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By the end of this section, you will be able to:
  • State Pascal’s principle
  • Describe applications of Pascal’s principle
  • Derive relationships between forces in a hydraulic system

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 ( [link] ). 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 .
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.
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 .

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 .

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:

Questions & Answers

scalar field define with example
Malik Reply
what is displacement
Isaac Reply
the change in the position of an object in a particular direction is called displacement
Noor
The physical quantity which have both magnitude and direction are known as vector.
Malik
good
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define line integral
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Louis Reply
what is Force?
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ans:loading...
Lumai
the sideways pressure exerted by fluid is equal and canceled out.how and why?
Chaurasia
what is blackbody radiation
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Particles emitted by black holes
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Iwelomen Reply
Bernoulli's equation which applies a fluid flow states that P+h✓g+½PV²=k. where ✓=density. P=pressure. h=height. V= velocity. g=acceleration due to gravity. k= constant. Show that the equation is dimensionally constant and show the S.I unit for k.
amoni Reply
The nature of physics
Darshan Reply
what physics
Darshan
Physics deals with nature and its natural phenomenons
Sushant
physics explains more about mechanics and other natural phenomenon.
Ferdinand
define realitives motion
Zahid Reply
Relative motion is the calculation of the motion of an object with regard to some other moving object. Thus, the motion is not calculated with reference to the earth, but is the velocity of the object in reference to the other moving object as if it were in a static state.
Lansana
I am unable to access the mcq can someone help me with it?
Harkamal Reply
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Barham Reply
when an object is falling under the the influence of the earth gravitational force, the term is called free fall.
Bra
V=E½-P-½ where v; velocity, P; density and E; constant. Find dimension and it's units of E (constant)
michael Reply
ML-3
LAWAL
derivation of simple harmonic equation
Daud Reply
if an equation is dimensionally correct does this mean that equation must be true?
michael Reply
how do I calculate angular velocity
Priscilla Reply
w=vr where w, angular velocity. v; velocity and r; radius of a circle
michael
sorry I meant Maximum positive angular velocity of
Priscilla
please can u tell me the formular for tension in angular velocity I kind of forget it please don't ignore this msg I need it nw
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Practice Key Terms 3

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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