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# Hydrostatic Pressure. Communicating Vessels. Pascal's Principle. Hydraulic Press

## 1.

Hydrostatic PressureCommunicating Vessels

Pascal's Principle

Hydraulic Press

## 2.

LEARNING OBJECTIVES:1. Describe hydrostatic pressure and recall,

rearrange and use the equation

р = ρgh;

2. Compare the effects of applying a force to

a compressible fluid and an incompressible

fluid;

3. Describe Pascal’s law and apply it to

connecting vessels and hydraulic presses.

## 3.

DENSITYThe mass density of a substance

is the mass of a substance

divided by its volume:

m

V

SI Unit of Density: g/cm3 or kg/m3

## 4.

## 5.

Example - Blood as a Fraction ofBody 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 5.2 10 m

3

3

1060 kg

m 5.5 kg

3

## 6.

(a)W mg 5.5 kg 9.80 m s 54 N

2

(b)

54 N

Percentage

100% 7.8%

690 N

## 7.

FP

A

SI Unit

of Pressure:

1 N/m2 = 1 Pa

Pascal

## 8.

Example: The Forceon 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.

## 9.

FP

A

F PA 1.2 10 N m

5

1.0 10 N

3

Since the water

pushes

perpendicularly

against the back of

the hand, the force

is directed downward

in the drawing.

2

8.4 10

3

m

2

## 10.

Atmospheric Pressure at SeaLevel:

5

1.013x10 Pa = 1 atmosphere

## 11.

Why do tetra packscrush or squeeze

itself when you sip

too much air

inside?

## 12. Pressure and Depth in a Static Fluid

PRESSURE AND DEPTH IN A STATIC FLUIDF

y

P2 A P1 A mg 0

P2 A P1 A mg

m V

## 13. Pressure and Depth in a Static Fluid

PRESSURE AND DEPTH IN A STATIC FLUIDV Ah

P2 A P1 A Vg

P2 A P1 A Ahg

P2 P1 hg

## 14. Pressure and Depth in a Static Fluid

PRESSURE AND DEPTH IN A STATIC FLUIDConceptual Example - 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?

## 15.

Answer:The force exerted on a given section of

the dam depends only on how far that

section is located vertically below the

surface. As we go deeper, the water

pressure and force becomes greater.

The force that water applies on the

dam does not depend on the amount of

water backed up behind the dam. Thus,

an EQUALLY MASSIVE HOOVER DAM

WOULD STILL BE NEEDED.

PRESSURE AND DEPTH IN A STATIC FLUID

## 16. Pressure and Depth in a Static Fluid

PRESSURE AND DEPTH IN ASTATIC FLUID

Example - 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.

## 17. Pressure and Depth in a Static Fluid

PRESSURE AND DEPTH IN A STATIC FLUIDP2 P1 gh

atmospheric pressure

P2 1.01 105 Pa 1.00 103 kg m 3 9.80 m s 2 5.50 m

1.55 105 Pa

## 18.

Pressure Gauges## 19. Pressure Gauges

PRESSURE GAUGESP2 P1 gh

Patm gh

Patm

1.01 105 Pa

h

g 13.6 103 kg m 3 9.80 m s 2

0.760 m 760 mm

## 20. 11.4 Pressure Gauges

11.4 PRESSURE GAUGESP2 PB PA

PA P1 gh

absolute pressure

P2 Patm gh

gauge pressure

## 21. Pressure Gauges

PRESSURE GAUGES## 22. Pascal’s Principle

PASCAL’SPRINCIPLE

Any change in the

pressure applied

to a completely

enclosed fluid is

transmitted

undiminished to all

parts of the fluid and

enclosing walls.

## 23. Pascal’s Principle

PASCAL’S PRINCIPLEP2 P1 g 0 m

F2 F1

A2 A1

A2

F2 F1

A1

## 24. Pascal’s Principle

PASCAL’S PRINCIPLEExample - A Car Lift

The input piston has a radius

of 0.0120 m and the output

plunger has a radius of 0.150

m. The combined weight of

the car and the plunger is

20,500 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?

## 25. Pascal’s Principle

PASCAL’S PRINCIPLEA2

F2 F1

A1

0.0120 m

F2 20500 N

131 N

2

0.150 m

2

## 26.

Communicating Vesselset

of

containers

containing

a

homogeneous fluid: when the liquid

settles, it balances out to the same level

in all of the containers regardless of the

shape and volume of the containers. If

additional liquid is added to one vessel,

the liquid will again find a new equal

level in all the connected vessels. This

occurs because gravity and pressure

are constant in each vessel (hydrostatic

pressure).

## 27.

Containing homogeneous fluid: when the liquid settles, itbalances out to the same level in all of the containers

regardless of the

shape and volume

of the containers.

This occurs

because gravity

and pressure are

constant in each

vessel (hydrostatic

pressure).