Section 13.3 Fluids at Rest and in Motion

1. Section 13.3 Fluids at Rest and in Motion Objectives Relate Pascal’s principle to simple machines and occurrences. Apply Archimedes’ principle to buoyancy. Apply Bernoulli’s principle to airflow.

2. FLUIDS AT REST • If you have ever dived deep into a swimming pool or lake, you know that your body, especially your ears, is sensitive to changes in pressure. • You may have noticed that the pressure you felt on your ears did not depend on whether your head was upright or tilted, but that if you swam deeper, the pressure increased. • Ideal Fluid – fluid with no internal friction among the particles.

3. FLUIDS AT REST • Blaise Pascal – a French physician, that noted that the shape of a container had no affect on the pressure at any given depth. He was the first to discover that any change in pressure applied to a confined fluid at any point is transmitted undiminished throughout the fluid. • Pascal’s Principle – pressure applied to a fluid is transmitted undiminished throughout it. Every time you squeeze a tube of toothpaste you use Pascal’s Principle.

4. FLUIDS AT REST • Pascal’s Principle is applied in the operation of machines that use fluids to multiply forces, as in hydraulic lifts. • P1 = F1 / A1 and P2 = F2 / A2 • Since pressure is transmitted without change P2 is the same as P1. • So F1 / A1 = F2 / A2 or F2 = F1*A2 / A1 • Do Practice Problem # 23 p. 353 F1 / A1 = F2 / A2 or F2 = F1*A2 / A1 1600 / 1440 = F / 72 F = 1600(72) / 1440 80 N = F F = 80 N

5. SWIMMING UNDER PRESSURE • When you are swimming, you feel the pressure of the water increase as you dive deeper. • This pressure is actually a result of gravity; it is related to the weight of the water above you. • The deeper you go, the more water there is above you, and the greater the pressure. • Pressure Of Water on a Body – the pressure that a column of water exerts on a body is equal to the density of water times the height of the column times the acceleration due to gravity. P = ρhg (ρ is small Greek letter rho) • That formula works for all fluids.

6. SWIMMING UNDER PRESSURE • The pressure of a fluid on a body depends on the density of the fluid, its depth, and g. • Buoyant Force – is equal to the weight of the fluid displaced by the object, which is equal to the Density of the fluid in which the object is immersed multiplied by the object’s volume and the acceleration due to gravity. It is the upward force on an object immersed in fluid. • Fbuoyant = ρVg ; Buoyant Force = Density * Volume * gravity • Archimedes – Greek scientist that found the relationship that the buoyant force has a magnitude equal to the weight of the fluid displaced by the immersed object. • Archimedes’ Principle – states that an object immersed in a fluid is buoyed up by a force (or has an upward force) equal to the weight of the fluid displaced by the object. It is important to note that the buoyant force does not depend on the weight of the submerged object, only the weight of the displaced fluid.

7. SWIMMING UNDER PRESSURE • If you want to know whether an object sinks or floats, you have to take into account all of the forces acting on the object. • The buoyant force pushes up, but the weight of the object pulls it down. • The difference between the buoyant force and the object’s weight determines whether an object sinks or floats. • Go over the Sink or Float? Example p. 354-355 • An object will float if its density is less than the density of the fluid in which it is immersed.

8. SWIMMING UNDER PRESSURE • Ships can float because the hull is hollow and large enough so the average density of the ship is less than the density of water. You can notice that a ship filled with cargo will be submerged more than a ship with no cargo. • Example 3 p. 356 a. Fbuoyant = ρVg b. Fg = mg = ρVg Fapparent = Fg – Fb Fbuoyant= 1000(.001)(9.8) Fg = 2700(.001)(9.8) Fa = 26.46 – 9.8 Fbuoyant = 9.8 N Fg = 26.46 N Fa = 16.66 N • Skip Practice Problems p. 356

9. FLUIDS IN MOTION: BERMOULLI’S PRINCIPLE • Bernoulli’s Principle – states that as the velocity of a fluid increases, the pressure exerted by that fluid decreases. Or when a fixed quantity of fluid flows, the pressure is decreased when the velocity increases. • There are many common applications of Bernoulli’s principle, such as paint sprayers and perfume bottles. • A gasoline engine’s carburetor, which is where air and gas are mixed, is another common application of Bernoulli’s principle. • Part of the carburetor is a tube with a constriction, as shown in figure 13-16b. • Streamlines – lines representing the flow of fluids around objects. • Skip 13.3 Section Review