Pascal’s Principle
Concept
Airplanes
With hydraulic system, pilots can control the movement of rudders and the aerofoil with a lot smaller force than moving the rudder with no hydraulic system. So, only a small movement is required to change the direction airplane flies.
However, if the hydraulic pipes broken up, the hydraulic fluid will leak and pilots can no longer control the rudders and aerofoil. The airplane will crash.
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When an incompressible liquid is being pushed through the system, the volume moved through the input piston will be the same with the output piston.
The cross-sectional area of output piston will be larger than the input one, as shown in diagram above, therefore the distance moved through the piston will be shorter than input piston.
Volume = Cross-sectional area x distance
D1 and D2 are the distance moved respectively.
Look at the diagram above, we know that in order to produce a larger for at the output piston, A1 must be larger than A2 so the force can be emphasized. But since the liquid is incompressible, therefore the volume of liquid moved in both side must be the same!
Car Brake Hydraulic System
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In a car brake system they apply Pascal’s Principle in the form of hydraulic system too. The master piston which is under the footstep of the driver can control all brake pad of the car simultaneously.
The hydraulic pipe contains the confined and incompressible brake oil which can transmit the force from the brake pedal (F1) to all brake pads (F2) which then slows down the car. The piston at the brake pedal is smaller in term of cross-sectional area (A1) will then pushes the fluid to all 4 brake pads which have a piston which is larger in terms of their cross-sectional areas (A2).
The importance of incompressible brake oil here is not only transmit the force efficiently under the footstep of the driver, but also it can control all braking systems in the car to stop at the same pace, letting the driver gain back his full control on his car. If the braking systems are not acting simultaneously, the car may flip or crash, harming the driver and the passengers.
Archimedes’ Principle
Concept
Usually, when an object is partially or totally immersed in a fluid, there will be two forces acting on it, its own weight, W (N) and the buoyant force, FB (N). the buoyant force is the upward movement force caused by the density of the fluid.
If an object is totally immersed in the fluid, means that volume of the object equals to the volume of fluid displaced, there will be three possibilities:
W > FB
The density of the object is larger than the fluid it displaces. So the object will sink or moves down the fluid. Real life examples of this situation such as an iron nail will sink to the bottom of the water.
W < FB
The density of the object is smaller than the fluid it displaces. The object will float or moves upward the fluid. Hindenburg, a Germany made hydrogen airplane is one of the example.
W = FB
This is rare to happen. The density of the object will be the same as the fluid it displaces. The object will stay and no longer move upward and downward as long as it stays in this situation. One of the example could be the submarine that submerged to a certain level where the overall density of the vessel is the same as the sea water outside.
Density and Buoyancy
According to the concept of Archimedes’ Principle, the buoyancy force, FB equals to the weight of fluid displaced by the object immersed in it, W.
Density = Mass / Volume
ρ = m / v
m = ρv
W = mg
W = ρvg
So the weight of the fluid displaced will be the product of density, ρ, volume, v and gravitational force, g.
Therefore the buoyant force is ρvg
The buoyant force depends solely on density of the object and density of the fluid displaced.
The Law of Floatation
Object that sinks in a fluid will sink till a level that its apparent weight to be zero, means the weight of the part of the object that immersed in a fluid will equal to the weight of fluid displaced.
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For example, when a ship is hand on the air, the apparent weight of the ship equals to the true weight of the ship minus the weight of the volume of the air it displaces.
Apparent weight = True weight – Weight of fluid displaced.
But the apparent weight is so close to the true weight because density of the air is too low that it can be neglected. But when the ship is immersed in the water, and the ship will submerge to a level that its apparent weight becomes zero. But this only applies when the density of the ship is lower than sea water!
To measure the level where the ship will sink on different temperature and salinity of water, they will draw a Plimsoll line on the hull and the side of the side, regardless of starboard or port.
Bernoulli’s Principle
Concept
The statement above can only be true under the following circumstances:
· The fluid is incompressible; the density throughout the fluid should be the same.
· The fluid must flow easily.
· The fluid flow in a streamline or in layers, such as no turbulence.
Atomizers
Perfume bottles or insecticides sprayers are atomizers, a stream of air is blow on top of the bottle or spray, sucking the fluid inside the container up and spray them is a fine mist.
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When the plunger is pressed fast, the air inside the syringe is rushed out in a fast speed, the speed is even faster when the cross-sectional area of the output hole become smaller. The fast and fine stream of air decease the pressure above the hole, thus sucking the fluid inside out and spray them in a fine mist.
The Venturi Tube
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The figure above shows a Venturi tube with three sections namely A, B and C. B has a smaller diameter than A and C. The water flowing speed will be faster at B, decreasing pressure of tube Y. That’s why the water level at tube Y will be lower. The friction energy cause a lower pressure at tube Z than tube X.
Bunsen burner
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When the hot burning air flows out of the nozzle, it creates a low air pressure zone which then suck more gas fuel for the combustion process. The process repeats again and again.
Aerofoil
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The aerofoil is shaped in air dynamic way so that it can create a high speed zone above the wing and decrease the pressure above the wing, this will then help the airplane to increase its altitude.
Carburetor
Carburetor is a device that used to mix air and petrol before they will be burned by the internal combustion engine. When the engine is switched on the air will be sucked into the Venturi tube. The mixture will then sucked into the combustion chamber.