2 11.1 Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: m V SI Unit of Mass Density: kg/m3
3 11.1 Mass Density
4 11.1 Mass Density Example 1 Blood as a Fraction of Body Weight The body of a man whose weight is 690 N contains about 5.2x10-3 m3 of blood. (a) Find the blood s weight and (b) express it as a percentage of the body weight. m V m kg m kg
5 11.1 Mass Density (a) W mg 5.5 kg 9.80 m s 2 54 N (b) 54 N Percentage 100% 7.8% 690 N
6 11.2 Pressure F P A SI Unit of Pressure: 1 N/m2 = 1Pa Pascal
7 11.2 Pressure Example 2 The Force on a Swimmer Suppose the pressure acting on the back of a swimmer s hand is 1.2x105 Pa. The surface area of the back of the hand is 8.4x10-3m2. (a) Determine the magnitude of the force that acts on it. (b) Discuss the direction of the force.
8 11.2 Pressure F P A F PA N m m N Since the water pushes perpendicularly against the back of the hand, the force is directed downward in the drawing.
9 11.2 Pressure Atmospheric Pressure at Sea Level: 1.013x105 Pa = 1 atmosphere
10 11.3 Pressure and Depth in a Static Fluid F y P2 A P1 A mg 0 P2 A P1 A mg m V
11 11.3 Pressure and Depth in a Static Fluid V Ah P2 A P1 A Vg P2 A P1 A Ahg P2 P1 hg
12 11.3 Pressure and Depth in a Static Fluid Conceptual Example 3 The Hoover Dam Lake Mead is the largest wholly artificial reservoir in the United States. The water in the reservoir backs up behind the dam for a considerable distance (120 miles). Suppose that all the water in Lake Mead were removed except a relatively narrow vertical column. Would the Hoover Same still be needed to contain the water, or could a much less massive structure do the job?
13 11.3 Pressure and Depth in a Static Fluid Example 4 The Swimming Hole Points A and B are located a distance of 5.50 m beneath the surface of the water. Find the pressure at each of these two locations.
14 11.3 Pressure and Depth in a Static Fluid P2 P1 gh atmospheri c pressure P Pa kg m m s m Pa
15 11.4 Pressure Gauges P2 P1 gh Patm gh Patm Pa h g kg m m s m 760 mm
16 11.4 Pressure Gauges P2 PB PA PA P1 gh absolute pressure P P gh 2 atm gauge pressure
17 11.4 Pressure Gauges
18 11.5 Pascal s Principle PASCAL S PRINCIPLE Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls.
19 11.5 Pascal s Principle P2 P1 g 0 m F2 F1 A2 A1 A2 F2 F1 A1
20 11.5 Pascal s Principle Example 7 A Car Lift The input piston has a radius of m and the output plunger has a radius of m. The combined weight of the car and the plunger is N. Suppose that the input piston has a negligible weight and the bottom surfaces of the piston and plunger are at the same level. What is the required input force?
21 11.5 Pascal s Principle A2 F2 F1 A m F N 131 N m 2
22 11.6 Archimedes Principle P2 P1 gh FB P2 A P1 A P2 P1 A V ha FB gha FB V g mass of displaced fluid
23 11.6 Archimedes Principle ARCHIMEDES PRINCIPLE Any fluid applies a buoyant force to an object that is partially or completely immersed in it; the magnitude of the buoyant force equals the weight of the fluid that the object displaces: F B Magnitude of buoyant force Wfluid Weight of displaced fluid
24 11.6 Archimedes Principle If the object is floating then the magnitude of the buoyant force is equal to the magnitude of its weight.
25 11.6 Archimedes Principle Example 9 A Swimming Raft The raft is made of solid square pinewood. Determine whether the raft floats in water and if so, how much of the raft is beneath the surface.
26 11.6 Archimedes Principle Vraft 4.0 m 4.0 m 0.30 m 4.8 m 3 FBmax Vg watervwater g 1000 kg m 3 4.8m m s N
27 11.6 Archimedes Principle Wraft mraft g pinevraft g 550 kg m 3 4.8m m s N N The raft floats!
28 11.6 Archimedes Principle If the raft is floating: Wraft FB N watervwater g N 1000 kg m m 4.0 m h 9.80 m s 2 h N 0.17 m kg m 4.0 m 4.0 m 9.80 m s
29 11.6 Archimedes Principle Conceptual Example 10 How Much Water is Needed to Float a Ship? A ship floating in the ocean is a familiar sight. But is all that water really necessary? Can an ocean vessel float in the amount of water than a swimming pool contains?
30 11.6 Archimedes Principle
31 11.7 Fluids in Motion In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point changes as time passes. Turbulent flow is an extreme kind of unsteady flow in which the velocity of the fluid particles at a point change erratically in both magnitude and direction.
32 11.7 Fluids in Motion Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible. Fluid flow can be viscous or nonviscous. An incompressible, nonviscous fluid is called an ideal fluid.
33 11.7 Fluids in Motion When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles.
34 11.7 Fluids in Motion Making streamlines with dye and smoke.
35 11.8 The Equation of Continuity The mass of fluid per second that flows through a tube is called the mass flow rate.
36 11.8 The Equation of Continuity m V A v t distance m2 2 A2 v2 t m1 1 A1v1 t
37 11.8 The Equation of Continuity EQUATION OF CONTINUITY The mass flow rate has the same value at every position along a tube that has a single entry and a single exit for fluid flow. 1 A1v1 2 A2 v2 SI Unit of Mass Flow Rate: kg/s
38 11.8 The Equation of Continuity Incompressible fluid: Volume flow rate Q: A1v1 A2 v2 Q Av
39 11.8 The Equation of Continuity Example 12 A Garden Hose A garden hose has an unobstructed opening with a cross sectional area of 2.85x10-4m2. It fills a bucket with a volume of 8.00x10-3m3 in 30 seconds. Find the speed of the water that leaves the hose through (a) the unobstructed opening and (b) an obstructed opening with half as much area.
40 11.8 The Equation of Continuity Q Av (a) Q m s v m s -4 2 A m (b) A1v1 A2 v2 v2 A1 v m s 1.87 m s A2
41 11.9 Bernoulli s Equation The fluid accelerates toward the lower pressure regions. According to the pressure-depth relationship, the pressure is lower at higher levels, provided the area of the pipe does not change.
42 11.9 Bernoulli s Equation W F s F s P As P2 P1 V Wnc 12 mv12 mgy1 1 2 mv22 mgy2
43 11.9 Bernoulli s Equation P2 P1 V 12 mv12 mgy1 12 mv22 mgy2 P2 P1 12 v12 gy1 12 v22 gy2 BERNOULLI S EQUATION In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by: P1 12 v12 gy1 P2 12 v22 gy2
44 11.10 Applications of Bernoulli s Equation Conceptual Example 14 Tarpaulins and Bernoulli s Equation When the truck is stationary, the tarpaulin lies flat, but it bulges outward when the truck is speeding down the highway. Account for this behavior.
45 11.10 Applications of Bernoulli s Equation
46 11.10 Applications of Bernoulli s Equation
47 11.10 Applications of Bernoulli s Equation
48 11.10 Applications of Bernoulli s Equation Example 16 Efflux Speed The tank is open to the atmosphere at the top. Find an expression for the speed of the liquid leaving the pipe at the bottom.
49 11.10 Applications of Bernoulli s Equation v2 0 P1 P2 Patm P1 12 v12 gy1 P2 12 v22 gy2 y2 y1 h 1 2 v12 gh v1 2 gh
50 11.11 Viscous Flow Flow of an ideal fluid. Flow of a viscous fluid.
51 11.11 Viscous Flow FORCE NEEDED TO MOVE A LAYER OF VISCOUS FLUID WITH CONSTANT VELOCITY The magnitude of the tangential force required to move a fluid layer at a constant speed is given by: Av F y coefficient of viscosity SI Unit of Viscosity: Pa s Common Unit of Viscosity: poise (P) 1 poise (P) = 0.1 Pa s
52 11.11 Viscous Flow POISEUILLE S LAW The volume flow rate is given by: R 4 P2 P1 Q 8 L
53 11.11 Viscous Flow Example 17 Giving and Injection A syringe is filled with a solution whose viscosity is 1.5x10-3 Pa s. The internal radius of the needle is 4.0x10-4m. The gauge pressure in the vein is 1900 Pa. What force must be applied to the plunger, so that 1.0x10-6m3 of fluid can be injected in 3.0 s?
54 11.11 Viscous Flow P2 P 8 LQ R Pa s m m s m Pa
55 11.11 Viscous Flow P Pa P2 P Pa P Pa F P2 A 3100 Pa m 0.25N 5 2
56 PITANJA ZA PONAVLJANJE 1. Fluid 2. Gustoća 3. Tlak 4. Atmosferski tlak 5. Pacalovo načelo 6. Uzgon 7. Arhimedov zakon 8. Idealni fluid 9. Jednadžba kontinuiteta 10. Bernoullijeva jednadžba PITANJA ZA PONAVLJANJE
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