PRESSURE  
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Pressure is the force acting normally per unit area.  
푭풐풓풄풆  
푷풓풆풔풔풖풓풆 =  
→ 푷 = 푭  
푨풓풆풂  
푨
•
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The SI units of pressure is Newton per metre square (N/m2)  
Other units of pressure are Pascal (Pa), Atmosphere (atm)  
mercury (mmHg) and Torre bar (bar).  
,
Millimeter of  
NB.  
1Pa = 1N/m2  
1atm = 760mmHg  
1atm = 100000N/m2  
1atm = 1bar  
Pressure due to Solid  
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Pressure on solid depends on force applied and the surface area.  
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That is 푷풓풆풔풔풖풓풆(푷) = 푭풐풓풄풆(푭)  
푨풓풆풂(푨)  
Example.  
4. Find the pressure exerted when a force of 640N acts in the area of 16m2  
Solution:  
Force (f) = 640N  
Area (A) =16m2  
Pressure (p) =?  
640  
16  
퐹
∴ Pressure= =  
40 Pascal  
퐴
Individual Task  
1. A pressure of 75N/m2 is resulted from a certain force acting on an area of  
0.8m2. Calculate its force acting on it. (ANS: F= 60N)  
2.  
Find the pressure exerted when a force of 3600N act on the area of 36m2  
(
ANS: P = 100N/m2)  
Maximum and minimum pressure  
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Maximum pressure is the value of high pressure and it is determined when a  
force acts perpendicular to the smallest area.  
푭풐풓풄풆  
푴풊풏풊풎풖풎 푨풓풆풂  
Minimum Pressure is the value of low pressure obtained when a force acts  
normally per largest area  
푭풐풓풄풆  
푴풂풙풊풎풖풎 푨풓풆풂  
N.B  
•
Pressure depends upon the area (The smaller the surface area the greater  
the pressure and vice verse)  
•
For example it is easy to cut the meat using a sharp knife than a blunt one,  
this is because the sharp knife has smaller area which produces the larger  
pressure than the blunt one.  
Examples  
1. A rectangular block weighting 320 N has dimensions 4 m by 2 m by 10 m. what  
is the greater pressure and the least (minimum) pressure it can be exerted on  
the ground  
SOLN  
Maximum area = 4 x 10 = 40 m2  
Minimum area = 2 x 4 = 8 m2  
320  
퐹표푟푐푒  
=
=
= 4 N/m2  
Maximum pressure =  
Minimum pressure =  
푀푖푛푖푚푢푚 푎푟푒푎  
8
320  
= 8 N/m2  
퐹표푟푐푒  
푀푎푥푖푚푢푚 푎푟푒푎  
40  
Individual Task  
1. A woman weighting 500N wear a pair of shoes with heels of area 250 m2, what  
is the pressure exerted on the floor by a heel of her shoes? (ANS: P = 2 N/m2 )  
2. Calculate the pressure under the feet of Fatima if the area of contact of her foot  
is 80 cm2 and her mass is 43.8 kg  
3.  
The tip of the needle with cross section area of 0.000001m2, if a doctor applied  
a force of 20N to a syringe that is connected to the needle. Find the pressure  
exerted at the tip of the needle ANS:P = 20000000 N/m2  
4.  
A
rectangular metal block with sides 1.5 m by 1.2 m by 1.0 m rests on a  
horizontal surface .If the density of the metal is 7000 kg/m3, calculate the  
maximum and minimum pressure that the block can exert on the surface.(Take  
the weight of 1 kg mass to be 10 N)  
5.  
T
he mass of cuboid is 60 kg. If it measures 50 cm by 30 cm by 20 cm. What is  
the maximum pressure that it can exert?  
6. A rectangular block of weight 15 N rests on a horizontal table. If it measures 40 cm  
by 30 cm by 20 cm, calculate the greatest and least pressure  
Examples of Solid Pressure in daily life  
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We experience pain discomfort when we lift a bucket of water made by thin handle  
❖
❖
Sharp edges of knife or razor cuts easily than blunt knife or razor  
Sharp pointer of nail, screw, push pin, spear and an arrow has high penetrating power  
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❖
❖
Wide wooden or concrete (large area) sleepers are placed below the railway  
track to prevent railway track to penetrate on ground.  
Buildings are constructed with wide (large area) foundation to increase surface  
area so as to prevent wall from penetrating on ground  
Feet of elephant cannot sink into soft soil even if it is very heavy due to large  
surface area over elephant feet  
❖
❖
❖
A tractor works on soft ground cannot sink due to wide tyres  
Duck cannot sink on soft mud due to large surface area on his webbed feet  
Potter puts some soft material on his/her head for heavy load to increase  
surface area  
❖
It is painfully to walk on barefoot on a road that is covered by pebbles  
Pressure in Liquids  
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A liquid will exert pressure on an immersed object as well as on the walls of the  
container holding it  
•
•
•
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The pressure in the liquid increases with the increase in depth of the liquid  
Pressure in a liquid acts equally in all directions  
Pressure in a liquid increases with the increase in density of the liquid  
From pressure:  
푷 = 푭  
푨
• But: 푭 = 풎품 = 흆 × 풗 × 품 = 흆 × 푨 × 풉 × 품  
휌ℎ퐴푔  
Now: 푷 =  
= 흆 × 풉 × 품 = ρhg  
퐴
•
The pressure in liquids is given by  
∴ 푷 = 흆풉품  
•
The pressure at any point in a liquid at rest depends on:  
(a) Depth (height through which the liquid rises  
)
(b) Density of the liquid  
Variation of pressure with depth  
•
The pressure in a liquid increases with depth (the greater the height above a  
point , the greater the pressure at that point)  
•
This can be demonstrated by the following experiment  
(a) Take a tall vessel and make three holes of the same diameter from the top  
downward  
(b) Fill the vessel with water up to the brim, and observe the way in which  
water spurts from each hole  
(
See the fig. below)  
Observations:  
•
•
•
Water is pushed through the holes at different speeds. More water is pushed  
through hole A than hole B, and least water is pushed through hole C  
The pressure at hole A is greater than that at hole C due to different in heights  
(ie. Pressure in a liquid increases with depth)  
That is why the bottom of a dam is made thicker than the top because the  
pressure at the bottom is much greater than at the top  
Question  
1. Explain why a diver at the bottom of the dam experiences greatest pressure  
ANS  
:
At the bottom of the dam the depth is greatest and therefore the diver  
experiences greatest pressure due to the weight above him  
Examples of Pressure in liquid in real life  
The water bubbles increase in its volume if moves from the bottom of the pond  
to the top of the pond (depth decreases)  
•
•
•
•
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Water tanks have their outlets fixed at the bottom (high depth)  
A person at great height suffers from nose bleeding  
A hole at the bottom of a ship is more dangerous than one near the surface  
A dam is thicker at the bottom than at the top  
Communicating  
Vessel  
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Communicating vessel finds its own level even though each part has different  
shape, the liquid will be at the same level in all parts  
Spirit Level  
•
•
Is an instrument used to test whether a surface is horizontal or vertical.  
It consists of a slightly curved glass tube which is not completely filled with a  
liquid (yellow in color) leaving a bubble in the tube  
Mechanism  
•
A spirit level works on the fact that a liquid in a vessel will always find its own level.  
A Spirit level is used by  
o Masons  
o Carpenters  
o
Surveyors e.t.c  
Examples  
1. What will be the pressure due to column of water of height 4m?  
Data given  
Solution  
Height, h = 4m  
Density of water, ρ = 1000kg/ m3 = 1g/cm3  
Gravitation force, g = 10N/kg  
Pressure exerted, P =?  
From: P = ρhg  
∴
P = 1000 x 4 x 10 = 40000 N/m2  
2. A cube of sides 2cm is completely submerged in water so that the bottom of  
the cube is at depth of 10cm. Find  
(a) Different pressure between top and bottom of the cube  
(b) Different force between top and bottom of the cube  
(c) Weight of water displaced by the cube  
Solution  
Consider the diagram below  
(a) Different pressure between the top and bottom of the cube, ΔP =?  
Data given  
Water density, ρ = 1000kg/ m3 = 1g/cm3  
Gravitation force, g = 10N/kg  
Height at top, h2 = 8cm = 0.08m  
Height at top, h1 = 8cm = 0.1m  
Solution  
ΔP = P2 – P1  
But: P = ρhg  
Then: ΔP = P2 – P1 = (ρ x h2 x g – ρ x h1 x g)  
ΔP = ρg (h2 - h1) = 1000 x 10 x (0.1 – 0.08)  
∴
ΔP = 1000 x 10 x 0.02 = 200 N/m2  
(b) Different force between top and bottom of the cube, ΔF =?  
From: 푷풓풆풔풔풖풓풆 = 푭풐풓풄풆  
푨풓풆풂  
But: A = 2cm x 2cm = 4cm2 = 0.0004 m2  
∴
Δ Force = ΔP x A = 200 x 0.0004 = 0.08  
N
(c) Weight of water displaced, w =?  
The volume of water displaced = Volume of the cube  
Then: volume of water (cube) = (2 x 2 x 2) cm3 = 8cm3  
Mass of water displaced = volume x density = 8 cm3 x 1 g/cm3 = 8 g  
ퟖ
∴ 푾풆풊품풉풕 풐풇 풘풂풕풆풓 풅풊풔풑풍풂풄풆풅 = 풎 × 품 =  
× ퟏퟎ = ퟎ. ퟎퟖ 푵  
ퟏퟎퟎퟎ  
Pascal’s Principle of the hydraulic Press  
It states that:  
“Any external pressure applied to the surface of an enclosed  
liquid will be transmitted equally throughout the liquid”  
OR  
“Pressure applied at a point in a fluid at rest is transmitted  
equally to all parts of the fluid”  
Consider the diagram below  
Hydraulic Press  
•
Is a machine press using a hydraulic cylinder to generate a compressive force  
•
Hydraulic press uses Pascal’s principle to multiply an applied effort using the  
pressure of a liquid or gas. This allows the lifting of a heavy load by applying  
little effort  
See the fig below  
•
According to Pascal’s principle, pressure will be transmitted equally through the  
fluid(oil) (P1 = P2)  
푭
푭
풇
From: P =  
→
P1 = ,  
P2  
=
푨
풂
푨
푭
풇
푭
풇
=
∴
=
ퟐ
ퟐ
푹
풓
Also, From: The principle of moment  
Anticlockwise moment = clockwise moment  
F x H = f x h  
Since: f = P1 x a  
F = P2 x A  
But  
:
P1 = P2 = P ..................................... According to Pascal principle  
P x A x H = P x a x h......................Divide by P  
Therefore  
:
AH = ah  
Example  
1. In a hydraulic press the area of the piston to which the effort is applied is 5 cm2.  
If the press can raise a weight of 2 KN when an effort of 400N is applied, what  
is the area of the piston under the load?  
Solution:  
Given: Small Piston Force, f =400 N  
Large Piston Force, F = 2 KN = 2000 N  
Small piston area, a = 5 cm2  
Large piston area, A =?  
푭
풇
From  
:
=
풂
푨
ퟐퟎퟎퟎ 풙ퟓ  
ퟒퟎퟎ  
A = 푭풂  
=
= ퟐퟓ  
풇
∴
The area of the piston A = 25 cm2  
Uses of Hydraulic Press in Daily Life  
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Used in lifting heavy loads to the required height  
In ginneries to compress a lump of cotton into small bales  
In industries to form car bodies into the required shapes  
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•
•
•
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Extraction of oil from the oil seed  
Cranes used during construction of any project  
Office chairs use hydraulic systems to lift or lower or lean back the seats  
Brakes of cars use hydraulic systems  
Hydraulic jack for lifting car up for any repair  
Hydraulic brake system  
•
•
When force is applied on the brake pedal, it exerts pressure on the master cylinder  
Then this pressure is transmitted by the brake fluid to the slave cylinders which  
cause the pistons of the slave cylinders to open the brake shoe and hence the  
brake lining presses the drum.  
•
The rotation of the wheel is then resisted and when the force on the brake pedal  
is withdrawn the return spring pulls back the brake shoe which then pushes the  
slave cylinders piston back  
NB  
:
Advantage of this system is that: The pressure exerted in master cylinder  
is transmitted equally to all other parts in the liquid.  
Manometer  
•
Is a device used for measuring fluid (gas) pressure  
•
It is a  
u
shaped glass tube, open at both ends and holding liquid (water/mercury)  
Mechanism of Manometer  
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One limb is connected to the fluid supply and the other limb is opened to the  
atmosphere. The pressure exerted on a fluid causes the level of water or  
mercury on manometer to rise at a certain height as shown in the figure above.  
•
The difference in level (h) of the liquid in the two limbs records the pressure  
and the height h is called “the liquid head”  
Liquids Densities  
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Hare’s apparatus is used to compare the densities of two liquids  
When the air at the top as shown in the fig. below is sucked out, the atmospheric  
pressure pushes the liquid up the tubes (This is because the atmospheric pressure  
acting on the surface is now greater than the pressure inside the straw)  
•
On closing the openings when the liquids have reached a convenient height for  
measurement, the liquids produce the same pressure at X and Y  
That is: P1 = P2  
→ 풉ퟏ품 = 흆ퟐ풉ퟐ품  
→ 흆ퟏ풉ퟏ = 흆ퟐ풉ퟐ