Write the relation connecting force and area of crosssection in hydraulic jack
Answers
Answer:
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Explanation:
In 1653, the French philosopher and scientist Blaise Pascal published his Treatise on the Equilibrium of Liquids, in which he discussed principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise the fluid will start to flow.
Pascal’s observations—since proven experimentally—provide the foundation for hydraulics, one of the most important developments in modern mechanical technology. Pascal observed that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and to the walls of its container. Because of this, we often know more about pressure than other physical quantities in fluids. Moreover, Pascal’s principle implies that the total pressure in a fluid is the sum of the pressures from different sources. A good example is the fluid at a depth depends on the depth of the fluid and the pressure of the atmosphere.
Pascal’s Principle
Pascal’s principle (also known as Pascal’s law) states that when a change in pressure is applied to an enclosed fluid, it is transmitted undiminished to all portions of the fluid and to the walls of its container. In an enclosed fluid, since atoms of the fluid are free to move about, they transmit pressure to all parts of the fluid and to the walls of the container. Any change in pressure is transmitted undiminished.
Note that this principle does not say that the pressure is the same at all points of a fluid—which is not true, since the pressure in a fluid near Earth varies with height. Rather, this principle applies to the change in pressure. Suppose you place some water in a cylindrical container of height H and cross-sectional area A that has a movable piston of mass m ((Figure)). Adding weight Mg at the top of the piston increases the pressure at the top by Mg/A, since the additional weight also acts over area A of the lid:
Δ
p
top
=
M
g
A
.
Δptop=MgA.
Figure A is a schematic drawing of a cylinder filled with fluid and opened to the atmosphere on one side. A disk of mass m and surface area A identical to the surface area of the cylinder is placed in the container. Distance between the disk and the bottom of the cylinder is h. Figure B is a schematic drawing of the cylinder with an additional disk of mass Mg placed atop mass m causing mass m to move lower.
Figure 14.15 Pressure in a fluid changes when the fluid is compressed. (a) The pressure at the top layer of the fluid is different from pressure at the bottom layer. (b) The increase in pressure by adding weight to the piston is the same everywhere, for example,
p
top new
−
p
top
=
p
bottom new
−
p
bottom
ptop new−ptop=pbottom new−pbottom.
According to Pascal’s principle, the pressure at all points in the water changes by the same amount, Mg/A. Thus, the pressure at the bottom also increases by Mg/A. The pressure at the bottom of the container is equal to the sum of the atmospheric pressure, the pressure due the fluid, and the pressure supplied by the mass. The change in pressure at the bottom of the container due to the mass is
Δ
p
bottom
=
M
g
A
.
Δpbottom=MgA.
Since the pressure changes are the same everywhere in the fluid, we no longer need subscripts to designate the pressure change for top or bottom:
Δ
p
=
Δ
p
top
=
Δ
p
bottom
=
Δ
p
everywhere
.
Δp=Δptop=Δpbottom=Δpeverywhere.
Pascal’s Barrel is a great demonstration of Pascal’s principle. Watch a simulation of Pascal’s 1646 experiment, in which he demonstrated the effects of changing pressure in a fluid.
Applications of Pascal’s Principle and Hydraulic Systems
Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems ((Figure)).
A schematic drawing of a hydraulic system with two fluid-filled cylinders, capped with pistons and connected by a tube. A downward force F1 on the left piston with the surface area A1 creates a change in pressure that results in an upward force F2on the right piston with the surface area A2. Surface area A2 is larger than the surface area A1.
Figure 14.16 A typical hydraulic system with two fluid-filled cylinders, capped with pistons and connected by a tube called a hydraulic line. A downward force
→
F
1
F→1 on the left piston creates a change in pressure that is transmitted undiminished to all parts of the enclosed fluid. This results in an upward force
→
F
2
F→2 on the right piston that is larger than
→
F
1
F→1 because the right piston has a larger surface area.
We can derive a relationship between the forces in this simple hydraulic system by applying Pascal’s principle. Note first that the two pistons in the system are at the same height, so there is no difference in pressure due to a difference in depth. The pressure due to