❤ 11th Fluids ❤
❇ State And Prove Pascal's Law!
✴ Quality Needed ❗
✴ Don't Copy ✖
Answers
Answered by
0
If a U-tube is filled with water and pistons are placed at each end, pressure exerted against the left piston will be transmitted throughout the liquid and against the bottom of the right piston. (The pistons are simply "plugs" that can slide freely but snugly inside the tube.) The pressure that the left piston exerts against the water will be exactly equal to the pressure the water exerts against the right piston. Suppose the tube on the right side is made wider and a piston of a larger area is used; for example, the piston on the right has 50 times the area of the piston on the left. If a 1 N load is placed on the left piston, an additional pressure due to the weight of the load is transmitted throughout the liquid and up against the larger piston. The difference between force and pressure is important: the additional pressure is exerted against the entire area of the larger piston. Since there is 50 times the area, 50 times as much force is exerted on the larger piston. Thus, the larger piston will support a 50 N load - fifty times the load on the smaller piston.
Forces can be multiplied using such a device. One newton input produces 50 newtons output. By further increasing the area of the larger piston (or reducing the area of the smaller piston), forces can be multiplied, in principle, by any amount. Pascal's principle underlies the operation of the hydraulic press. The hydraulic press does not violate energy conservation, because a decrease in distance moved compensates for the increase in force. When the small piston is moved downward 100 centimeters, the large piston will be raised only one-fiftieth of this, or 2 centimeters. The input force multiplied by the distance moved by the smaller piston is equal to the output force multiplied by the distance moved by the larger piston; this is one more example of a simple machine operating on the same principle as a mechanical lever.
Pascal's principle applies to all fluids, whether gases or liquids. A typical application of Pascal's principle for gases and liquids is the automobile lift seen in many service stations (the hydraulic jack). Increased air pressure produced by an air compressor is transmitted through the air to the surface of oil in an underground reservoir. The oil, in turn, transmits the pressure to a piston, which lifts the automobile. The relatively low pressure that exerts the lifting force against the piston is about the same as the air pressure in automobile tires. Hydraulics is employed by modern devices ranging from very small to enormous. For example, there are hydraulic pistons in almost all construction machines where heavy loads are involved.
Forces can be multiplied using such a device. One newton input produces 50 newtons output. By further increasing the area of the larger piston (or reducing the area of the smaller piston), forces can be multiplied, in principle, by any amount. Pascal's principle underlies the operation of the hydraulic press. The hydraulic press does not violate energy conservation, because a decrease in distance moved compensates for the increase in force. When the small piston is moved downward 100 centimeters, the large piston will be raised only one-fiftieth of this, or 2 centimeters. The input force multiplied by the distance moved by the smaller piston is equal to the output force multiplied by the distance moved by the larger piston; this is one more example of a simple machine operating on the same principle as a mechanical lever.
Pascal's principle applies to all fluids, whether gases or liquids. A typical application of Pascal's principle for gases and liquids is the automobile lift seen in many service stations (the hydraulic jack). Increased air pressure produced by an air compressor is transmitted through the air to the surface of oil in an underground reservoir. The oil, in turn, transmits the pressure to a piston, which lifts the automobile. The relatively low pressure that exerts the lifting force against the piston is about the same as the air pressure in automobile tires. Hydraulics is employed by modern devices ranging from very small to enormous. For example, there are hydraulic pistons in almost all construction machines where heavy loads are involved.
Answered by
0
Please mark as brain list
It. states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same.
Proof : Consider two points C and D inside the liquid in a container which is in equilibrium of rest. Imagine a right circular cylinder with axis CD of uniform cross-sectional area A such that points C and D lie on float faces of the cylinder in figure
The liquid inside the cylinder is in equilibrium under the action of forces exerted by the liquid outside the cylinder. These forces are acting every where perpendicular to the surface of the cylinder. Thus force on the flat faces of the cylinder at C and D will perpendicular to the forces on the curved surface of the cylinder. Since the liquid is in equilibrium, therefore, the sum of forces acting on the curved surface of the cylinder must be zero. If P1 and P2 are the pressure at points C and D and F1 and F2 are the forces acting on the flat faces of the cylinder due to liquid,
Experimental Proof. Consider a spherical vessel having for cylinderical tubes A, B, C and D each fitted with air tight frictioriless piston of area of corss-section a, a/2, 2a and 3a respectively.
Fill the vessel with an incompressible liquid so that no air gap is left inside the vessel and piston fitted in the various cylindrical tubes. Push the piston A with force F.
It is seen that all other pistons will be pushed outwards. To keep the pistons at their respective original positions, the force F/2, 2F and 3F respectively required to be applied on pistons of tubes B, C and D respectively to hold them. Now pressure developed on liquid in tubes, B, C and D are F/2, 2F/2a, 3F/3a i.e., such,equal to F/a. This indicates that the pressure applied is transmitted equally to all parts of liquid. This proves Pascal law
It. states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same.
Proof : Consider two points C and D inside the liquid in a container which is in equilibrium of rest. Imagine a right circular cylinder with axis CD of uniform cross-sectional area A such that points C and D lie on float faces of the cylinder in figure
The liquid inside the cylinder is in equilibrium under the action of forces exerted by the liquid outside the cylinder. These forces are acting every where perpendicular to the surface of the cylinder. Thus force on the flat faces of the cylinder at C and D will perpendicular to the forces on the curved surface of the cylinder. Since the liquid is in equilibrium, therefore, the sum of forces acting on the curved surface of the cylinder must be zero. If P1 and P2 are the pressure at points C and D and F1 and F2 are the forces acting on the flat faces of the cylinder due to liquid,
Experimental Proof. Consider a spherical vessel having for cylinderical tubes A, B, C and D each fitted with air tight frictioriless piston of area of corss-section a, a/2, 2a and 3a respectively.
Fill the vessel with an incompressible liquid so that no air gap is left inside the vessel and piston fitted in the various cylindrical tubes. Push the piston A with force F.
It is seen that all other pistons will be pushed outwards. To keep the pistons at their respective original positions, the force F/2, 2F and 3F respectively required to be applied on pistons of tubes B, C and D respectively to hold them. Now pressure developed on liquid in tubes, B, C and D are F/2, 2F/2a, 3F/3a i.e., such,equal to F/a. This indicates that the pressure applied is transmitted equally to all parts of liquid. This proves Pascal law
Similar questions