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April 10, 2006
1
Engineers 1
Engineers 1
Spring Semester 2006
Lecture 43
April 10, 2006
2
Review  Pressure
Review  Pressure
!
The pressure at a given depth in a liquid is given
by
!
The
gauge pressure
is defined as the pressure
difference relative to atmospheric pressure
p
=
p
0
+
!
gh
April 10, 2006
3
Barometric Altitude Relation for Gases
Barometric Altitude Relation for Gases
!
In the derivation of the depth pressure
relationship, we have made use of the
incompressibility
of liquids.
!
However, if our fluid is a gas, we cannot make this
assumption.
!
We start again with a thin layer of fluid in a fluid
column.
!
The pressure difference between bottom and top
surface is still given by the weight of the thin layer
of fluid divided by the area
"
p
=
#
mg
A
=
#
$
Vg
A
=
#
(
"
hA
)
g
A
=
#
g
"
h
April 10, 2006
4
Barometric Altitude Relation for Gases (2)
Barometric Altitude Relation for Gases (2)
!
The negative sign indicates pressure decreases
with increasing altitude
!
So far nothing is different from the derivation of
the incompressible case
!
However, for compressible fluids we find that the
density is proportional to the pressure
!
Strictly, this relationship is only true for ideal
gasses
0
=
p
p
0
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View Full DocumentApril 10, 2006
5
Barometric Altitude Relation for Gases (3)
Barometric Altitude Relation for Gases (3)
!
Combining our two equations gives us
!
Taking the limit of
!
h
!
0, we find the equation
!
This equation is a differential equation, which has the
solution
!
This equation is known as the
barometric pressure formula
!
Assumptions:
•
Ideal gas
•
temperature does not change with altitude
•
gravitation is constant
!
p
!
h
=
"
g
#
0
p
0
p
dp
dh
=
!
g
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.
 Spring '08
 Wolf
 Physics

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