12/8/2017 Pascal's Principle
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Pascal's Principle
Pascal's Principle states that pressure is transmitted and undiminished in a closed
static fluid.
LEARNING OBJECTIVE
Apply Pascal’s Principle to describe pressure behavior in static fluids
KEY POINTS
Pascal's Principle is used to quantitatively relate the pressure at two points in an incompressible, static
fluid. It states that pressure is transmitted, undiminished, in a closed static fluid.
The total pressure at any point within an incompressible, static fluid is equal to the sum of the applied
pressure at any point in that fluid and the hydrostatic pressure change due to a difference in height within
that fluid.
Through the application of Pascal's Principle, a static liquid can be utilized to generate a large output force
using a much smaller input force, yielding important devices such as hydraulic presses.
TERM
hydraulic press
Device that uses a hydraulic cylinder (closed static fluid) to generate a compressive force.
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FULL TEXT
Pascal's Principle
Pascal's Principle (or Pascal's Law) applies to static
fluids and takes advantage of the height dependency
of pressure in static fluids. Named after French
mathematician Blaise Pascal, who established this
important relationship, Pascal's Principle can be used
to exploit pressure of a static liquid as a measure of
energy per unit volume to perform work in
applications such as hydraulic presses. Qualitatively,
Pascal's Principle states that pressure is transmitted
undiminished in an enclosed static liquid.
Quantitatively, Pascal's Law is derived from the expression for determining the pressure at a given height (or
depth) within a fluid and is defined by Pascal's Principle:
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AP Physics 2 - Pressure and Pascal's Principle
Pressure and Pascal's Principle
A brief introduction to pressure and Pascal's Principle, including hydraulics.
where p1 is the external applied pressure, ρ is the density of the fluid, Δh is the difference in height of the static
liquid, and g is the acceleration due to gravity. Pascal's Law explicitly determines the pressure difference
between two different heights (or depths) within a static liquid. As, by Pascal's Law, a change in pressure is
linearly proportional to a change in height within an incompressible, static liquid of constant density, doubling
the height between the two points of reference will double the change of pressure, while halving the height
between the two points will half the change in pressure.
Enclosed Static Liquids
While Pascal's Principle applies to any static fluid, it is most useful in terms of applications when considering
systems involving rigid wall closed column configurations containing homogeneous fluids of constant density.
By exploiting the fact that pressure is transmitted undiminished in an enclosed static liquid, such as in this type
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of system, static liquids can be used to transform small amounts of force into large amounts of force for many
applications such as hydraulic presses.
As an example, referring to , a downwards force of 10 N is applied to a bottle filled with a static liquid of
constant density ρ at the spout of cross-sectional area of 5 cm2, yielding an applied pressure of 2 N/cm2. The
cross-sectional area of the bottle changes with height so that at the bottom of the bottle the cross-sectional area
is 500 cm2. As a result of Pascal's Law, the pressure change (pressure applied to the static liquid) is transmitted
undiminished in the static liquid so that the applied pressure is 2 N/m2 at the bottom of the bottle as well.
Furthermore, the hydrostatic pressure due to the difference in height of the liquid is given by Equation 1 and
yields the total pressure at the bottom surface of the bottle. Since the cross-sectional area at the bottom of the
bottle is 100 times larger than at the top, the force contributing to the pressure at the bottom of the bottle is
1000 N plus the force from the weight of the static fluid in the bottle. This example shows how, through Pascal's
Principle, the force exerted by a static fluid in a closed system can be multiplied by changing the height and the
surface area of contact.
Pressure Applied to a Hydrostatic Fluid
A downwards force of 10 N is applied to a bottle filled with a static liquid of constant density ρ at the spout of
cross-sectional area of 5 cm2, yielding an applied pressure of 2 N/cm2.
Pressure Transmitted Throughout an Entire Fluid
As stated by Pascal's Principle, the pressure applied to a static fluid in a closed container is transmitted
throughout the entire fluid. Taking advantage of this phenomenon, hydraulic presses are able to exert a large
amount of force requiring a much smaller amount of input force. This gives two different types of hydraulic
press configurations, the first in which there is no difference in height of the static liquid and the second in
which there is a difference in height Δh of the static liquid. In the first configuration, a force F1 is applied to a
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static liquid of density ρ across a surface area of contact A1, yielding an input pressure of P2. On the other side
of the press configuration, the fluid exerts an output pressure P1 across a surface area of contact A2, where A2 >
A1. By Pascal's Principle, P1 = P2, yielding a force exerted by the static fluid of F2, where F2 > F1. Depending on
the applied pressure and geometry of the hydraulic press, the magnitude of F2 can be changed. In the second
configuration, the geometry of the system is the same, except that the height of the fluid on the output end is a
height Δh less than the height of the fluid at the input end. The difference in height of the fluid between the
input and the output ends contributes to the total force exerted by the fluid. For a hydraulic press, the force
multiplication factor is the ratio of the output to the input contact areas.
Hydraulic Press Diagrams
Two different types of hydraulic press configurations, the first in which there is no difference in height of the
static liquid and the second in which there is a difference in height Δh of the static liquid.
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Referenced in 2 quiz questions
The total pressure at any point within an incompressible, static fluid is equal to the
sum of the applied pressure at any point in that fluid and the
Pascal’s Principle is used to
KEY TERM REFERENCE
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Law — Appears in these related concepts: Two-Component Forces, Damped Harmonic Motion, and
Models, Theories, and Laws
Pressure — Appears in these related concepts: SI Units of Pressure, Physics and Engineering: Fluid
Pressure and Force, and Surface Tension and Capillary Action
acceleration — Appears in these related concepts: Position, Displacement, Velocity, and Acceleration
as Vectors, Scientific Applications of Quadratic Functions, and Centripetial Acceleration
application — Appears in these related concepts: Introduction to Elementary operations and Gaussian
Elimination, Physics and Other Fields, and X-Ray Imaging and CT Scans
closed system — Appears in these related concepts: Rotational Collisions, Momentum, Force, and
Newton's Second Law, and Gauge Pressure and Atmospheric Pressure
energy — Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction
to Work and Energy
equation — Appears in these related concepts: Equations and Inequalities, Graphs of Equations as
Graphs of Solutions, and What is an Equation?
fluid — Appears in these related concepts: Pumps and the Heart, Drag, and B.11 Chapter 11
force — Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
gravity — Appears in these related concepts: Defining Graviational Potential Energy, Key Points:
Range, Symmetry, Maximum Height, and Properties of Electric Charges
incompressible — Appears in these related concepts: Application of Bernoulli's Equation: Pressure
and Speed, Flow Rate and the Equation of Continuity, and Variation of Pressure With Depth
magnitude — Appears in these related concepts: Multiplying Vectors by a Scalar, Round-off Error,
and Components of a Vector
rigid — Appears in these related concepts: Connected Objects, The Physical Pendulum, and Center of
Mass and Translational Motion
static — Appears in these related concepts: Friction: Static, Time and Motion, and Alternative Views
weight — Appears in these related concepts: Locating the Center of Mass, Weight of the Earth, and B.9
Chapter 9
work — Appears in these related concepts: Heat and Work, Free Energy and Work, and The First Law
of Thermodynamics
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