Pressure
Pressure is defined as the force per unit area. It is a scalar quantity. Its SI unit is N/m2 or Pascal (Pa). If the force of different magnitude is applied on the same area, the pressure varies. Pressure is more when more force acts on the body. Likewise, if same force acts on two different areas, the pressure varies. Pressure goes on increasing when force is increased and vice-versa. When force is applied to the small area the pressure and increases when force is applied to a large area.
Let us consider a force 'F' is applied to a certain surface area 'A' , then pressure is directly proportional to the force and inversely proportional to the area of the surface in which the force acts normally. Mathematically,
Pressure is defined as the force per unit area. It is a scalar quantity. Its SI unit is N/m2 or Pascal (Pa). If the force of different magnitude is applied on the same area, the pressure varies. Pressure is more when more force acts on the body. Likewise, if same force acts on two different areas, the pressure varies. Pressure goes on increasing when force is increased and vice-versa. When force is applied to the small area the pressure and increases when force is applied to a large area.
Let us consider a force 'F' is applied to a certain surface area 'A' , then pressure is directly proportional to the force and inversely proportional to the area of the surface in which the force acts normally. Mathematically,
$P\alpha F$..................(a)
$P\alpha \frac{1}{A}$....................(b)
Combining equation (a) and (b), we get,
$P\alpha \frac{F}{A}$...............(c)
$P=k\frac{F}{A}$.................(d)
[Where, k is proportionality constant and its value is 1 because when 1 N force is applied in 1 m2, the pressure is 1N/m2]
Therefore,
$P=\frac{F}{A}$....................(e)
Pressure in liquid:
Let us consider a container with base area 'A' filled with liquid of density 'd'. Let the depth of liquid inside the container be 'h'. 'F' be the force exerted by the liquid on the base of the container which is equal to the weight of the liquid inside the column.
By the definition of pressure,
$P=\frac{F}{A}$..............(a)
$P=\frac{mg}{A}$..............(b) [As, F=mg]
$P=\frac{dvg}{A}$...............(c) [As, d=m/v and m = dv]
$P=\frac{d(A\times h)g}{A}$.........(d) [As, V=A×l]
$P=dgh$.........(e)
Equation (e) shows that pressure exerted by the liquid is directly proportional to the height of the liquid column, density of the liquid and acceleration due to gravity.
Laws of liquid pressure:
Equation (e) shows that pressure exerted by liquid in a column depends on:
- density of liquid 'd'
- height of liquid column 'h'
- acceleration due to gravity 'g'
Equation (e) shows that pressure exerted by the liquid is directly proportional to the height of the liquid column, density of the liquid and acceleration due to gravity.
Laws of liquid pressure:
- Liquid pressure is directly proportional to its density
- liquid pressure at a point is same in all directions within the liquid.
- Liquid pressure is independent of the shape of the vessel.
- Liquid pressure is directly proportional to the depth.
Pascal's law:
Pascal's law states that 'Pressure is equally exerted perpendicularly on all directions as pressure is applied at a point on liquid contained in a enclosed container.'
Pascal's law is based on the principle that liquids are in-compressible and liquid transmits pressure equally in all directions. With the help of Pascal's law we can produce large force by applying small forces. In other words Pascal's law amplifies the applied force and helps in doing work. Hydraulic machines were developed on the basis of Pascal's law. Examples of hydraulic machines are hydraulic machine, hydraulic jack and hydraulic lift etc.
Let us consider a F1, F2, F3, and F4 be the forces applied at pistons p1, p2, p3 and p4, at the same time P1,P2, P3 and P4 are the pressures in the respective pistons. According to Pascal's law, pressure at piston p1 is equally distributed in all other pistons. Mathematically,
Upthrust:
Thrust is the force acting perpendicular to the surface. Its unit is Newton. Only liquid and gas exerts up-thrust.
We feel easier to lift a bucketful of water until it is under the surface of the water but becomes heavy when it is out of the surface of water. Similarly, we have experienced during swimming it is easier to lift a friend inside the water but becomes heavy out of the water. These examples show that when a body is wholly or partially immersed in water, water pushes the body up with certain force. This force is called upthrust.
Upthrust is defined as the upward force exerted by liquid on an object immersed in in the liquid. It is also called buoyant force or bouncy.
How to measure the upthrust:
Let a stone be tied on a string and suspend it with a spring balance, the weight of the stone in the air be w1 N. The weight of the stone will be w2 N when completely immersed inside the water contained in beaker. There is difference between w1 and w2 due the up-thrust exerted by water in upward direction. This difference in weight gives the up-thrust. Mathematically,
Weight of stone air =w1
Weight of stone inside the water = w2
Then,
Up-thrust = Difference in weight in air and water
= (w1 - w2)N
Archimedes' Principle:
Archimedes' principle states that when a body is wholly or partially immersed in a liquid, it experiences a loss in wight due to up-thrust which is equal to the weight of the liquid displaced by it.
This principle can be applied for both liquid and gas.
Properties of Archimedes' Principle:
Let us tie a stone by a thread with a spring balance. Measure the weight of the stone in the air, let the weight be w1. Insert the stone completely inside the overflow can (Eureka can) filled with water upto the spout. Due to the up-thrust there is loss in weight of the stone, the weight of the stone be w2. At same time place a empty beaker in pan balance just below the spout of overflow can. Consider the weight of the of the beaker be w3. When the stone is inserted into the water it displaces some water which flows out from the spout into the beaker. Let the weight of the displaced water and beaker be w4. Then,
Loss in weight of the stone in water = w1 - w2
Weight of water displaced by water = Weight of beaker and water - weight of the beaker
= w4 - w3
The loss in weight of the stone w1 - w2 = Weight of water displaced by the stone w4 - w3
Up-thrust = Weight of liquid displaced
Hence, it found that up-thrust is equal to the weight of water displaced by it.
Density:
Density is defined as the mass per unit volume. Its is scalar quantity. Its SI unit is kg / m3. Mathematically,
Density $D=\frac{M}{V}$
Relative density:
Relative density is defined as the ratio of density of a substance to the density of water at 4°C.
Mathematically,
Relative density \[\text{R}\text{.D}=\frac{\text{Density of substance}}{\text{Density of water at 4 }\!\!{}^\circ\!\!\text{ C}}\]
Relative density has no unit because it the ratio between two densities.
Meaning of Relative Density:
When a body is immersed in a liquid experiences two types of forces. They are:
i.The force of gravity directed vertically downward.
ii.The up thrust directed vertically upward.
Due to the action of these two forces, a body moves in the direction of greater force. There will be three possible cases if an object is immersed in liquid:
Principle of flotation states that a body floats in liquid if it can displace the liquid equal to its won weight i.e
Weight of floating body = Weight of the liquid displaced = Up-thrust.
When a body is immersed in a liquid, it experiences two type of forces:
a. Up-thrust: Acting in upward direction.
b. Gravity: Acting in downward direction.
Due to the action to these two forces, a body will move in the direction of greater force. According to the resultant of the forces, there are three cases:
i. If the weight of an object is less than up-thrust the body will floats on the surface
of the liquid in which it is immersed.
ii. If the weight of an object is equal to the up-thrust, the body can be
in equilibrium condition at any point in liquid.
iii. If the weight of an object is greater than up-thrust, the body
sinks to the bottom
Hydrometer:
Pascal's law is based on the principle that liquids are in-compressible and liquid transmits pressure equally in all directions. With the help of Pascal's law we can produce large force by applying small forces. In other words Pascal's law amplifies the applied force and helps in doing work. Hydraulic machines were developed on the basis of Pascal's law. Examples of hydraulic machines are hydraulic machine, hydraulic jack and hydraulic lift etc.
Let us consider a F1, F2, F3, and F4 be the forces applied at pistons p1, p2, p3 and p4, at the same time P1,P2, P3 and P4 are the pressures in the respective pistons. According to Pascal's law, pressure at piston p1 is equally distributed in all other pistons. Mathematically,
p1 = p2 = p3 = p4
Similarly,
$\frac{{{F}_{1}}}{{{A}_{1}}}=\frac{{{F}_{2}}}{{{A}_{2}}}=\frac{{{F}_{3}}}{{{A}_{3}}}=\frac{{{F}_{4}}}{{{A}_{4}}}$
Hydraulic press:
Hydraulic press is a machine that works under the principle
of Pascal’s law. It is usually ‘U’ shaped tube filled with liquid and fitted
with air tight pistons. It magnifies the applied force. In other words it
converts small applied force into large force. When a small force is applied in
a piston of small cross-section area, pressure is equally transmitted in all directions;
a large force appears over the piston with larger cross-section area.
 |
| Hydraulic press |
Hydraulic press as a force multiplier:
Let us consider a hydraulic press filled with water and
fitted with air pistons P1 and P2 with cross-section area A1 and A2
respectively. Here, area A1 is smaller than area A2.
When force F1 is applied on a small piston in downward
direction , it produces force F2 on piston P2 which moves upward direction due
to equal transmission of pressure in all direction according to Pascal’s law.
According to Pascal’s law,
Pressure on small cylinder with piston P1 = Pressure on big
cylinder with piston P2.
So, P1 = P2
Where P1
and P2 are pressure on small and big piston.
Or, $\frac{{{F}_{1}}}{{{A}_{1}}}=\frac{{{F}_{2}}}{{{A}_{2}}}$
Or, ${{F}_{2}}=\frac{{{F}_{1}}\times {{A}_{2}}}{{{A}_{1}}}$
Since, A2 >A1 then F2
>F1.
Therefore, hydraulic press or hydraulic lift acts as force
multiplier.
Hydraulic brake
A hydraulic brake is a mechanical component used mostly in
vehicles which works on Pascals’s law. In consists of a master cylinder filled
with a fluid which is attached to the wheel cylinder with the help of a pipe. The
wheel cylinder also consists of the same fluid inside it that is connected to
the brake shoe. When foot pedal is pressed the piston in master cylinder is
pushed inward along with the special fluid. Then the pressure in the master
cylinder is transmitted to the wheel cylinder. The pistons in the wheel
cylinder apply force to the brake shoe that widens the brake shoe. Widening of break
shoe come in contact with the wheel and produces friction. As a result vehicle
stops.
 |
| Hydraulic brake |
Upthrust:
Thrust is the force acting perpendicular to the surface. Its unit is Newton. Only liquid and gas exerts up-thrust.
We feel easier to lift a bucketful of water until it is under the surface of the water but becomes heavy when it is out of the surface of water. Similarly, we have experienced during swimming it is easier to lift a friend inside the water but becomes heavy out of the water. These examples show that when a body is wholly or partially immersed in water, water pushes the body up with certain force. This force is called upthrust.
Upthrust is defined as the upward force exerted by liquid on an object immersed in in the liquid. It is also called buoyant force or bouncy.
How to measure the upthrust:
Weight of stone air =w1
Weight of stone inside the water = w2
Then,
Up-thrust = Difference in weight in air and water
= (w1 - w2)N
Archimedes' Principle:
Archimedes' principle states that when a body is wholly or partially immersed in a liquid, it experiences a loss in wight due to up-thrust which is equal to the weight of the liquid displaced by it.
This principle can be applied for both liquid and gas.
Properties of Archimedes' Principle:
- This law can be applied for both liquid and gas.
- Archimedes' principle holds true when an object is wholly or partially immersed in liquid.
- Up-thrust is independent of weight of an object.
Let us tie a stone by a thread with a spring balance. Measure the weight of the stone in the air, let the weight be w1. Insert the stone completely inside the overflow can (Eureka can) filled with water upto the spout. Due to the up-thrust there is loss in weight of the stone, the weight of the stone be w2. At same time place a empty beaker in pan balance just below the spout of overflow can. Consider the weight of the of the beaker be w3. When the stone is inserted into the water it displaces some water which flows out from the spout into the beaker. Let the weight of the displaced water and beaker be w4. Then,
Weight of water displaced by water = Weight of beaker and water - weight of the beaker
= w4 - w3
The loss in weight of the stone w1 - w2 = Weight of water displaced by the stone w4 - w3
Up-thrust = Weight of liquid displaced
Hence, it found that up-thrust is equal to the weight of water displaced by it.
Density:
Density is defined as the mass per unit volume. Its is scalar quantity. Its SI unit is kg / m3. Mathematically,
Density $D=\frac{M}{V}$
Relative density:
Relative density is defined as the ratio of density of a substance to the density of water at 4°C.
Mathematically,
Relative density \[\text{R}\text{.D}=\frac{\text{Density of substance}}{\text{Density of water at 4 }\!\!{}^\circ\!\!\text{ C}}\]
Relative density has no unit because it the ratio between two densities.
Meaning of Relative Density:
- If a substance has relative density less then 1, it will float in the liquid taken.
- If a substance has relative density equal to 1, it will float with completely immersed in the liquid.
- If a substance has relative density greater then 1, it will sink in the liquid.
When a body is immersed in a liquid experiences two types of forces. They are:
i.The force of gravity directed vertically downward.
ii.The up thrust directed vertically upward.
Due to the action of these two forces, a body moves in the direction of greater force. There will be three possible cases if an object is immersed in liquid:
- If the weight of an object is greater than up-thrust, the body will sink to the bottom.
- If the weight of an object is equal to the up-thrust, the body will remain anywhere inside the liquid.
- If the weight of an object is less than up-thrust, the body will rise to the surface of the liquid and floats.
Principle of flotation states that a body floats in liquid if it can displace the liquid equal to its won weight i.e
Weight of floating body = Weight of the liquid displaced = Up-thrust.
a. Up-thrust: Acting in upward direction.
b. Gravity: Acting in downward direction.
Due to the action to these two forces, a body will move in the direction of greater force. According to the resultant of the forces, there are three cases:
i. If the weight of an object is less than up-thrust the body will floats on the surface
of the liquid in which it is immersed.
ii. If the weight of an object is equal to the up-thrust, the body can be
in equilibrium condition at any point in liquid.
iii. If the weight of an object is greater than up-thrust, the body
sinks to the bottom
Hydrometer:
a. Constant weight or variable immersion hydrometer: The hydrometer which measures the density by observing the scale of he floating neck is called constant weight hydrometer. It consists of a bulb containing mercury of lead shots to keep it upright while floating. The stem is unevenly calibrated in kg/m3 or g/cm3 units of density. The numbers denoting density in the stem are bigger at the bottom, decreasing upward because a hydrometer sinks less in liquids having more density and sinks more in liquids of less density.
b. Constant immersion or variable weight hydrometer: The hydrometer which measure the density by adding the weights to immerse to the constant level is called constant immersion hydrometer. It measures the relative density. It is also called the Nicholson hydrometer. It is made to sink to the same level in the water as well as in the liquid by placing weights on its pan at the top so that it displaces the same volume of liquids.
Atmosphereic pressure:
The pressure exerted by column of air on unit surface area is called atmospheric pressure. It is measured by barometer. Atmospheric pressure can not be changed by us. The atmospheric pressure at sea level is considered as normal or slandered pressure. Its value at sea level is about 101300 N per meter or 760 mm of Hg.
Air pressure:
It is the pressure exerted by the air enclosed in a container. It is measured by manometer. Air pressure inside the enclosed container can be changed.
Barometer:
A barometer is an instrument that is used to measure the atmospheric pressure of certain place. There are two types of barometers, a. Mercury barometer (or Fortin's barometer ) and b. Aneroid barometer.
A simple barometer consists of a long glass tube filled with mercury and turned upside down in a container of mercury. It works by balancing the mercury level inside the glass tube against the air pressure outside. The level of mercury in the tube gives the measurement of the air pressure.
Syringe:
A syringe is a medical instrument which is used to draw blood out from a body and to inject medicine through blood. It consists of three parts; piston, barrel and needle. It is made up of glass or plastic. It has a scale on the barrel that indicates the volume of liquid inside it.
When piston is pulled outward keeping needle inside the medicine or liquid, a partial vacuum is created inside the barrel. As a result, there is low pressure inside it so liquid or medicine flows into the the syringe. Likewise, When the piston is pushed inside, there is high pressure in the barrel and pushes the liquid or medicine out of the syringe.
Air Pump:
Air pump is an instrument used to pump air inside a tube.
Water Pump:
A water pump is an instrument that is used to pull under-ground water.
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