The Concept of Pressure
Explain the
concept of pressure
Pressure is defined as the force per unit
area. Mathematically, the force discussed here is the force which acts normally
or perpendicularly to a unit surface area.
That is to say, pressure
depends on the force applied and the surface 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/m2).
This unit is usually referred to as the Pascal (Pa).
However, because measurement of
pressure may result in very large numbers or small numbers, there are other
units used in the measurement of pressure. These are atmosphere(atm), Millimetres
of mercury (mmHg), torr and bar.
Whereby; -
Note: For a given amount of force, the
smaller the area of application, the greater the pressure exerted.
When a man lifts a bucket of water by its
handle, which is made of a thin metal, he would experience some discomfort, but
if the bucket were made with a thicker handle, the discomfort would 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 the Surface of Contact
Explain the dependence of pressure on the surface of contact
The pressure in a solid depends on the surface area of
contact. A force (F) applied by a small area exerts a higher pressure as
compared to when it is applied by a large surface.
This is well explained by the formula P =F/A, meaning that
when the value of the area is small, then the value of pressure will be large, and when the area is large for the same amount of force, the value of pressure
will be small. That is to say, an increase in area causes a decrease in pressure
for the same amount of force.
That is why:
The feet of an elephant cannot sink into soft soil, even is very heavy due to the large surface area of elephant feet.
Sharp edges of a knife cut easily than a blunt
knife because a sharp knife has a smaller surface area.
A tractor and other heavy trucks working on
soft ground cannot sink due to the large surface area of the tyres (wide tyres).
We feel great pain if we carry a bucket of
water with a thin handle than when we use a wide (enhanced) handle.
Example 5
A block of wood that weighs 30N and measures
5m by 10m by 4m. If it were placed on a table with the largest possible area
(5mx10m) in contact with the table, exert less pressure than it would when placed
with its smallest possible area (5mx4m) in contact with the table.
Solution
Data:
Force = 30N
Largest base area = ?
AL = 10mx5m
= 50m2
P = F/A = 30N = 0.6N/30m2
Pressure = 0.6N/m2
Force (F) = 30N.
Small base are = ?
As = 5mx4m
As = 20m2
P= F/A = 30N/20M2 =
1.5 N/M2
Pressure = 1.5 N/M2
Example 6
A tip of needle has a cross- sectional area
of 1x106m2. 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) = 1x106m2
Force (F) = 20N
Pressure =?
P = F/A
P = 20 = 2.0x107 N/M2
The pressure extended by
the needle lip is 2.0x107N/m2
Example 7
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:
Dimension = 1.2m,1.5m,1.0m.
Density = 7000kg/m3
Maximum pressure (Pmx) = ?
Minimum pressure (Pmn) = ?
Volume = 1.2x1.5x1=18m3
Density = mass/ Volume
7000kg/m3 =
mass/18
Mass = 7000x18 = 126000Kg
1kg = 10N
126000Kg = ?
F = 1260000 = 1.26 x 106
Force of metal = 1.26 x 106
A1 = 1.2 x
1.5= 18m2
A2= 1.2m2=
1.2mx1m=1.2m2
A3= 1.5 x 1m=
1.5m2
Amx = 18m2
Amin = 102m2
Pmn = F/Amx =1.26 x 106N/18M2 =
1.26X106/1.8 X101
Maximum pressure = 1.05x106N/m2/maximum
pressure= 0.7x105N/m2
The Applications of Pressure due to Solids
Identify the
applications of pressure due to solids
It is used to make different 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-defense. A fish uses its sharp fins to protect itself.
When one walks on shoes with sharp pointed heels they
exert greater pressure 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 safety 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
The pressure at any point in a liquid at rest
depends on the following factors;
1. Depth
of the liquid
2.
Density of liquid
This
can be shown from the general formula for pressure as follows;
Pressure in liquids has the
following characteristics: -
1. Pressure in a liquid increases with depth
2. Pressure in a liquid acts equally in all
directions
3. Pressure in a liquid increases with the increase in the density of the liquid.
Number 3 explains the reason why Mercury exerts more
pressure than an equal volume of water. It is simply because mercury is denser
than water.
The Variation of Pressure with Depth in
Liquids
Examine the variation of pressure with
depth in liquids
The pressure in liquids increases with the
increase in depth. Consider the cylindrical vessel containing water and with
holes A, B, and C punched on one of its sides.
Pressure of the water at hole A is small because the
depth of water or length of water column from point A to the top is small. This
causes water to flow at a low speed and at a small distance from the bottom of
the vessel.
Pressure of the water at hole B is larger than at A
because the depth of water or length of water column from point B to the top is
somehow larger. This causes water to flow at a greater speed and at a larger
distance from the bottom of the vessel.
Pressure of the water at hole C is large because the
depth of water or length of water column from point C to the top is very large.
This causes water to flow at a high speed and at a small distance from the
bottom of the vessel.
Problems Involving Pressure in Liquids
Solve problems involving Pressure in
Liquids
Example 2
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/s2 and
s=1000kg/m3
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/m3
g = 10m/s
h= 8cm= 0.08
formular
p= sgh
p=1000kg/m3x10m/s2x0.1m=1000N/m2
At the h= 0.08m p=
1000x10x0.08= 800N/m2
Change in pressure =
1000N/m =200N/m2
So that different in
pressure between the bottom the top is 200N/m2
Pressure = Force/Area = P=
F/A
Area =L2=
(10.02)2= 0.0004m2
Distance in water 200N/m2x0.0004m2
This is the upthrust acting
on the cube
Water displaced by the cube
in weight= volume of the cube
Volume = l3 (2cm) 3 =
8cm3
For water, 1cm3=
1g 50.8cm3 = 8g
Weight of displaced water
Mass
of displaced water/100=8g = 0.08N
Example 3
Calculate the pressure at the bottom of tank of water 15m
deep due to the water above it is (s=1000kg/m3).
Solution:
Data:
Height =15m
S=1000kg/m3
g= 10m/s2
Formula
Pressure in liquid sgh
= 1000x10x15=150000N/M2
The Principle of a Hydraulic Pressure
Explain the principle of a hydraulic pressure
The hydraulic press is
the simple device that works under the Pascal’s principle of transmission of
pressure. It contains a small piston on one side and a large piston on the
other side.
A force is applied to a
small piston and pressure is transmitted to the large piston through the fluid
inside it.
According to Pascal’s
principle the pressure is transmitted equally to the large piston which is then
converted to a large amount of force.
The Pascal’s principle states that; - “Any
external pressure applied to the surface of an enclosed liquid will be
transmitted equally throughout liquid.”
From Pascal’s Principle
Example 7
The
pistons of a hydraulic press have their areas given as 3.0x10-4m2 and
2x102m2 respectively. If the smaller piston is
pushed down with a force of 12N, what is the force required to push the larger
piston?
Soln:
Data:
F1 =
120N, A2= 2X102m2
A2 = 3X104m2
Application of Hydraulic Press
Measure the pressure of a liquid
A hydraulic press is used in industries to press bulk items.
Hydraulic brake system
When pressure is applied to the brake pedal,
it pushes the piston in the master cylinder forward, creating pressure in the
brake fluid. This pressure is transferred to the slave cylinders, where it is
multiplied and pushes the brake shoes against the brake drum that is attached
to the wheel of the vehicle.
It is used in industries in
the forming of metals.
Since the hydraulic press
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 1.01x105N/m2.
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
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
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
A lift pump is used to raise water from underground 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:
1. They
can be fitted with hypodermic needles and used to administer injections.
2. They
are used to measure liquids and gases in a laboratory.
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.
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.
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.
Post a Comment