ch-15

Chapter 15 Fluid Mechanics

F I G U R E 15.1

The force exerte d by the uid on a submerged object at any point is perpendicular to the surface of the object. The forc e exerted by the uid on the walls of the container is perpendicular to the walls at all points .

A F Vacuum

F I G U R E 15.2 A simple device for measuring pressure in a fluid.

–P0Ajˆ d d+h

Mg PAjˆ

F I G U R E 15.4

The net force on the sample of liquid within the darker region must be zero because the sample is in equilibrium.

∆x 1

F1

A2

A1

∆x 2

(a)

F I G U R E 15.5

(David Frazier)

F2

(b)

(a) Diagram of a hydraulic press. Because the increase in pressure is the same at the left and right sides, a : : small force F 1 at the left produces a much larger force F 2 at the right. (b) A vehicle under repair is supported by a hydraulic lift in a garage. :

h H

dy w

y O

F I G U R E 15.6

(Example 15.2) The total force on a dam is obtained from the expression F Pd A, where dA is the area of the red strip.

P=0 h P0 A B

(a)

P0

h

P A

B

(b)

F I G U R E 15.7

Two devices for measuring pressure: (a) a mercury barometer and (b) an open-tube manometer.

B h Fg

F I G U R E 15.8 The external forces on the cube of liquid are the : gravitational force F g and the buoyant : force Under equilibrium B. conditions, B Fg .

B Fg

a

(a)

B a Fg

(b)

Figure 15.9 (a) A totally submerged object that is less dense than the fluid in which it is submerged experiences a net upward force. (b) A totally submerged object that is denser than the fluid sinks.

B

Fg

figure 15.10 An object floating on the surface of a liquid experiences two forces, the : gravitational force F g and the : buoyant force B. Because the object floats in equilibrium, B F g .

T2 B T1 Fg Fg

(a)

F I G U R E 15.11

(b)

(Example 15.3) (a) When the crown is suspended in air, the scale reads its true weight because T1 Fg (the buoyancy due to air is negligible). (b) When : the crown is immersed in water, the buoyant force B reduces the scale reading to T2 Fg B .

(a)

(b)

F I G U R E 15.12

(Example 15.4) (a) When the sphere hangs in air, the string vibrates in its second harmonic. (b) When the sphere is immersed in water, the string vibrates in its fifth harmonic.

(Andy Sacks/Tony Stone Images/Getty Images)

F I G U R E 15.13

An illustration of steady flow around an automobile in a test wind tunnel. The streamlines in the airflow are made visible by smoke particles.

v

(Werner Wolff/Black Star)

P

F I G U R E 15.14

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.

F I G U R E 15.15

This diagram represents a set of streamlines (blue lines). A particle at P follows one of these streamlines, and its velocity is tangent to the streamline at each point along its path.

Point 2 A2 v2 ∆x2

Point 1 A1 ∆x1

F I G U R E 15.16

v1

A fluid moving with steady flow through a pipe of varying cross-sectional area. The volume of fluid flowing through A1 in a time interval t must equal the volume flowing through A2 in the same time interval.

Point 2 ∆x2

–P2A2ˆi

Point 1 P1A1ˆi y1

∆x1

v2 y2

v1

F I G U R E 15.17

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.

A2

P h

A1

y2 y1

F I G U R E 15.18

P0

v1

(Example 15.7) A liquid leaves a hole in a tank at speed v1.

Drag

F

F I G U R E 15.19

Lift

Streamline flow around a moving airplane wing. The air approaching from the right is deflected downward by the wing.

Plaque

Artery

F I G U R E 15.20

A stream of air passing over a tube dipped into a liquid will cause the liquid to rise in the tube.

F I G U R E 15.21

Blood must travel faster than normal through a constricted region of an artery.

Dam

Dam

Figure Q15.2

(Pamela Zilly/The Image Bank/Getty)

(© TempSport/CORBIS)

Figure Q15.10

Figure Q15.20

(a)

(b)

Figure P15.8

500 lb 2.00 in. 10.0 in.

F

Figure P15.11

Figure P15.12

h

P0

Figure P15.13 A1

A2

A1

Water

h

Mercury (a)

(b)

Figure P15.14

A2

Figure P15.16

Figure P15.21

96 98 96 98 100 102 104

L

100 102 104

Figure P15.24

h

h0

h

(George

Semple)

Figure P15.33 Problems 15.33 and 15.34.

(Stan Osolinski/Dembinsky Photo Associates)

Figure P15.37

Figure P15.40

y h

v

ρ

Figure P15.43

A v

F a

Figure P15.45