Pressure

Сентябрь 2, 2022

Содержание

2. Fluid Mechanics A fluid is a collection of molecules that are randomly arranged and held together
3. Figure 7.1 At any point on the surface of a submerged object, the force exerted by
4. Pressure Figure 7.2 A simple device for measuring the pressure exerted by a fluid. If F
5. If the pressure varies over an area, we can evaluate the infinitesimal force dF on an
6. Snowshoes keep you from sinking into soft snow because they spread the downward force you exert
7. Table 7.1 Variation of Pressure with Depth
8. Variation of Pressure with Depth Figure 7.3 A parcel of fluid (darker region) in a larger
9. Variation of Pressure with Depth That is, the pressure P at a depth h below a
10. If the liquid is open to the atmosphere and P0 is the pressure at the surface
11. Figure 7.4 (a) Diagram of a hydraulic press. Because the increase in pressure is the same
12. (b) Figure 7.4 (a) Diagram of a hydraulic press. Because the increase in pressure is the
13. Pressure Measurements Figure 7.5 (a) a mercury barometer. (a)
14. Pressure Measurements Figure 7.5 (b) an open-tube manometer. (b) The difference in pressure P - P0
15. Buoyant Forces and Archimedes’s Principle Figure 7.6 (a) A swimmer attempts to push a beach ball
16. The upward force exerted by a fluid on any immersed object is called a buoyant force.
17. Buoyant Forces and Archimedes’s Principle Figure 7.7 The external forces acting on the cube of liquid
18. Case 1: Totally Submerged Object Figure 7.8 The external forces acting on the cube of liquid
19. Thus, the direction of motion of an object submerged in a fluid is determined only by
20. Figure 7.9 An object floating on the surface of a fluid experiences two forces, the gravitational
21. This equation tells us that the fraction of the volume of a floating object that is
22. Fluid Dynamics When fluid is in motion, its flow can be characterized as being one of
23. Figure 7.11 Hot gases from a cigarette made visible by smoke particles. The smoke first moves
24. Fluid Dynamics The term viscosity is commonly used in the description of fluid flow to characterize
25. Fluid Dynamics Because the motion of real fluids is very complex and not fully understood, we
26. The path taken by a fluid particle under steady flow is called a streamline. The velocity
27. Fluid Dynamics Figure 7.13 A fluid moving with steady flow through a pipe of varying cross-sectional
28. Fluid Dynamics This expression is called the equation of continuity for fluids. It states that the
29. Bernoulli’s Equation Figure 7.14 A fluid in laminar flow through a constricted pipe. The volume of
30. Bernoulli’s Equation
31. Bernoulli’s Equation This is Bernoulli’s equation as applied to an ideal fluid. It is often expressed
32. Bernoulli’s Equation This Bernoulli effect explains the experience with the truck on the highway at the
33. Other Applications of Fluid Dynamics Figure 7.15 Streamline flow around a moving airplane wing. The air
34. Other Applications of Fluid Dynamics Figure 7.16 Because of the deflection of air, a spinning golf
35. Other Applications of Fluid Dynamics Figure 7.17 A stream of air passing over a tube dipped
36. Quick Quiz 7.1 Suppose you are standing directly behind someone who steps back and accidentally stomps
37. Quick Quiz 7.2 The pressure at the bottom of a filled glass of water (ρ=1 000
38. Quick Quiz 7.3 Several common barometers are built, with a variety of fluids. For which of
39. Quick Quiz 7.4 An apple is held completely submerged just below the surface of a container
40. Quick Quiz 7.5 You observe two helium balloons floating next to each other at the ends
42. Скачать презентацию

Слайд 2

Fluid Mechanics
A fluid is a collection of molecules that are randomly

arranged and held together by weak cohesive forces and by forces exerted by the walls of a container. Both liquids and gases are fluids.

In our treatment of the mechanics of fluids, we do not need to learn any new physical principles to explain such effects as the buoyant force acting on a submerged object and the dynamic lift acting on an airplane wing. First, we consider the mechanics of a fluid at rest—that is, fluid statics. We then treat the mechanics of fluids in motion— that is, fluid dynamics. We can describe a fluid in motion by using a model that is based upon certain simplifying assumptions.

Слайд 3

Figure 7.1 At any point on the surface of a submerged

object, the force exerted by the fluid is perpendicular to the surface of the object. The force exerted by the fluid on the walls of the container is perpendicular to the walls at all points.

Pressure

Слайд 4

Pressure
Figure 7.2 A simple device for measuring the pressure exerted by

a fluid.

If F is the magnitude of the force exerted on the piston and A is the surface area of the piston, then the pressure P of the fluid at the level to which the device has been submerged is defined as the ratio F/A:

(7.1)

Note that pressure is a scalar quantity because it is proportional to the magnitude of the force on the piston.

Слайд 5

If the pressure varies over an area, we can evaluate the

infinitesimal force dF on an infinitesimal surface element of area dA as

where P is the pressure at the location of the area dA. The pressure exerted by a fluid varies with depth. Therefore, to calculate the total force exerted on a flat vertical wall of a container, we must integrate Equation 7.2 over the surface area of the wall.

(7.2)

Because pressure is force per unit area, it has units of newtons per square meter (N/m2) in the SI system. Another name for the SI unit of pressure is pascal (Pa):

(7.3)

Слайд 6

Snowshoes keep you from sinking into soft snow because they spread

the downward force you exert on the snow over a large area, reducing the pressure on the snow surface.

Слайд 7

Table 7.1
Variation of Pressure with Depth

Слайд 8

Variation of Pressure with Depth
Figure 7.3 A parcel of fluid (darker

region) in a larger volume of fluid is singled out. The net force exerted on the parcel of fluid must be zero because it is in equilibrium.

Слайд 9

Variation of Pressure with Depth
That is, the pressure P at a

depth h below a point in the liquid at which the pressure is P0 is greater by an amount ρgh.

(7.4)

Слайд 10

If the liquid is open to the atmosphere and P0 is

the pressure at the surface of the liquid, then P0 is atmospheric pressure. In our calculations and working of end-of-chapter problems, we usually take atmospheric pressure to be

In view of the fact that the pressure in a fluid depends on depth and on the value of P0, any increase in pressure at the surface must be transmitted to every other point in the fluid. This concept was first recognized by the French scientist Blaise Pascal (1623–1662) and is called Pascal’s law: a change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container.

Слайд 11

Figure 7.4 (a) Diagram of a hydraulic press. Because the increase

in pressure is the same on the two sides, a small force Fl at the left produces a much greater force F2 at the right.

Слайд 12

(b)
Figure 7.4 (a) Diagram of a hydraulic press. Because the increase

in pressure is the same on the two sides, a small force Fl at the left produces a much greater force F2 at the right. (b) A vehicle undergoing repair is supported by a hydraulic lift in a garage.

Слайд 13

Pressure Measurements
Figure 7.5 (a) a mercury barometer.
(a)

Слайд 14

Pressure Measurements
Figure 7.5 (b) an open-tube manometer.
(b)
The difference in pressure P

- P0 is equal to ρgh. The pressure P is called the absolute pressure, while the difference P - P0 is called the gauge pressure. For example, the pressure you measure in your bicycle tire is gauge pressure.

Слайд 15

Buoyant Forces and Archimedes’s Principle
Figure 7.6 (a) A swimmer attempts to

push a beach ball underwater. (b) The forces on a beach ball–sized parcel of water. The buoyant force B on a beach ball that replaces this parcel is exactly the same as the buoyant force on the parcel.

(b)

(a)

Слайд 16

The upward force exerted by a fluid on any immersed object

is called a buoyant force.

Buoyant Forces and Archimedes’s Principle

The magnitude of the buoyant force always equals the weight of the fluid displaced by the object. This statement is known as Archimedes’s principle.

Слайд 17

Buoyant Forces and Archimedes’s Principle
Figure 7.7 The external forces acting on

the cube of liquid are the gravitational force Fg and the buoyant force B. Under equilibrium conditions, B = Fg .

(7.5)

Слайд 18

Case 1: Totally Submerged Object
Figure 7.8 The external forces acting on

the cube of liquid are the gravitational force Fg and the buoyant force B. Under equilibrium conditions, B = Fg .

(b)

(a)

Слайд 19

Thus, the direction of motion of an object submerged in a

fluid is determined only by the densities of the object and the fluid.

Case 1: Totally Submerged Object

Слайд 20

Figure 7.9 An object floating on the surface of a fluid

experiences two forces, the gravitational force Fg and the buoyant force B. Because the object floats in equilibrium, B = Fg .

Case 2: Floating Object

Слайд 21

$This equation tells us that the fraction of the volume of$

This equation tells us that the fraction of the volume of

a floating object that is below the fluid surface is equal to the ratio of the density of the object to that of the fluid.

(7.6)

Case 2: Floating Object

Слайд 22

Fluid Dynamics
When fluid is in motion, its flow can be characterized

as being one of two main types. The flow is said to be steady, or laminar, if each particle of the fluid follows a smooth path, such that the paths of different particles never cross each other. In steady flow, the velocity of fluid particles passing any point remains constant in time.

Figure 7.10 Laminar flow around an automobile in a test wind tunnel.

Слайд 23

Figure 7.11 Hot gases from a cigarette made visible by smoke

particles. The smoke first moves in laminar flow at the bottom and then in turbulent flow above.

Above a certain critical speed, fluid flow becomes turbulent; turbulent flow is irregular flow characterized by small whirlpool-like regions, as shown in Figure 7.11.

Fluid Dynamics

Слайд 24

Fluid Dynamics
The term viscosity is commonly used in the description of

fluid flow to characterize the degree of internal friction in the fluid. This internal friction, or viscous force, is associated with the resistance that two adjacent layers of fluid have to moving relative to each other. Viscosity causes part of the kinetic energy of a fluid to be converted to internal energy. This mechanism is similar to the one by which an object sliding on a rough horizontal surface loses kinetic energy.

Слайд 25

Fluid Dynamics
Because the motion of real fluids is very complex and

not fully understood, we make some simplifying assumptions in our approach. In our model of ideal fluid flow, we make the following four assumptions:
1. The fluid is nonviscous. In a nonviscous fluid, internal friction is neglected. An object moving through the fluid experiences no viscous force.
2. The flow is steady. In steady (laminar) flow, the velocity of the fluid at each point remains constant.
3. The fluid is incompressible. The density of an incompressible fluid is constant.
4. The flow is irrotational. In irrotational flow, the fluid has no angular momentum about any point. If a small paddle wheel placed anywhere in the fluid does not rotate about the wheel’s center of mass, then the flow is irrotational.

Слайд 26

The path taken by a fluid particle under steady flow is

called a streamline. The velocity of the particle is always tangent to the streamline, as shown in Figure 7.12. A set of streamlines like the ones shown in Figure 7.12 form a tube of flow. Note that fluid particles cannot flow into or out of the sides of this tube; if they could, then the streamlines would cross each other.

Fluid Dynamics

Figure 7.12 A particle in laminar flow follows a streamline, and at each point along its path the particle’s velocity is tangent to the streamline.

Слайд 27

Fluid Dynamics
Figure 7.13 A fluid moving with steady flow through a

pipe of varying cross-sectional area. The volume of fluid flowing through area A1 in a time interval ∆t must equal the volume flowing through are A2 in the same time interval. Therefore, A1v1 = A2v2.

Слайд 28

Fluid Dynamics
This expression is called the equation of continuity for fluids.

It states that

the product of the area and the fluid speed at all points along a pipe is constant for an incompressible fluid.

(7.7)

Слайд 29

Bernoulli’s Equation
Figure 7.14 A fluid in laminar flow through a constricted

pipe. The volume of the shaded portion on the left is equal to the volume of the shaded portion on the right.

Слайд 30

Bernoulli’s Equation

Слайд 31

Bernoulli’s Equation
This is Bernoulli’s equation as applied to an ideal fluid.

It is often expressed as

(7.8)

(7.9)

Слайд 32

Bernoulli’s Equation
This Bernoulli effect explains the experience with the truck on

the highway at the opening of this section. As air passes between you and the truck, it must pass through a relatively narrow channel. According to the continuity equation, the speed of the air is higher. According to the Bernoulli effect, this higher speed air exerts less pressure on your car than the slower moving air on the other side of your car. Thus, there is a net force pushing you toward the truck!

Слайд 33

Other Applications of Fluid Dynamics
Figure 7.15 Streamline flow around a moving

airplane wing. The air approaching from the right is deflected downward by the wing. By Newton’s third law, this must coincide with an upward force on the wing from the air—lift. Because of air resistance, there is also a force opposite the velocity of the wing— drag.

Слайд 34

Other Applications of Fluid Dynamics
Figure 7.16 Because of the deflection of

air, a spinning golf ball experiences a lifting force that allows it to travel much farther than it would if it were not spinning.

Слайд 35

Other Applications of Fluid Dynamics
Figure 7.17 A stream of air passing

over a tube dipped into a liquid causes the liquid to rise in the tube.

Слайд 36

Quick Quiz 7.1
Suppose you are standing directly behind someone who

steps back and accidentally stomps on your foot with the heel of one shoe. Would you be better off if that person were (a) a large professional basketball player wearing sneakers (b) a petite woman wearing spike-heeled shoes?

Слайд 37

Quick Quiz 7.2
The pressure at the bottom of a filled

glass of water (ρ=1 000 kg/m3) is P. The water is poured out and the glass is filled with ethyl alcohol ρ=806 kg/m3). The pressure at the bottom of the glass is (a) smaller than P (b) equal to P (c) larger than P (d) indeterminate.

Слайд 38

Quick Quiz 7.3
Several common barometers are built, with a variety

of fluids. For which of the following fluids will the column of fluid in the barometer be the highest? (a) mercury (b) water (c) ethyl alcohol (d) benzene

Слайд 39

Quick Quiz 7.4
An apple is held completely submerged just below

the surface of a container of water. The apple is then moved to a deeper point in the water. Compared to the force needed to hold the apple just below the surface, the force needed to hold it at a deeper point is (a) larger (b) the same (c) smaller (d) impossible to determine.

Слайд 40

Quick Quiz 7.5
You observe two helium balloons floating next to

each other at the ends of strings secured to a table. The facing surfaces of the balloons are separated by 1–2 cm. You blow through the small space between the balloons. What happens to the balloons? (a) They move toward each other. (b) They move away from each other. (c) They are unaffected.