What is Pressure?
“The force acting normally per unit area on the surface of a body is called pressure”.
Press a pencil from its ends between the palms. The palm pressing the tip feels much more pain than the palm pressing its blunt end. We can push a drawing pin into a wooden board by pressing it by our thumb. It is because the force we apply the drawing pin is confined just at a very small area under its sharp tip. A drawing pin with a blunt tip would be very difficult to push into the board due to the large area of its tip. In these examples, we find that the effectiveness of a small force is increased if the effective area of the force is reduced. The area of the tip of pencil or that of the nail is very small and hence increases the effectiveness of the force. The quantity that depends upon the force and increases with decrease in the area on which force is acting is called pressure. Thus pressure is defined as:
Thus Pressure P=F/A
Pressure is a scalar quantity. In SI units, the unit of pressure is Nm-2 also called pascal (Pa). Thus:
1N m-2 = 1 Pa
The Earth is surrounded by a cover of air called atmosphere. It extends to a few hundred kilometers above sea level. Just as certain sea creatures live at the bottom of ocean, we live at the bottom of a huge ocean of air. Air is a mixture of gases. The density of air in the atmosphere is not uniform. It decreases continuously as we go up.
Atmospheric pressure acts in all directions. Soap bubbles expand till the pressure of air in them is equal to the atmospheric pressure. Why the soap bubbles so formed have spherical shapes? Can you conclude that the atmospheric pressure acts on a bubble equally in all directions?
A balloon expands as we fill air into it. In what direction does the balloon expands? The fact that atmosphere exerts pressure can be explained by the simple experiment.
Take an empty tin can with a lid. Open its cap and put some water in it. Place it over flame. Wait till water begins to boil and the steam expels the air out of the can. Now place the can under tap water. The can will squeeze due to atmospheric pressure. Why?
When the can is cooled by tap water, the steam in it condenses. As the steam changes into water, it leaves an empty space behind it. This lowers the pressure inside the can as compared to the atmospheric pressure outside the can . this will cause the direction to collapse from all directions. This experiment shows that atmosphere exerts pressure in all directions.
The fact can also be demonstrated by collapsing of an empty plastic bottle when air is sucked out of it.
Measuring Atmosphere Pressure:
At sea level, the atmospheric pressure is about 101,300 Pa or 101,300 Nm-2. The instruments that measure atmospheric pressure are called barometers. One of the simple barometers is a mercury barometer. It consists of a glass tube 1 m long closed at one end. After filling it with mercury, it is inverted in a mercury trough. Mercury in the tube descends and stops at a certain height. The column of mercury held in the tube exerts pressure at its base. At sea level the height of mercury column above the mercury in the trough is found to be about 76 cm. Pressure exerted by 76 cm of mercury column is nearly 101,300 Nm-2 equal to atmospheric pressure. It is common to express atmospheric pressure in terms of the height of mercury column. As the atmospheric pressure at a place does not remains constant,hence, the height of mercury column also varies with atmospheric pressure.
Mercury is 13.6 times denser than water. Atmospheric pressure can hold vertical column of water about 13.6 times the height of mercury column at a place. Thus, the sea level, vertical height of water column would be 0.76 m 13.6=10.34 m. Thus, a glass tube more than 10 m long is required to make a water barometer.
Variation in Atmospheric Pressure:
The atmospheric pressure decreases as we go up. The atmospheric pressure on mountains is lower than at sea level. At a height of about 30 km, the atmospheric pressure becomes only 7 mm of mercury which is approximately 100 Pa. It would become zero at an altitude where there is no air. Thus, we can determine the altitude of a place by knowing the atmospheric pressure at that place.
Atmospheric pressure may also indicate s change in the weather. On a hot day, the above the Earth becomes and expands. This causes a fall of atmospheric pressure in that regions. On the other hand, during cold chilly nights, this above the Earth cools down. This causes an increase in atmospheric pressure.
The changes in atmospheric pressure at a certain place indicate the expected changes in the weather conditions of that place. For example, a gradual and average drop in atmospheric pressure means a low pressure in a neighbouring locality. Minor but rapid fall in atmospheric pressure indicates s windy and showery condition in the nearby regions. A decrease in atmospheric pressure is accompanied by breeze and rain. Whereas a sudden fall in atmospheric pressure often followed by a steam, rain and typhoon to occur in few hours time.
One the other hand, an increasing atmospheric pressure with a decline later on predicts an intense whether conditions. A gradual large increase in the atmospheric pressure indicates a long spell of pleasant weather. A rapid increase in atmospheric pressure means that it will soon be followed by a decrease in the atmospheric pressure indicating poor weather ahead.
Pressure in Liquids:
Liquids exert pressure. The pressure of a liquid acts in all directions. If we take a pressure sensor (a device that measures pressure) inside a liquid of the liquid varies with the depth of sensor.
Consider a surface of area A in a liquid at a depth h by shaded region. The length of the cylinder of liquid over this surface will be h. The force acting on this surface will be the height w of the liquid above this surface. If ρ is the density of the liquid and m is mass of liquid above the surface, then:
Mass of the liquid cylinder m = volume×density
= (A×h)× ρ
Force acting on area A is, F= w = mg
= A h ρ g
As pressure P=F/A
=A h ρ g/A
- Liquid pressure at depth h = P = ρ g h ……(1)
Equation (1) gives the pressure at the depth h in a liquid of a density ρ. It shows that its pressure in a liquid increases with depth.
An external force applied on the surface of a liquid increases the liquid pressure at the surface of the liquid. This increase in liquid pressure in transmitted equally in all directions and to the walls of the container in which it is filled. This result is called Pascal’s law which is stated:
“ Pressure applied at any point of a liquid enclosed in a container, is transmitted without loss to all other parts of the liquid”.
It can be demonstrated with the help of the glass vessel having holes all over its surface. Fill it with water. Push the piston. The water rushes out of the holes in the vessel with the same pressure. The force applied on the piston exerts pressure on water. This pressure is transmitted equally throughout the liquid in all directions.
In general, this law holds good for fluids both for liquids as well as gases.
Application of Pascal’s Law:
Pascal’s law finds numerous applications in our daily life such as automobiles, hydraulic brake system, hydraulic jack, hydraulic press and other hydraulic machines.
Hydraulic jack principle Press:
Hydraulic press is a machine which works on Pascal’s law. It consists of two cylinders of different cross-sectional areas. They are fitted with pistons of cross-sectional areas a and A. The object to be compressed is placed over the piston of large cross-sectional area A. The force F1 is applied on the piston of small cross-sectional area a. The pressure P produced by small piston transmitted equally to large piston and a force F2 acts on A which is much larger than F1.
Press on piston of small area a is given by :
Apply pascal’s law, the pressure on large piston of area A will be the same as on small piston.
- P =F2/A
Comparing the above equations, we get:
F2= A ×F1/a
F2 = F1 ×A/a
Since the ratio is greater than 1, hence the force F2 that acts on the larger piston is greater than the force F1 acting on the smaller piston. Hydraulic systems working in this way are known as force multipliers.
The braking systems of cars, buses, etc.also work on pascal’s law. The hydraulic brakes allow equal pressure to be transmitted throughout the liquid. When brake pedal is pushed, it exerts a force on the master cylinder, which increases the liquid pressure in it. The liquid pressure is transmitted equally through the liquid in the metal pipes to all the pistons of the other cylinders. Due to the increase in liquid pressure, the pistons in the cylinders move outward pressing the brake pads with the brake drums. The force of friction between the brake pads and the brake drums stops the wheels.