Cartesian Diver Essay
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“Cartesian” is named after the French mathematician and philosopher Rene Descartes, who lived from 1596 until 1650. Cartesian diver lab is used commonly in scientific experiments to illustrate principle of buoyancy. The objective of this Cartesian diver lab is to demonstrate Pascal’s law and Archimedes’ principles. Observation is the key to conduct this experimental study of the Cartesian diver.
First a 2-liter bottle is filled with water to almost all the way to the top, then prepare the diver which is a test tube, fill the test tube about 50-60% with water, place the diver inside the bottle the diver should float near the water surface then secure the cap on the bottle.
When the container is squeezed, the diver should sink to the bottom of the container. Release the bottle slowly, the diver should come up in reverse order. The Cartesian diver shows that air is compressible and water is incompressible.
When the container is squeeze, the pressure from squeeze is distributed equal throughout the container and the volume of air in the diver decreases because of the increased pressure of the water surrounding the diver. Since the volume of air inside the diver decreased, and water filled up where the air use to be, the diver becomes denser and will begin to sink if enough pressure is applied. It begins to sink because it becomes denser so the upward force of the water is not great enough to keep the diver floating.
When the container is not squeezed, the diver will float back to the top because the pressure that was compressing the air in the diver was relived so the air could take is normal volume again which make it least dense. Therefore the Cartesian diver does demonstrate the compressibility of a gas, the incompressibility of water. The Cartesian diver experiment also demonstrates the Pascal’s law. According to Pascal’s law, when the bottle is squeezed, the applied pressure increase throughout the bottle by the same amount include inside of the diver.
The control volume for this lab experiment is the entire water bottle including the diver inside. Objects float or sink as a result of their density. Density can be described as the amount of weight in a specific volume. An object is buoyant if its relative density is less than the density of the fluid that is surrounding it. According to Archimedes’ principle, an object will be buoyed up by a force that is equal to the weight of water that it displaces. The air inside the diver can be compressed much more easily than water, therefore the water level inside the diver increase as the bottle is queezed due to the pressure increase.
The applied pressure by squeezed the bottle can be determine by using this equation: P =F/A(1) Where P is the applied pressure, F is the force by the fingers and A is the area of the fingers touch the bottle 14. 14? cm? ^2. With the applied pressure, the pressure rise in the bottle based on water level change inside the diver can be estimate by using this equation: P =? gh (2) Where P is the applied pressure, ? is the water density, g is gravity and h is the height of the water rise, 0. 3cm. Combine equation (1) and (2) the force by the figure equals 0. 416N and applied pressure equals 29. 43pa The Cartesian diver experiment demonstrates Archimedes’ principles. Objects either float or sink because of buoyancy, buoyancy is the upward force that keeps objects floating. If the buoyancy exceeds the weight then the object floats and if the weight exceeds the buoyancy then the object sinks, therefore Neutral buoyancy is achieved when the mass of an object equals the mass it displaces in a surrounding medium. This offsets the force of gravity that would otherwise cause the object to sink.
An object that has neutral buoyancy will neither sink nor rise. According to Archimedes’ principles the buoyant force acting on a body of uniform density immersed in a fluid is equal to the weight of the fluid displaced by the body, and it acts upward through the centroid of the displaced volume: F_B=? _f gV_sub (3) Where F_B is the buoyancy force, ? _f is fluid density, g is gravity and V_sub is the submerge volume. F=mg (4) Where F is the weight of the object, m is the mass of the object and g is the gravity. By relating equation (3) and (4) the buoyancy force equals 0. 1N and mass of the tube is about 1g. PV=? RT (5) Where P is the pressure, V is the volume, ? is the density, R is the gas constant and T is the temperature. P_2/P_1 =h_1/h_2 (6) Where P_1 the pressure rise of the bottle, P_2 Pressure rise of the diver, h_1 is the height of pressure rise in bottle and h_2 is the height of pressure rise in diver. Cartesian diver can achieve a neutrally buoyant state. However when the Cartesian diver reach the neutrally buoyant state it will be an unstable equilibrium like a ball on a hill, a very small change can cause to rise or sink again.
The hydrostatic pressure is a very important factor in the Cartesian diver, the hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. The hydrostatic pressure of the water increase as the diver sinks, for this particular Cartesian diver a small change in hydrostatic pressure will affect the diver to sink, rise or stay and the key to achieve the diver to stay neutrally buoyant is the precise measurement of how far the diver sinks before it sinks completely or floats. The principle of buoyancy of a submarines are very similar to the Cartesian diver.
Submarines can control their buoyancy by pumping air into the ballast tanks increases the submarine’s buoyancy and allows it to float to the surface like Cartesian diver at initial state when there is enough air inside of the diver, the Cartesian diver can also control buoyancy depends on how hard the person squeezed the bottle. Submarines could also releasing air and allowing water to fill the ballast tanks to decreases the submarine’s buoyancy and allows it to sink, similar to the Cartesian diver when the bottle is squeezed, the water level in diver increase which also decrease its buoyancy, so the Cartesian diver sinks.
For submarines to reach neutral buoyancy, the water filling in the ballast tanks must be precise so the buoyancy force will equals to the weight of submarine, similar to the Cartesian diver when the applied force is just right, the diver will to reach neutral buoyancy. The Cartesian diver lab shows the fundamental principles of Pascal’s law and buoyancy. At the initial state of the Cartesian diver, the diver floats on top of the water.
Because of buoyancy is greater than the diver’s weight then as bottle is squeezed the pressure increase uniformly which cause the diver increase its water level which decrease its buoyancy so it drops to the bottom of the bottle. When the bottle is release the diver rise to top of the water again due to the pressure that was compressing the air in the diver was relived so the air could take is normal volume again which increased the buoyancy back to its initial state.