1.

8 Pressure
Objectives

Force
1 Define pressure as force per unit area; recall and use the equation Pressure=
Area
2 Describe how pressure varies with force and area in the context of everyday examples

3 Describe, qualitatively, how the pressure beneath the surface of a liquid changes with depth and
density of the liquid

Supplement

4 Recall and use the equation for the change in pressure beneath the surface of a liquid

Δp = ρgΔh

Pressure is the force acting per unit area on a given surface.

Force( N)
Pressure= 2
Area(m )

The SI unit of pressure is the pascal (Pa). 1 Pa=1 N m−2

The factors which affect pressure are the force and the area.

The higher the force the greater the pressure.

 If a force is spread over a large area it will result in a small pressure

 If it is spread over a small area it will result in a large pressure.

So the smaller the area the greater the pressure.

For example a concrete block has a mass of 2600kg. If the block measures 0.5m by 1.0m by 2m.

a) What is the maximum pressure it can exert on the ground?

2m

0.5m 1m

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 Force
Pressure=
Area
Force=weight=mass ( m ) × acceleration due gravity ( g ) =mg
Force=2600 ×10=26000 N
Maximum pressure is associated with the smallest area
2
A=0.5 m×1.0 m=0.5 m
26000 N −2
Maximum Pressure p= 2
=52000 Pa( N m )
0.5 m

b) What is the minimum pressure

Minimum pressure is associated with the largest area.
A=1.0 m×2.0 m=2 m2
26000 N −2
Minimum pressure p= 2
=13000 Pa( N m )
2m
Formula relating pressure with force and area

Force=Pressure × Area
Force
Pressure=
Area
Force
Area=
Pressure
Remark: The equation shows that pressure is directly proportional to force, but inversely proportional to
area.

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The following simple experiment can be performed to illustrate the concept of pressure:

1. Suppose a thumb is pressed against the flat and pointed ends of a pin, in turn, using the
same force as illustrated below.

It is more hurting (painful) with the pointed end than with the flat end. This can be
explained as follows:

The pointed end of the pin has a smaller surface area than the flat end so the force is
exerted on the smaller area creates greater pressure on the finger, hence the greater
pain.
2. A lady wearing stiletto heels (high heels) would sink further into soft ground than when she
wears a pair sneakers (flat soles). The pressure on stiletto heel is greater than that on the flat
sole since the area of the stiletto heel is smaller.

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3. A bicycle will sink in soft ground yet a tractor will not. (Can you explain?)

Pressure in liquids
The pressure in liquid is due to its weight.

o When an object is immersed in a liquid, the weight of the liquid exerts a

pressure on the object thus squeezing the object.

Liquid pressure is the pressure exerted by the liquid on the object immersed in the liquid.
o This pressure is exerted evenly across the whole surface of the liquid, and in all
directions.

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o Therefore pressure, at a point in a liquid, acts equally in all directions

Pressure at a certain depth

Let’s find out how to determine the pressure at a certain depth of liquid. Consider column of liquid of
height h base area A and density ρ as shown in the figure below.

The volume of the liquid is given by V=Ah.

The mass of the liquid is given by m=density ρ ×Volume V =ρV

The weight of the liquid column is given by

W=mg

= ρVg, but V=Ah

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 W= ρAhg

The pressure at the base of the liquid column is:

weight W
P=
Area A
ρAhg
P¿
A
P=hρg
From this equation it’s deduced that pressure depends on depth of the liquid and density of the liquid.

An experiment to demonstrate that pressure increases with depth

 The holes are blocked and the tin is filled with water.
 On opening the holes at once, the hole at the bottom throws water furthest from the tin
showing that pressure is greatest at the bottom. Therefore pressure increases with the depth of
the liquid.

Worked example 1:

Find the pressure acting on a diver when he is (i) at the surface and (ii) 10m in the water.

Density of water,
−3 −2 5
ρ=1000 kg m , accelerationdue ¿ gravity g=10 m s , atmospheric pressure p0 =1.01× 10 Pa

(i) at the surface its only atmospheric pressure p0 that acts on him. Usually
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p0=1.01 ×10 Pa

(ii) At 10m in the water, i.e. h=10m , then the pressure acting is both atmospheric pressure
and the pressure due to water at a depth of 10m.

P= p 0+ hρg
5
P=1.01 ×10 +10 ×1000 × 10

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 5 5
P=1.01 ×10 +1.0 ×10
P=2.01 ×10 5 Pa
Worked Example 2

0.05m

0.07m

A rectangular block of cross-section area A of 25 cm 2 is submerged in water of density 1000kg m−3 as

shown in the figure above.

a) Find:

i) The pressure P1 due to the water only acting on the top of the surface.

The pressure due to water on top of the block surface P1= h1 ρg

=0.05 ×1000 ×10=500 Pa

ii) The pressure P2 due to the water only acting on the bottom surface.

The pressure due to the water only acting on the bottom surface P2=h 2 ρg

= 0.07×1000 ×10=700 Pa

(Take acceleration due to gravity, g=10 m s−2 the actual gis 9.81m s−2).

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b) Calculate

(i) the force exerted by water on the top surface.

2 25
Given that area A=25 cm = m2 = 2.5 ×10−3 m2
10000
−3
Force F 1= p1 A=500 ×2.5 × 10 =1.25 N

(ii) the force exerted by water on the bottom surface.

−3
Force F 2= p2 A=700 × 2.5× 10 =1.75 N

C) Find the up thrust or the net upward force acting on the object.

Upthrust=1.75−1.25=0.50 N
Pressure increases with density

At the same depth mercury exerts more pressure than water. For a depth of 1.5m, find

i) the pressure due the column of water of density 1000kg m−3

p=h ρwater g=1.5 m× 1000× 10=15000 Pa

ii) the pressure due the column of mercury of density 13600kg m−3

p=h ρHg g =1.5 m× 13600× 10=204,000 Pa

From the above calculation pressure increases with increase in density of the liquid.

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 Transmission of pressure in liquids (hydraulic system)

o The transmission of pressure in liquids depends on the key principle called Pascal’s principle. It
states that the pressure applied at one point in a liquid is transmitted equally in all directions.

Consider an incompressible liquid enclosed in a container as shown in figure above .A small force, F 1
applied on the small piston causes a large force, F 2 to lift the object placed on the large piston.

F1
Since the force F1 is acting down on piston1 then the pressure at point at small piston is P1= where
A1
A1 isthe area of small piston .

Because pressure is transmitted equally throughout the liquid pressure P 1 at small piston is equal to
F2
pressure P2 at big piston with area A2 thus P2= . Hence P1= P2
A2
F1 F 2 F1
There fore = this implies that F 2= × A2
A1 A2 A1

Since A2 is larger than A1 it means that F2 is larger than F1

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When a small force, F1 applied on the small piston causes a large force, F 2 to lift the object placed on the
large piston.

In a simple hydraulic system a small piston has a cross-section area of 0.000050 m 2, and a large piston
has a cross-section area of 0.00025 m2. If a force of 35 N is applied to the small piston,

(a) What is the pressure exerted by the small piston onto the liquid?

F1 35
Pressure p1 = = =700,000 Pa
A 1 0.000050
(b) Find the pressure exerted by the large piston.

The pressure exerted on the large piston is P 2 = P1= 700,000 Pa since pressure is transmitted
equally throughout the liquid.

(c) What is the force exerted by the large piston?

Force exerted on large piston F 2=P2 × A 2=700000 ×0.00025=175 N

Aga Khan High School Kampala Uganda

Year 9 Exercise/ HW first term 2022

1 a) i) Define pressure and state its SI unit.

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 ii) Pressure= _____________. Its unit’s are_____________per square ___________
(or____________).

b) In liquids pressure acts in_____________directions, and pressure_________as depth increases.

2 a) A box weighs 100N and its base has an area of 10 m 2 . What pressure does it exert on the
ground?

c) A rectangular glass block of dimensions 30.0cm by 5.0cm by 10.0cm weighs 37.5N. Calculate the
least and greatest pressure?

3 What is the height of a column of turpentine that would exert the same pressure as 5.0cm of
mercury? (Take the density of turpentine to be
−3 −3
840 kg m , density of mercury=13600 kg m ¿
4 Explain the following:

a) Stiletto heels mark the floor.

b) Heavy Lorries have eight rear wheels?

c) You can fill a bucket from a down stairs tap quicker than the upstairs tap?

d)

The above figure shows the design of a dam. Explain why the thickness of the dam increases
down wards?

5. If the density of sea water is1150 kg m−3 . Calculate:

a) The pressure below 40m due to sea water alone.

b) The pressure at the same depth when the atmospheric pressure of 100kPa on the
surface of the sea water is included.

c) The depth at which the pressure due water alone is 92kPa.

d) The depth at which the total pressure is double the surface atmospheric pressure.

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