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Section 13.3 Fluids at Rest and in Motion

- Objectives
- Relate Pascals principle to simple machines and

occurrences. - Apply Archimedes principle to buoyancy.
- Apply Bernoullis principle to airflow.

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.

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. - Pascals Principle pressure applied to a fluid

is transmitted undiminished throughout it. Every

time you squeeze a tube of toothpaste you use

Pascals Principle.

FLUIDS AT REST

- Pascals 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 F1A2 / A1

- Do Practice Problem 23 p. 353
- F1 / A1 F2 / A2 or F2 F1A2 / A1
- 1600 / 1440 F / 72 F 1600(72) / 1440
- 80 N F F 80 N

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 ?hg (? is small Greek letter rho)
- That formula works for all fluids.

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 objects volume and

the acceleration due to gravity. It is the

upward force on an object immersed in fluid. - Fbuoyant ?Vg 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.

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

objects 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.

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 ?Vg b. Fg mg ?Vg

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

FLUIDS IN MOTION BERMOULLIS PRINCIPLE

- Bernoullis 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 Bernoullis

principle, such as paint sprayers and perfume

bottles. - A gasoline engines carburetor, which is where

air and gas are mixed, is another common

application of Bernoullis 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

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