2 Pressure

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Chapter 2 - Pressure

PRESSURE

INTRODUCTION

In this chapter we will consider an important class of

problems in which the fluid is either at rest or moving

in such a manner that there is no relative motion

between adjacent particles.

In both instances there will be no shearing stresses inthe fluid, and the only forces that develop on the

surfaces of the particles will be due to the pressure.

The absence of shearing stresses greatly simplifies

the analysis

There are no shearing stresses present in a fluid at

rest.

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PRESSURE

The term pressure is used to indicate the normal force

per unit area at a given point acting on a given planewithin the fluid mass of interest.

The equations of motion (Newton's second law,

(F=ma) in they andz directions are, respectively.

ysyy a

zyx

sxpzxpF 2sin

==

zszz azyxzyx

gsxpyxpF22

cos

==

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where ps, py, and pz are the average pressures on the

faces, and are the fluid specific weight and

density, respectively, and ay, az the accelerations.

Note that a pressure must be multiplied by an

appropriate area to obtain the force generated by the

pressure.

Since we are really interested in what is happening at

a point, we take the limit as x, y, and z approach

zero (while maintaining the angle ), and it follows

that

szy ppp ==

The pressure at a point in a fluid at rest is

independent of direction.

We can conclude that the pressure at a point in a fluid

at rest, or in motion, is independent of direction as

long as there are no shearing stresses present.

This important result is known as Pascal's law named

in honor ofBlaise Pascal (16231662),

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BASIC EQUATION FOR PRESSURE FIELD

For liquids or gases at rest the pressure gradient in the

vertical direction at any point in a fluid depends only

on the specific weight of the fluid at that point.

0=dx

dp 0=dy

dp =

dz

dp

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INCOMPRESSIBLE FLOW

g

pph

21 =

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Pascals Paradox

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STANDARD ATMOSPHERE

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MEASUREMENT OF PRESSURE

The pressure at a point within a fluid mass will be

designated as either an absolute pressure or a gagepressure. Absolute pressure is measured relative to a

perfect vacuum (absolute zero pressure), whereas

gage pressure is measured relative to the local

atmospheric pressure.

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A barometer is used to measure atmospheric pressure.

mercury barometer

vaporatm pghp +=

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MANOMETRY

A standard technique for measuring pressure involves

the use of liquid columns in vertical or inclined tubes.

Pressure measuring devices based on this technique

are called manometers.

The mercury barometeris an example of one type of

manometer, but there are many other configurations

possible, depending on the particular application.

Three common types of manometers include the

piezometer tube, the U-tube manometer, and the

inclined-tube manometer.

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PIEZOMETER TUBE

opghp +=

1111 ghhpA ==

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U-TUBE MANOMETER

1122 ghghpA =

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INCLINED-TUBE MANOMETER

113322 sin ghghgpp BA += l

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MECHANICAL AND ELECTRONIC PRESSURE

DEVICES

ABourdon tube pressure gage uses a hollow, elastic,and curved tube to measure pressure.

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2 Pressure

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