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Conversion of pressure units
Name of unit Unit Conversion
Pascal Pa 1 Pa = 1 N/m2
Bar bar 1 bar = 0.1 MPa
Water column metre mH20 1mH20 = 9806.65 PaAtmospheric pressure
atm 1 atm = 101325 Pa
Mercury column metre mHg 1 mHg = 1/0.76atm
Torr torr 1 torr = 1 mmHg
The Fundamental Equation of hydrostatics
We assume the following hypothesis:
the liquid is incompressible
the liquid is a gravitational field, thereforeIn general, in a
fluid at rest the pressure varies according to the depth. Consider
a minute
column in the fluid as shown in Fig. 3.4. Assume that the
sectional area is dA and the pressure
acting upward on the bottom surface is p and the pressure acting
downward on the upper surface(dz above the bottom surface) is p +
(dp/dz)dz. Then, from the balance of forces acting on the
column, the following equation is obtained:
p dA-(p+ (dp/dz)dA-gdAdz=0
ordp/ dz = -g=- (1)
Since is constant for liquid, the following equation ensues:
p = - dz = -z + c
When the base point is set at zo below the upper surface of
liquid as shown in upper fig.,and p0 is the pressure acting on that
surface, then p = po when z = zo, so
c = po + z (2)Substituting this equation into eqn (2),
p = p0 + (zo - z) = po + h (3)
(The fundamental equation of Hydrostatics in a gravitational
field)
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This equation is valid if Oxy water surface.
The extra pressure po is in most civil engineering cases the
atmospheric pressure (pa)
which in its turn (see last lecture) is totally transmitted to
all points of liquid. Therefore, in thesecases, the fundamental
equations of Hydrostatics becomes
zp (also called relative pressure)
Geometric interpretation of hydrostatic pressure
Using the form 0pzp one gets
0p
zp
which has a geometric meaning, all the terms having an
interpretation of height
p- absolute height
zrelative height
0p
.supplementary height
With this, the equation can be geometrically represented as
follows:
Case 1: free water surface and atmospheric pressure
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Case 2: closed vessels
(p0>pa) (p0
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1. Differential manometer.
In the case of measuring the pressure difference between two
pipes in both of which a
liquid of density flows, a differential manometer as shown:
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To measure a minute pressure, a glass tube inclined at an
appropriate angle as shown in
Fig. 3.9 is used as an inclined manometer. When the angle of
inclination is and the movementof the liquid surface level is L,
the differential pressure H is as shown in the following
equation:
H = Lsin
Accordingly, if is made smaller, the reading of the pressure is
magnified.
1.2. Hydrostatic forces (h.f)
Hydrostatic forces are the resultant forces of the distribute
pressure on a liquid surface. Theydepend on the surface geometry
and its orientation in the space.
1.2.1. H.p. on plane horizontal surface
By definition we have:
dAhdApdF
)( )( )( A A A
ApAhdAhpdAdFF ,
which is the traditional meaning of force-pressure
relationship.
The direction ofFis the direction ofp (vertical). To define
C(application point ofF), we take
Varignons theorem:
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A A
e dAhydFyFy)(
'''
From which:
and Cis also called centru de carena
1.2.2. Hydrostatics forces on plane vertical surfaces
)(''
AGyAhdAyh
Gy yAS '' Theorem of static moments
GG
c yF
yAhy '
''
Similarly: GC xx ''
GC
AzSGy
)(
)(
A
GG
A A
ApAzzdA
zdAdFF
pdAdF
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Using Varignons theorem:
1.2.3. H.f. on plane inclined surfaces
z=zsin for any point
)( )( )(
22
A A A
C dAzdAzdFzFz
Iy
G
Gy
y
y
y
y
CzA
zAI
S
I
S
Iz
2
0
G
G
yz
zA
I 0
>0
CGzz
Cover Calways
)(
)( )( )(
'sin'sin
sin'
A
GG
A A A
ApAzdAz
dAzzdAdFF
dApdF
AzS Gy ''
But: yc
Iz
'
'' (similar to above)
and then: sin'cc zz
