus contents) as a whole divided by the volume below the waterline is equal to the density of water (1 kg/l). If weight is added to the boat, the volume below the waterline will increase to keep the weight balance equal, and so the boat sinks a little to compensate. But that’s how it flows and doesn’t sink under water.
Submarine The deeper you go under water, the higher the pressure becomes. So a submarine needs a strong hull. Otherwise it would implode. For every 10 meters under water, the pressure becomes higher with 1 bar. 1 bar = 10 N pushes on 1 cm² which means 100 000 newton on 1 m². The pressure hull is generally constructed of thick high strength steel with a complex structure and high strength reserve, and is separated with watertight bulkheads into several compartments. Submarines in World War 1 could dive 100 meters. This means a pressure of 10 bar. That’s 10 times more than above the water surface. A human can dive approximately 198 meters before the pressure is too high. But the record is 330 meters. (with scuba)
FORMULAS As seen before, the formula for pressure: =
But, for pressure in liquids, there is another formula which can also be used: =ρ ℎ ρ = density = gravitational acceleration ℎ = depth But why? = = = We know the formula for density, ρ= We use the cross product to replace Therefore, =ρ
by ρ
And, since = =
ρ
since
= length x width x height, and
This brings us to: =ρ ℎ
= length x width, / = ℎ.
UNITS The instrument we use for measuring liquid pressure is a manometer. A manometer measures the pressure in bars. The units for pressure in liquids are: Pa pascal 1 N/m² atm atmosphere the atmospheric pressure at sea level at 20 °C bar bar 100 kPa Torr torr 1/760 of an atm mmHg millimetre of Hg equal to 1 Torr pascal
bar
atmosphere
torr/mmHg
1 Pa
1 N/m2
0.00001 bar
0.0000098692 atm
0.0075006 Torr
1 bar
100 000 Pa
100 kPa
0.98692 atm
750.06 Torr
1 atm
101 325 Pa
1.01325 bar
=
760 Torr
1 Torr
133.322 Pa
0.0013332 bar
0.0013158 atm
Note:
0
means standard/starting pressure.
0
= 1 mmHg