PRESSURE

Concept of Pressure

The Concept of Pressure

Explain the concept of pressure

Pressure  is  defined  as  the  for ce  per  unit  area.  OR  Pressure  is  the  force  acting  normally

(perpendicularly) per unit surface area.

It is calculated by the formula:

Pressure = Force (f)/Area (A)

P = F/A

Where

P – Pressure

F – Force

A – Area

The S.I Unit of Pressure

State the S.I unit of pressure

The SI unit of Pressure is Newton per square metre (N/M

2

). This unit is usually referred to as the

Pascal (Pa).

1Pa = 1 N/M

2

The other units of pressure are atmosphere, torr bar and mmHg.

1 atmosphere = 780mmHg

1 atmosphere = 1 10

N/M

= 1bar (used by meteorologists)

5

2

Note:

for a given amount  of force, the smaller the area  of application  the greater  the  pressur e

exerted.

63

When  a  man  lifts  a  bucket  of  water  by  its  handle  that  is  made  with  a  thin  metal,  he  would

experience some discomfort but if the bucket was made with a thicker handle the discomfort will

be much less if any.

This is because the area over which the force is applied is larger.

Pressure due to Solids

Dependence of Pressure on Surface of Contact

Explain dependence of pressure on surface of contact

The pressure in  solid depends on the surface area of  contact. A force (F) applied onto  a small

area exerts a higher pressure as compared to when it is applied onto a large surface.

Pressure in solid = Force applied/Area of contact.

Example 1

A block of wood that weighs 30N and measures 5m by 10m by 4m. If it was placed on a table

with the largest possible area (5mx10m) in contact with table, exerts less pressure than it would

when placed with its smallest possible area (5mx4m) in contact with table.

Solution

Data:

Force = 30N

Largest base area = ?

A

= 10mx5m = 50m

2

L

P = F/A = 30N = 0.6N/30m

2

Pressure = 0.6N/m

2

Force (F) = 30N.

Small base are = ?

64

As = 5mx4m

As = 20m

2

P= F/A = 30N/20M

= 1.5 N/M

2

2

Pressure = 1.5 N/M

2

Example 2

A tip of needle has a cross- sectional area of 1x10

6

m

2

. If doctor applies a force of 2N to a syringe

that is connected to the needle, what is pressure is exerted at the tip of the needle?

Soln:

Data:

Area (A) = 1x10

6

m

2

Force (F) = 20N

Pressure =?

P = F/A

P = 20 = 2.0x107 N/M

2

The pressure extended by the needle lip is 2.0x10

N/m

7

2

Example 3

A rectangle metal block with sides  105m by 1.0m by 1.2m rests on a horizontal surface. If the

density of the metal is 7000kg/m3. Calculate the maximum and minimum pressure that the block

can exerts on the surface.

(Take the weight of 1kg mass to be 10N)

Solution:

Data:

65

Dimension = 1.2m,1.5m,1.0m.

Density = 7000kg/m

3

Maximum pressure (Pmx) = ?

Minimum pressure (Pmn) = ?

Volume = 1.2x1.5x1=18m

3

Density = mass/ Volume

7000kg/m

= mass/18

3

Mass = 7000x18 = 126000Kg

1kg = 10N

126000Kg = ?

F = 1260000 = 1.26 x 10

6

Force of metal = 1.26 x 10

6

A

= 1.2 x 1.5= 18m

2

1

A

= 1.2m

= 1.2mx1m=1.2m

2

2

2

A

= 1.5 x 1m= 1.5m

2

3

A

= 18m

2

mx

A

= 102m

2

min

P

= F/A

=1.26 x 10

6

N/18M

2

= 1.26X10

6

/1.8 X10

1

mn

mx

Maximum pressure = 1.05x10

6

N/m

2

/maximum pressure= 0.7x10

5

N/m

2

The Applications of Pressure due to Solids

Identify the applications of pressure due to solids

66

It is used to make differ ent objects like screw, nails, pins, spears and arrows. This item is given

sharp points to increase their penetrating power.

It helps some of living organisms for self-defence. A fish uses its sharp fins to protect itself.

When one walks on shoes with sharp pointed heels they exert greater pr essure on the ground than

when wearing flat shoes.

It  helps  in  construction  of  railways.  During  the  constructions  of  railways,  wide  wooden  or

concrete sleepers are placed below the railways tracks. This provides a larger surface area over

which the weight of the train acts. This is a saf ety measure to train tracks.

Buildings are constructed  with wide foundations to  ensure that  the  weight  of the building acts

over the layer area.

Pressure in Liquids

A  liquid  will  exert  pressure  on  an  immersed  object  as  well  as  on  the  walls  of  the  container

holding  it.  Note  that  the  pressure  exerted  by  liquids  is  due  to  the  weight  of  the  liquid.  Also

increase in water level in liquid cause increase in pressure.

The Characteristics of Pressure in Liquids

Describe the characteristics of pressure in liquids

Note:

Pressure in liquids =Force/Area

But force= hApg/A

=Hsg

Hence pressure in liquids is given as hsg.

67

H= Height of the liquid column

A= Area of the base

The pressure at any point in a liquid at rest then depends

1.

Depth

2.

Density of liquid

Note

: It does not defend on the area

Pressure in liquids is characterized using the following parameters

1.

Pressure in a liquid increase with depth

2.

Pressure in a liquid acts equally in all directors

3.

Pressure in a liquid increases with increase in density of the liquid.

Mercury  exerts  more  pressure than an  equal volume of  water.  This because  mercury is denser

than water.

68

The Variation of Pressure with Depth in Liquids

Examine the variation of pressure with depth in liquids

Demonstration of water spurting from holes at different heights.

As  pressure at point  A  is  low due  to  small height  of water above it  but  at  point B  the height

increase and the distance of water increase while at  point C the height is greatest therefore the

level of water distance will be large distance.

Demonstration of pressure in a communicating vessel

69

The shape of vessel found in point A, B, C and D is different but the pressure is the same due to

the equal height (L) of the liquid above the points.

Problems Involving Pressure in Liquids

Solve problems involving Pressure in Liquids

Example 4

A cube of side 2cm is completely submerged in water so that the bottom of the cube is at a depth

of 10cm. use g=10m/s

and s=1000kg/m

2

3

1.

What is different between the pressure on the bottom of the cable and the pressure on its

tap?

2.

Determine the difference in the force on the top and bottom.

3.

What is the weight of the water displaced by the cube?

Solution;

Data.

Depth = 10cm = 0.1m

s = 1000kg/m

3

70

g = 10m/s

h= 8cm= 0.08

formular

p= sgh

p=1000kg/m

3

x10m/s

2

x0.1m=1000N/m

2

At the h= 0.08m p= 1000x10x0.08= 800N/m

2

Change in pressure = 1000N/m =200N/m

2

So that different in pressure between the bottom the top is 200N/m

2

Pressure = Force/Area = P= F/A

Area =L

= (10.02)

= 0.0004m

2

2

2

Distance in water 200N/m

2

x0.0004m

2

This is the upthrust acting on the cube

Water displaced by the cube in weight= volume of the cube

Volume = l3 (2cm)

= 8cm

3

3

For water, 1cm

3

= 1g 50.8cm

3

= 8g

Weight of displaced water

mass of displaced water/100=8g = 0.08N

Example 5

Calculate  the  pressure  at  the  bottom  of  tank  of  water  15m  deep  due  to  the  water  above  it  is

(s=1000kg/m

3

).

Solution:

Data:

71

Height =15m

S=1000kg/m

3

g= 10m/s

2

Formula

Pressure in liquid sgh

= 1000x10x15=150000N/M

2

The Principle of a Hydraulic Pressure

Explain the principle of a hydraulic pressure

It  state  that  “Any  external  pressure  applied  to  the  surface  of  an  enclosed  liquid  will  be

transmitted equally throughout liquid.”

Illustration of Pascal s Principle.

Note: in all side of vessel will experience equal pressure.

72

The  hydraulic  press  works  on  Pascal s  principle,  when  using  this  principle  a  small  force

converted into a large force and vice versa.

From Pascal s Principle

Note:

The distance moved (d) is inversely proportional to the cross sectional area.

Example 6

The pistons of a hydraulic press have their areas given as 3.

and 2x10

m

respectively. If

0x10-4m2

2

2

the smaller  piston is  pushed down with  a force of 12N, what is the force required to push the

larger piston?

Soln:

Data:

F

= 120N, A

= 2X10

2

m

2

1

2

73

A

= 3X10

4

m

2

2

Application of Hydraulic Press

Measure pressure of a liquid

Hydraulic press is used in industries to express bulk items.

Hydraulic brake system

When pressure is applied to the brake pedal, it pushes the piston in the master cylinder forward

creating a pressure in the brake fluid. This pressure is transferred to the slave cylinders where it

74

is multiplied and pushes the brake shoes against the brake dram that is attached to the wheel of

the vehicle.

It is used in industries in the forming of metals.

Since the hydraulic pr ess act like a lift, it is used for lifting heavy loads.

Measuring  the  pressure of  liquids  using a  manometer. Manometer is  the  device for  measuring

pressure (commonly gas).

Atmospheric Pressure

The Existence of Atmospheric Pressure

Describe the existence of atmospheric pressure

Atmospheric pressure is  as a  result  of  the  weight  of this layer of  gases, the act  at atmospheric

pressure is surrounded the layer of air consisting of a mixture of gases.

Note. The atmospheric pressure on the earth s surface and objects on the earth is a approximately

1.01x10

5

N/m

2.

75

The experiment which demonstrate the existence of atmospheric pressure.

Umbler experiment

When you fill a glass timber with cord and gentle turned upside down. It will be seen that water

will not poured down.

Plunger

76

Pulling the plunger is not easy. This is so because all the air is squeezed out from the table when

the surrounding pressure being high the plunger sticks.

Crushed bottle

77

When putting hot  water  in, the bottle  is cooled under  cold water the steam condenses; leaving

partial vacuum inside the bottle consequently the greater atmospheric pressure outside the bottle

crushes it in wards.

Applications of Atmospheric Pressure

Identify the applications of atmospheric pressure

A siphon

A siphon is applied in areas and devices that we use everyday

1.

It is used in the toilet flushing cisterns (chain and ball tank). The flush is triggered by a

handle that operates a simple diaphragm like piston pump that lifts enough water.

2.

It is used in special rain gauges called siphon rain gauge which are able to automatically

drain out excess water.

3.

A siphon cup is a reservoir attached to a gum.

4.

It is used is some drainage systems to drain water to one point.

The lift pump

78

A lift pump is used to raise water from under ground sources. This is a pump that is used to lift

the liquid, rather than force liquid up.

A  syringe  is  a  simple  piston  pump  that  lifts  a  tube.  The  plunger  that  lifts  can  be  pulled  and

pushed through  inside  a cylindrical  tube or barrel. This enables  the  syringe to  take in or  expel

fluid through the opening (nozzle) at the end of the tube.

Uses of syringe:

79

1.

They can be fitted with hypodermic needles and used to administer injections.

2.

They are used to measure liquids and gases in a laborator y.

3.

They are used to apply certain compounds such as a glue or lubricant.

Bicycle pump

This is a type of force pump that consists of a hollow metal cylinder and a movable piston.

Meassuring Atmospheric Pressure

Measure atmospheric pressure

Atmospheric pressure is measured by using barometer;

Types of barometer:

1.

The simple barometer

2.

Fortin barometer

3.

Aneroid barometer

This is a type of force pump that consists of a hollow metal cylinder and a movable piston.

80

A simple  barometer is  the most fundamental  of  the  other types of  barometer. The  barometric

liquid used is mercury.

A simple barometer consists of a hard glass tube closed at one end.

Fortin barometer

A Fortin barometer is a modified simple barometer. It consists of an inverted tube closed at its

upper end with the lower open end immersed in a reserve of mercury. The atmospheric pressure

is measured in terms of the height of the column of mercury.

81

Disadvantages of Fortin barometer:

1.

Mercury  is  very  expensive  to  use  and  is  very  toxic.  For  these  reasons,  an  aneroid

barometer is usually preferred.

2.

It is not portable as it is generally big and contains liquid.

3.

It must be mounted in a vertical position.

82