Pressure - Hydraulic Machines and Their Applications
Pressure
Pressure is generated by the normal force (thrust) exerted by liquids and gases on the walls of various objects. A force acting perpendicular to the surface of an object is called thrust. Its SI unit is Newton. The thrust acting per unit area of an object is called pressure. The SI unit of pressure is Pascal, i.e. Newton per square meter (N.m-2). Other units of pressure are mm Hg, bar, and atm.
Since liquid and gas are substances that can flow easily, they are called fluids. Like solids, the fluids too exert pressure. Fluid not only exerts pressure on the bottom of the vessel in which it is kept but on the walls of the vessel. When an object is placed in a fluid, the fluid exerts pressure on the surfaces of the object.
Pressure is measured using different instruments such as a barometer, pressure gauge, and manometer. The pressure exerted by ambient air on the earth's surface is called atmospheric pressure. The atmospheric pressure at the mean sea level of eath is 101,325 pascals.
Transmission of Pressure
Molecules in solids are packed very close to each other. They have a definite shape and volume. The molecules in a solid do not move and change their position. When a force is applied to one side of the solid object, the pressure generated is not transmitted throughout the solid object. But, since molecules can move in liquid and gas, pressure is transmitted in the fluid kept in a closed container.
Activity: Transmission of pressure in fluid
Take two syringes. Fill one of them with water and leave the other empty. Close the nozzle of the empty syringe using a finger and push the piston inside. Do the same with the syringe filled with water. Piston of which syringe can be pushed in? When the piston of an air-filled syringe is pushed in, did it show the same effect as in the water-filled syringe?
In this activity, when the piston of the water-filled syringe is pushed in it does not move in. This means the water in the syringe cannot be compressed. But in the syringe filled with air, it is easy to push the piston in. But, when the air in it gets compressed, it becomes difficult to push the piston further just like in the syringe filled with water.
The intermolecular spaces between the molecules of liquids are very small. So, the external pressure cannot move the liquid molecules closer together. Therefore, since the liquid in the vessel cannot be pressed by pressure, its volume does not decrease. Hence, the pressure exerted at any point in the liquid gets transmitted uniformly in all directions. For example, toothpaste comes out of the mouth because the pressure generated by pressing the tube gets transmitted to the paste. But in gases, the space between the molecules is larger than in liquids. The volume of gas can be reduced by applying external pressure to them. Therefore, pressure is transmitted in compressed gas but not effectively as in a liquid.
Pascal's Law
Activity: Pascal's law
Fill a polythene bag with water. Squeeze the bah from the top with a fist and make fine holes around it and observe the water coming out of these holes. Does the water come out of all the holes uniformly? As the level of water decreases in the polythene bag, move the first downward and tighten the grip.
In the above activity, when the fist is tightened, the pressure generated in the water at the upper part of the polythene bag is transmitted through the water to the walls of the bag. As a result, water streams come out from all the holes perpendicular to the surface of the bag. Here, the pressure generated at a point in the water enclosed inside the polythene bag is transmitted normally in all directions.
French mathematician Blaise Pascal profounded a law about this in 1653 BC and, it is known as Pascal's law.
Pascal's law states that when a force is exerted at a point in an enclosed liquid, the pressure generated is transmitted normally throughout the liquid in all directions.
| From, pascal's law
P1=P2=P3 We know P=F/A So, F1/A1=F2/A2=F3/A3 |
Applications of Pascal's Law
Based on Pascal's law, various types of hydraulic machines such as hydraulic brakes, hydraulic lifts, hydraulic presses, etc are manufactured.
Hydraulic Machine
Activity: Making a model of a hydraulic machine
Take two syringes of different thicknesses, a saline pipe, and water. Connect the mouths of both syringes with a saline pipe.
Pull out the piston of a syringe and fill it with water. While filling the water, the barrel of the syringe should be filled a little more than halfway, leaving space for the piston to move outwards. If a weight is placed on the top of a small piston and an object with a heavier weight is placed on the other side of the piston, will the heavier object be lifted?
When the weight on the top of the larger piston increases and becomes equal to the maximum weight that can be lifted by the small piston, both pistons remain in a balanced condition. What is the weight necessary for that? Data can be tabulated in a table similar to the one shown be
A hydraulic machine is a force-multiplying device that is based on Pascal's law. The excavator or backhoe is an example of a hydraulic machine used for digging purposes.
Construction and Working Mechanism of Hydraulic Machine
For the construction of a hydraulic machine, at least two cylinders with different cross-sectional areas are connected. A piston is connected to each cylinder in such a way that the liquid inside does not leak.
The cross-sectional areas of the small piston and the large piston of the hydraulic machine shown in the figure are A1 and A2 respectively. Similarly, F2 is the outward force produced on the large piston when a force F1 is applied on the small piston.
In a hydraulic machine, conditions are created for Pascal's law to apply. That is when force is applied via the small piston of the machine, then the pressure generated on the surface of the piston (P1=F1/A1) is transmitted perpendicularly and equally in all directions by the incompressible liquid in the cylinders. According to Pascal's law, the pressure generated on the surface of the small piston (P1) = the pressure generated on the surface of the large piston (P2).
Or, F1/A1 = F2/A2
F2=F1 (A2/A1) -- (i)
From equation (i), the force acting on the larger piston (F2) is (A2/A1) (the ratio of the area of the larger piston to the smaller piston) times F1. In this equation, the factor is always more than 1 because in (A2/A1), a bigger number is divided by a smaller number. For example, if the cross-sectional area of the large piston is twice (A2/A1=2), the cross-sectional area of the small piston, then the force exerted on the small piston of the machine becomes double when it is transferred to the large piston.
Some Examples of Hydraulic Machine
Hydraulic machines are constructed in various designs, shapes, and sizes depending on their uses. Some of the examples are presented below.
Hydraulic Lift
Hydraulic lift is used to lift heavy objects easily.
Hydraulic Brake
In the hydraulic brake system, the pipe is connected to the master cylinder, and the brake cylinder is filled with a special type of brake oil. Pistons are fitted in both cylinders so that they become air-tight.
Brake cylinders are located on the wheels of vehicles. the piston of the brake cylinder is connected to the brake shoes or brake pads. By applying a small force on the small piston of the master cylinder, the pressure is generated by pushing the fluid inside it is transmitted and a large force is applied to the large piston connected to the brake cylinder. Due to this a vehicle moving at high speed can be stopped at an instant.
Hydraulic Jack
Trucks, buses, cars, etc are lifted at a certain above the ground by the use of hydraulic jacks. A pumping piston with a small cross-sectional area and a lifting piston with a large cross-sectional area are connected. A bottom valve is kept between these two pistons for the one-way flow of the oil, from right to left only.
Similarly, a top valve is placed for the flow of oil from left to right, from the oil reservoir to the pumping piston. In a hydraulic jack, when the releasing valve is tightened and the lever is pushed down, the upper valve closes and the lower valve opens. As a result, the force exerted on the pumping piston of the jack increases and the load on the lifting piston is pushed a little higher. After that, when the lever is pulled up, the bottom valve closes due to high pressure and the top valve opens. As a result, the oil from the reservoir fills the cylinder of the pumping piston. Then, in the next stage of pumping, the load is pushed up again. By repeatedly pushing the lever up and down, the load can be pushed up to the required height.
Hydraulic Press
Various objects can be pressed by applying a small force to the small piston of a hydraulic press. The hydraulic press is used to fit mechanical parts of vehicles, bend metal sheets or make holes in them, to pack paper, cotton, and straw by compressing them.
Important Questions on Pressure and Pascal's Law
Here are some important questions 'Pressure'.
a. What is Pressure? Write its SI unit.
Ans. Pressure can be defined as the perpendicular force acting perpendicular to the per unit area of the surface.
The SI unit of pressure is Pascal (Pa). It is N.m-2.
b. State Pascal's law. Write any two applications of Pascal's law.
Ans. Pascal's law states that when a force is exerted at a point in an enclosed liquid, the pressure generated is transmitted normally throughout the liquid in all directions.
The applications of Pascal's law are- a) Hydraulic Brake, and b) Hydraulic Lift
c. What is a hydraulic machine?
Hydraulic machines are machines based on Pascal's law of pressure, where the liquid is used to perform heavy work such as lifting vehicles. Some examples of hydraulic machines are hydraulic press, hydraulic lift, and hydraulic brake.
d. A special type of oil is used in hydraulic brakes. Give reason.
A special type of oil is used in hydraulic brakes because it is incompressible and hence transmits the pressure effectively and by applying a small force on the small piston of the master cylinder, the pressure is generated by pushing the fluid inside it is transmitted and a large force is applied to the large piston connected to the brake cylinder.
e. Choose the correct option.
Q. In a hydraulic machine, if the cross-sectional area of the larger piston is twice the area of the smaller piston, what is the correct group of weights on the smaller piston (W1) and the larger piston (W2) to keep the machine balanced?
i. W1= 4N, W2= 2N (✓)
ii. W1=5N, W2= 10 N
iii. W1= 2N, W2=1N
iv. W1= 3N, W2= 1.5 N