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Pressure can be represented as Pressure= Force/Area Fluids in its simplest form Fluids exerts a net upward force on any object. Archimedes Principle and Buoyancy Fluid Flow and Continuity Food for thought... When you turn on a hose the water flowing through it is slow... What do you do at the end of the hose to make it flow faster. IMPORTANT! Fluids are now applied to the work energy theorem. Relationship between pressure, speed and height of the fluid. The Adventures of Pressure Fluids Important as well is the density of a fluid. known as the letter p or Rho. Density=Mass/Volume Hydrostatic pressure or still fluid is determined by Depth and Density. key idea: The deeper in a fluid the more pressure is felt.
Equation P=Po+pgh This is called absolute pressure. The pgh is gauge pressure. Or P-Po Example: A water bed is 2.0 m on a side an 30.0 cm deep.
(a) Find its weight if the density of water is 1000 kg/m3.
(b) Find the pressure the that the water bed exerts on the floor. Assume that the
entire lower surface of the bed makes contact with the floor. Example of pressure varying at depths is a barometer.
Key Concept: Water likes to seek its own level. U shaped tube. Pascals Principle: An external pressure is applied to an inclosed incompressible static fluid. The energy is transmitted undiminished through the fluid.
Example: Hydraulic lift. Use P=F/A to find the pressure in the first cylinder then insert that into the second P=F/A for the opposing cylinder. Advantage to this is a small area piston can move a large mass with little pressure. If the area is 100 times greater on one side through the equations we can see that it would mean our force was magnified 100 times. EXAMPLE This is buoyancy The force can be found by the equation F=pgV Archimedes' principle An object fully submerged in a fluid will experience an upward force equal to the weight of the fluid displaced. Example: A cube of steel that measures 5.0 cm on each side is immersed in water. The density of steel is 9.0 x 103 kg/m3. The density of water is 1.0 x 103 kg/m3. What is the (a) buoyant force acting on the cube and what is (b) its apparent weight? Ideas:
The buoyancy formula can be used to find the density of a body and then used to find the percentage of body fat.
Also through the equation Vsub=Vs(ps/pf) the amount of an object floating below the fluid level can be found.
Floatation: The block example.
The metal example.
Change buoyancy the density needs to change.
Apparent weight is the difference between the actual weight and the buoyant force. This is know as fluid flow. In a straight system the fluid will not be gained or lost.
The equation AV=A2V2 can be used to find different portions of incompressible fluid passing through certain parts of the system. The concept of continuity can only be used in a system that has
no bends in the system. Example: You turn on the hose to water your sassafras garden. When the hose is turned on the water starts to flow at a rate of 5 m/s. The hose goes from .005 m to .0025m at the end of the hose. What is the new speed of the water. Bernoulli Key idea: The faster a fluid flows the less pressure there is. Reasoning the fire hose. Key Idea: As height increases in a pipe the pressure decreases. Combine the two ideas and you get the complete Bernoulli equation: Applications of Bernoulli:
Air Planes force faster air on top of the wing and slower on the bottom of the wing to create lift. There are basically two ways to make fluid flow through a pipe. One way is to tilt the pipe so the flow is downhill, this means gravitational kinetic energy is transformed to kinetic energy. The second way is to make the pressure at one end of the pipe larger than the pressure at the other end. A pressure difference is like a net force, producing acceleration of the fluid.
As long as the fluid flow is steady, and the fluid is non-viscous and incompressible, the flow can be considered on an energy perspective. Example: Consider a geyser that shoots water 25 m into the air. How fast is the water traveling when it emerges from the ground? If the water originates in a chamber 35 m below the ground, what is the pressure there? Key Formulas Pressure= p=f/a
hydrostatic pressure= Po+pgh
Archimedes= Fb=W displaced