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Chapter 10: Fluid Mechanics What is a fluid? What are examples of fluids? What is density? How is the formula for density expressed on the AP test? What is the density of water? Define pressure. How is the formula for pressure expressed on the AP test? What units will we be using to express pressure? Any material that flows and offers little resistance to changing its shape. An important property of matter is density. Density is defined as mass per unit volume. The symbol is . • • • • 1.0 g/ml 1.0 g/cm3 1,000 kg/m3 Force per unit area. What is the value for standard pressure? Measured in atm or Pascals (Pa) How does pressure change as you increase the depth of water? Which would exert a greater pressure, a large but shallow lake, or a small but deep lake? Standard atmospheric pressure = force per 1 m2 of air at sea level. 1.01 x 105 Pa or 101 kPa The pressure due to fresh water (P=F/A) increases about 1 atm or about 100 kPa for every 10 m of water depth. Water pressure is greater in the deeper lake. State Pascal’s Principle The force exerted by a fluid on the walls of its container always acts perpendicular to the walls. What does this mean for an object that is completely immersed in a fluid? When you are under water the water’s pressure pushes in on you from all sides. The force is perpendicular to your body. Describe a Pascal vase. How does it demonstrate pressure exerted by a liquid? What is the formula for pressure in a column? The pressure of a liquid is the same at any depth regardless of the shape of its container. The pressure in a fluid column can be found using this equation: AP test version of the same equation: What is the pressure exerted by water at a depth of 45 m? P = (1000 kg/m3)(9.8 m/s2)(45 m) P = 4.41 x105 Pa or 441 kPa What is buoyancy? Buoyancy is an upward force that a fluid exerts on an object that is immersed in it. This is called the buoyant force. What is the formula for buoyancy on the AP test? State Archimedes’ Principle How is apparent weight different from buoyancy? What is the formula for apparent weight? An object is buoyed up by a force equal to the weight of the fluid it displaces If the object’s weight is less than the buoyant force, the object will float. If the object’s weight is greater than the buoyant force, the object will sink, but it will weigh less. The apparent weight, FA, is the difference between its actual weight and the buoyant force. Problem (part 1) A cube of steel that measures 5.0 cm on each side is FB = (1000 kg/m3)(0.05 m)3(9.8m/s2) immersed in fresh water. The FB = 1.23 N density of steel is 9.0 x 103 kg/m3. What is the buoyant force acting on the cube? Problem (part 2) What is the apparent weight of the steel? Pascal’s Principle => m = ρV FW = (9.0 x 103 kg/m3)(0.05 m)3(9.8m/s2) FA = W – FB FA = 11.03 N – 1.23 N = 9.8 N The force exerted by a fluid on the walls of its container always acts perpendicular to the walls. It also says that the pressure on a fluid is transmitted unchanged throughout the fluid. Pressure on a fluid is transmitted unchanged throughout the fluid. A hydraulic press uses this principle. If you apply 10 lbs of pressure to one end, 10 lbs of pressure will be experience on the other end. If the tube is wider on the other side, that pressure is exerted throughout the liquid on the other side. If a 1 N/cm2 pressure were exerted on one side, the other side would also experience a 1N force for every square centimeter. Is Energy Conserved? Energy is always conserved! The distance moved on one side will be proportional the distance on the other side. In this scenario, the final distance would be 1/50 of the original distance.