Location: Ch 8: Liquids
PROPERTIES OF MATTER

IN THIS CHAPTER: 

  • Liquid Pressure
  • Buoyancy
  • Archimedes' Principle
  • Does it Sink or Float?
  • Flotation
  • Pascal's Principle
The liquid phase is the state of matter where molecules can flow freely by sliding over each other. Since liquids take the shape of their containers, the liquid exerts forces on the walls and bottom of the container. Pressure describes the interaction between the weight of the block against the area of contact. Thus, . Pressure can be measured as newtons per square meters, or pascals (Pa). Scientists more often use kilopascals (kPa) because a pascal itself is very small. A liquid’s weight depends on its density. It turns out that the pressure of a liquid at rest depends only on the density and depth of the liquid, not on the shape of the container or the size of its bottom surface. The pressure of a liquid can be calculated with this formula: Pressure = weight density ´ depth. However, the above formula only works if the liquid is in a airtight container that contains no air. Thus, Total pressure = weight density ´ depth + pressure of the atmosphere. Therefore, at any given depth, a liquid always exerts the same pressure against any surface, whether it be the bottom or the sides of a container, or a submerged object. It does not matter how much liquid there is in the container; pressure only depends on the depth of the water. At any point within a liquid, the forces that produce pressure are exerted in every direction. If the container holding the liquid has holes in it, then the water will shoot out of the container on a path perpendicular to the surface.

    When objects are submerged in water, the apparent loss of weight actually results from buoyancy. Buoyancy results from water exerting an upward force on an object. This upward force is known as the buoyant force. Since the forces that act on the sides of a submerged object are equal, they cancel each other out. However, the forces that act on the top and bottom of the object are not equal. The bottom force is greater than the top force and thus it appears as though the object loses weight. Buoyant force can be calculated with this formula: Bottom force – upper force. If the weight of a submerged object is greater than the buoyant force, it sinks. If they are equal then the object will remain at its current level. If the buoyant force is greater than the weight of the object, it will be pushed to the top where it will float. If a stone is placed in a container of water, the volume of the water displaced is equal to the volume of the stone. Since a completely submerged object always displaces a volume of fluid equal to its own volume, that is a good way to measure the volume of an irregular shaped object.

    The Greek philosopher Archimedes discovered the relationship between buoyancy and displaced liquid in 3 BC. Archimedes’ principle states that any immersed object is buoyed up by a force equal to the weight of the fluid it displaces. Thus, if we submerge a 3N brick into a full pitcher of water, and discover that it displaced 2N of water, then the brick should be buoyed up by a force of 2N and appear to weight only 1N. The depth of the stone does not make a difference; only the difference between the top and bottom forces on the object. If the object floats, then the principle of floatation applies. This principle states, "A floating object displaces a weight of fluid equal to its own weight." Thus, a 10,000 ton ship must displace 10,000 tons of water or it will sink.

    Whether or not an object floats is dependent on how great the buoyant force is compared with the object’s weight. If an object floats, then the volumes of the object and the displaced water must be equal, and so are the densities of the two. Therefore, whether or not an object floats can be summarized into the following three rules:
 
    1.     An object more dense than the fluid in which it is immersed sinks.
    2.     An object less dense than the fluid in which it is immersed floats.
    3.     An object with the same density as the fluid in which it is immersed neither sinks nor floats.
    If you change the pressure in one part of a fluid, the change is transmitted to all other parts. This rule is known as Pascal’s principle, which states, "Changes in pressure at any point in an enclosed fluid at rest are transmitted undiminished to all points in the fluid and act in all directions. Pascal’s principle was discovered in the 17th century by Blaise Pascal, for whom the unit of pressure (and a programming language) were named. Pascal’s principle, however, cannot be easily applied to a gas such as air because air is compressible. Pascal’s principle is most famous for use in a hydraulic lift. If you create a U-shaped tube with two pistons at each end and press on one of the pistons, the other one will go up. But if you make the pressed one smaller and the other larger, the result is impressive. If the left piston is 1cm2 in area and is pressed on with a load of 1N and the right piston is 50cm2 in area with a 50N load, the small piston will support the large piston.  Since the 1cm2 piston has a load of 1N, it can be said that it carries a load of 1N/cm2.  Since this pressure is applied to every square centimeter of the larger piston the total force exerted on the piston is 50N.  Thus the 1N weight will support the 50N weight.  However, this hydraulic press is not without drawbacks.  For every 10cm that the small piston plunges down, the larger piston only rises 1/50th of that, or 0.2 cm.  Pascal’s principle also applies to a hydraulic lift in the same manner as the hydraulic press but backwards.  An air compressor pumps relatively low-pressured air into a large chamber.  The water that is pressed out of the chamber then pushes the lift up.  A low amount of pressure exerted over a large area produces considerable force.

     
    In conclusion, liquids are the phase of matter where molecules can easily slide over each other. Pressure is the measure of force per area. Liquids exert pressure in all directions at all points within the liquid. The total pressure in a liquid at any point is proportional to the density of the liquid and the depth below the liquid surface. The total pressure in a liquid is the pressure created by the liquid + the pressure of the air above it. Buoyancy is the apparent loss of weight of an object immersed in fluid.
Location: Ch 8: Liquids